Level 4 · Science S4.7

Reactions, equations and amounts

Write formulae and equations, count particles by weighing, and see how metals, acids and energy decide what reacts.

Write the formula of a compound from its ions and balance an equation. Use the mole to turn masses into numbers of particles, then work out how much product a reaction makes. Then follow acids, metals and electricity through reactions, and see why some reactions give out heat and why some are faster than others.

You are ready for this book if

You can write a word equation for something burning.

Written and drawn by attnom. Free to read, print and share.

S4.7.1 Chapter 1

Chemical formulae

Why is salt written NaCl, but magnesium chloride written MgCl₂?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

A formula is a short way to write what a substance is made of. It uses the symbols of the elements, and small numbers that say how many.

Water is H₂O. The small 2 sits after the H, so it counts hydrogen atoms. There is no number after the O, so that means 1. One water molecule has 2 hydrogen atoms and 1 oxygen atom.

Three molecules drawn as touching circles with the symbol of each atom inside. Water, H₂O, has one O atom and two H atoms. Carbon dioxide, CO₂, has one C atom between two O atoms. Methane, CH₄, has one C atom with four H atoms round it.OHHOCOCHHHH
Left to right: water H₂O, carbon dioxide CO₂ and methane CH₄. The circles show which atoms are joined, not their true sizes or angles.

A bracket groups atoms that belong together. The small number after the bracket multiplies everything inside it. In Ca(OH)₂ the group OH is there twice.

Three discs in a row. A hatched disc is Ca²⁺. Two plain discs are OH⁻. Under them the sum reads +2 −1 −1 = 0, and under the sum is the formula Ca(OH)₂.Ca²⁺OH⁻OH⁻+2 −1 −1 = 0Ca(OH)₂
Calcium hydroxide. One Ca²⁺ ion goes with two OH⁻ ions, and OH⁻ is a group, so it gets a bracket.

Worked example

How many atoms of each element are in Ca(OH)₂?

  1. Ca has no number after it, so there is 1 calcium atom.
  2. The bracket holds one O and one H. The small 2 after the bracket multiplies both.
  3. O: 1 × 2 = 2 oxygen atoms. H: 1 × 2 = 2 hydrogen atoms.

Answer: 1 Ca, 2 O and 2 H

Now think about salt. Sodium chloride is made of ions, which are atoms or groups of atoms with an electric charge. Na⁺ has a charge of 1+. Cl⁻ has a charge of 1−.

In an ionic compound the charges of all the ions add up to zero. The formula gives the smallest whole-number ratio of the ions that does this. It does not describe a molecule.

A table of positive ions with the columns Ion, Name and Charge. H⁺ hydrogen 1+. Na⁺ sodium 1+. NH₄⁺ ammonium 1+. Mg²⁺ magnesium 2+. Ca²⁺ calcium 2+. Cu²⁺ copper(II) 2+. Al³⁺ aluminium 3+.IonNameChargeH⁺hydrogen1+Na⁺sodium1+NH₄⁺ammonium1+Mg²⁺magnesium2+Ca²⁺calcium2+Cu²⁺copper(II)2+Al³⁺aluminium3+
Positive ions. Metals form positive ions. Hydrogen, H⁺, and ammonium, NH₄⁺, are positive ions too. Copper can form other ions too, so its name carries the charge: copper(II) means 2+.
A table of negative ions with the columns Ion, Name and Charge. Cl⁻ chloride 1−. OH⁻ hydroxide 1−. NO₃⁻ nitrate 1−. O²⁻ oxide 2−. CO₃²⁻ carbonate 2−. SO₄²⁻ sulfate 2−.IonNameChargeCl⁻chloride1−OH⁻hydroxide1−NO₃⁻nitrate1−O²⁻oxide2−CO₃²⁻carbonate2−SO₄²⁻sulfate2−
Negative ions. OH⁻, NO₃⁻, CO₃²⁻ and SO₄²⁻ are each a group of atoms that carries one charge together.

A group of atoms with one charge is a polyatomic ion. NH₄⁺, OH⁻ and SO₄²⁻ are polyatomic ions. They stay together when they join with other ions.

Draw it first

Make magnesium chloride from its ions

  1. Three steps, drawn in the same place. Step 1: a hatched disc Mg²⁺ with the charge +2. Step 2: a plain disc Cl⁻ is added, and the sum reads +2 −1 = +1. Step 3: a second plain disc Cl⁻ is added, the sum reads +2 −1 −1 = 0, and the formula MgCl₂ appears.Mg²⁺+2

    1 Start with the magnesium ion, Mg²⁺. Its charge is +2.

  2. Three steps, drawn in the same place. Step 1: a hatched disc Mg²⁺ with the charge +2. Step 2: a plain disc Cl⁻ is added, and the sum reads +2 −1 = +1. Step 3: a second plain disc Cl⁻ is added, the sum reads +2 −1 −1 = 0, and the formula MgCl₂ appears.Mg²⁺Cl⁻+2 −1 = +1

    2 Add a chloride ion, Cl⁻, with a charge of −1. The sum is +1, not zero. A charge is left over.

  3. Three steps, drawn in the same place. Step 1: a hatched disc Mg²⁺ with the charge +2. Step 2: a plain disc Cl⁻ is added, and the sum reads +2 −1 = +1. Step 3: a second plain disc Cl⁻ is added, the sum reads +2 −1 −1 = 0, and the formula MgCl₂ appears.Mg²⁺Cl⁻Cl⁻+2 −1 −1 = 0MgCl₂

    3 Add a second Cl⁻. Now +2 −1 −1 = 0, so the formula is MgCl₂.

The rule has four parts. Find the smallest numbers of each ion that make the charges add to zero. Write the positive ion first. Write each number small and low, after its symbol. Leave out a 1.

Worked example

Write the formula of aluminium oxide. It is made of Al³⁺ ions and O²⁻ ions.

  1. The ions are Al³⁺ and O²⁻. The charges are 3+ and 2−.
  2. Find the smallest number that both 3 and 2 go into. It is 6.
  3. Aluminium: 6 ÷ 3 = 2 ions.
  4. Oxygen: 6 ÷ 2 = 3 ions.
  5. Write the numbers low, after each symbol: Al₂O₃.

Answer: 2 aluminium ions and 3 oxide ions, so Al₂O₃

See it three ways

As a picture

Five discs in a row. Two hatched discs are Al³⁺. Three plain discs are O²⁻. Under them the sum reads +3 +3 −2 −2 −2 = 0, and under the sum is the formula Al₂O₃.Al³⁺Al³⁺O²⁻O²⁻O²⁻+3 +3 −2 −2 −2 = 0Al₂O₃

In words

Two Al³⁺ ions give a charge of +6. Three O²⁻ ions give −6. The charges cancel, so two aluminium ions go with three oxide ions.

In symbols

2 × (+3) + 3 × (−2) = 0, so the formula is Al₂O₃.

When a polyatomic ion is needed more than once, put it in a bracket. Calcium hydroxide is Ca(OH)₂. Without the bracket, CaOH₂ would mean one oxygen atom and two hydrogen atoms. With one OH⁻ only, as in NaOH, no bracket is needed.

Molecules are different. Water, carbon dioxide and methane are made of non-metal atoms that share electrons. Their formulae count the atoms in one molecule.

Try it

Ion cards: make the charges add to zero

You need: paper, torn into 15 small pieces, a pencil.

  1. Write Na⁺ on three pieces, Al³⁺ on three, and Mg²⁺ on three. Write Cl⁻ on three pieces and O²⁻ on three.
  2. Put cards side by side, positive or negative, until the charges add up to zero.
  3. Use as few cards as you can. Write down the formula each time.
  4. Try every positive card with Cl⁻, and then with O²⁻.

What you will see: Na⁺ takes one Cl⁻. Two Na⁺ take one O²⁻. Mg²⁺ takes two Cl⁻ or one O²⁻. Al³⁺ takes three Cl⁻. Two Al³⁺ take three O²⁻. The cards show why the numbers in a formula are what they are.

If you cannot try it, this is what happens.
Four discs in a row. One hatched disc is Al³⁺. Three plain discs are Cl⁻. Under them the sum reads +3 −1 −1 −1 = 0, and under the sum is the formula AlCl₃.Al³⁺Cl⁻Cl⁻Cl⁻+3 −1 −1 −1 = 0AlCl₃

A wrong idea many people have

In MgCl₂ the small 2 belongs to the magnesium, or is a charge.

Why it feels right: The 2 sits in the middle of the formula, and charges and small numbers look alike.

The test that breaks it: Draw MgCl₂ as discs. Count: there is one Mg²⁺ disc and two Cl⁻ discs. The 2 counted the Cl.

What is true: A small number counts the symbol just before it, or the bracket just before it. A charge is written raised, as in Mg²⁺. A count is written low, as in Cl₂.

Key words

formula
symbols and small numbers that show what a substance is made of.
ion
an atom, or a group of atoms, with an electric charge.
polyatomic ion
a group of atoms that carries one charge together, such as OH⁻.

Back to your guess

The answer is B: The charges of the ions must add up to zero.

The charges must add up to zero. A Mg²⁺ ion has a charge of 2+, and each Cl⁻ ion has 1−. So one magnesium ion needs two chloride ions.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. One Ca²⁺ ion and one Cl⁻ ion are drawn, and their charges do not add up to zero. In calcium chloride, how many Cl⁻ ions go with each Ca²⁺ ion?

    Two discs in a row. A hatched disc is Ca²⁺. A plain disc is Cl⁻. Under them the sum reads +2 −1 = +1.Ca²⁺Cl⁻+2 −1 = +1
    Tap your answer.

    1. Not this one. One Cl⁻ cancels only 1 of the 2 positive charges. The sum is +1, so a charge is left over. Go to S4.6.6. Try another.

    2. Yes, that is right. Ca²⁺ has a charge of +2. Each Cl⁻ has −1. Two Cl⁻ ions give −2, so +2 −1 −1 = 0. The formula is CaCl₂.

    3. Not this one. Three Cl⁻ give −3, which is more than the +2 of the calcium ion. The sum would be −1. Try another.

    See the answer

    2 chloride ions

    Ca²⁺ has a charge of +2. Each Cl⁻ has −1. Two Cl⁻ ions give −2, so +2 −1 −1 = 0. The formula is CaCl₂.

    • If you chose A: One Cl⁻ cancels only 1 of the 2 positive charges. The sum is +1, so a charge is left over. Go to S4.6.6.
    • If you chose C: Three Cl⁻ give −3, which is more than the +2 of the calcium ion. The sum would be −1.

  2. Aluminium ions are Al³⁺ and chloride ions are Cl⁻. What is the formula of aluminium chloride?

    Tap your answer.

    1. Not this one. That is one of each. The charges would be +3 and −1, so +2 is left over. Go to S4.6.6. Try another.

    2. Not this one. The numbers are the wrong way round. Three aluminium ions would give +9, and one chloride ion only −1. Try another.

    3. Yes, that is right. One Al³⁺ has a charge of +3. It needs three Cl⁻ ions, each −1, so the charges add to zero.

    See the answer

    AlCl₃

    One Al³⁺ has a charge of +3. It needs three Cl⁻ ions, each −1, so the charges add to zero.

    • If you chose A: That is one of each. The charges would be +3 and −1, so +2 is left over. Go to S4.6.6.
    • If you chose B: The numbers are the wrong way round. Three aluminium ions would give +9, and one chloride ion only −1.

  3. Sodium ions are Na⁺ and sulfate ions are SO₄²⁻. Which formula is right for sodium sulfate?

    Tap your answer.

    1. Yes, that is right. Two Na⁺ ions give +2. One SO₄²⁻ ion gives −2. The sum is zero, and the sulfate is needed once, so it needs no bracket.

    2. Not this one. One Na⁺ and one SO₄²⁻ give +1 −2 = −1. The charges do not add to zero. Try another.

    3. Not this one. Two sulfate ions would give −4, and one sodium ion only +1. It is the sodium that is needed twice. Try another.

    See the answer

    Na₂SO₄

    Two Na⁺ ions give +2. One SO₄²⁻ ion gives −2. The sum is zero, and the sulfate is needed once, so it needs no bracket.

    • If you chose B: One Na⁺ and one SO₄²⁻ give +1 −2 = −1. The charges do not add to zero.
    • If you chose C: Two sulfate ions would give −4, and one sodium ion only +1. It is the sodium that is needed twice.

  4. One Ca²⁺ ion needs two OH⁻ ions. Which formula for calcium hydroxide shows this?

    Tap your answer.

    1. Not this one. Here the small number counts only the H. That is 1 Ca, 1 O and 2 H. OH is a group, so it needs a bracket. Try another.

    2. Not this one. This has two calcium atoms and one OH. The count is on the wrong symbol. Try another.

    3. Yes, that is right. The bracket groups O and H, and the 2 after it multiplies both. The formula has 1 Ca, 2 O and 2 H.

    See the answer

    Ca(OH)₂

    The bracket groups O and H, and the 2 after it multiplies both. The formula has 1 Ca, 2 O and 2 H.

    • If you chose A: Here the small number counts only the H. That is 1 Ca, 1 O and 2 H. OH is a group, so it needs a bracket.
    • If you chose B: This has two calcium atoms and one OH. The count is on the wrong symbol.

  5. How many oxygen atoms are in one unit of Al₂(SO₄)₃?

    Tap your answer.

    1. Not this one. The 3 after the bracket is the number of sulfate groups. Each group has 4 oxygen atoms. Try another.

    2. Yes, that is right. Each SO₄ has 4 oxygen atoms, and there are 3 of them: 4 × 3 = 12. The count also includes 2 Al and 3 S.

    3. Not this one. That is the oxygen in one sulfate group. The bracket holds 3 groups. Try another.

    See the answer

    12 oxygen atoms

    Each SO₄ has 4 oxygen atoms, and there are 3 of them: 4 × 3 = 12. The count also includes 2 Al and 3 S.

    • If you chose A: The 3 after the bracket is the number of sulfate groups. Each group has 4 oxygen atoms.
    • If you chose C: That is the oxygen in one sulfate group. The bracket holds 3 groups.

  6. What does the formula MgCl₂ tell you?

    Tap your answer.

    1. Yes, that is right. The low 2 sits after Cl, so it counts chlorine. The formula gives the ratio of the ions in the lattice: 1 Mg²⁺ to 2 Cl⁻.

    2. Not this one. A charge is written raised, as in Cl⁻, and the chloride ion is 1−. The low 2 after Cl counts chloride ions. Go to S4.6.6. Try another.

    3. Not this one. There is only one Mg, and magnesium chloride is a lattice of ions, not a molecule. The formula gives the ratio of the ions. Go to S4.6.6. Try another.

    See the answer

    There are two chloride ions for each magnesium ion.

    The low 2 sits after Cl, so it counts chlorine. The formula gives the ratio of the ions in the lattice: 1 Mg²⁺ to 2 Cl⁻.

    • If you chose B: A charge is written raised, as in Cl⁻, and the chloride ion is 1−. The low 2 after Cl counts chloride ions. Go to S4.6.6.
    • If you chose C: There is only one Mg, and magnesium chloride is a lattice of ions, not a molecule. The formula gives the ratio of the ions. Go to S4.6.6.

  7. A molecule is drawn as circles. Which formula matches it?

    A molecule drawn as touching circles. One circle with the symbol C has four circles with the symbol H touching it.CHHHH
    Tap your answer.

    1. Not this one. That would be four carbon atoms and one hydrogen. Count the circles: one C and four H. Try another.

    2. Yes, that is right. One C circle and four H circles. The small number goes low, after the symbol it counts: CH₄.

    3. Not this one. That is one carbon and one hydrogen. Count again: there are four H circles. Try another.

    See the answer

    CH₄

    One C circle and four H circles. The small number goes low, after the symbol it counts: CH₄.

    • If you chose A: That would be four carbon atoms and one hydrogen. Count the circles: one C and four H.
    • If you chose C: That is one carbon and one hydrogen. Count again: there are four H circles.

  8. How many atoms in all are in one unit of Ca(OH)₂?

    See the answer

    5 atoms

    Ca 1, O 2 and H 2. The bracket multiplies the O and the H by 2. 1 + 2 + 2 = 5.

  9. A positive ion has a charge of 3+ and a negative ion has a charge of 2−. How many of each ion are in one unit of the compound?

    See the answer

    2 positive ions and 3 negative ions

    The smallest number that 3 and 2 both go into is 6. 6 ÷ 3 = 2 positive ions and 6 ÷ 2 = 3 negative ions.

Keep it

Copy this into your exercise book.

Write the positive ion first. Use the smallest numbers that make the charges add to zero. Write them low, after the symbol. Put a bracket round a group that is counted more than once.

Draw: MgCl₂ as one Mg²⁺ disc and two Cl⁻ discs, with the sum +2 −1 −1 = 0 under them.

S4.7.2 Chapter 2

Balancing equations

A candle burns away and leaves almost nothing. Where did the wax go?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

When a candle burns, the wax seems to vanish. It does not. It changes into new substances. A reaction makes new substances from old ones.

We write a reaction as an equation. A word equation uses names: hydrogen + oxygen → water. The substances on the left are the reactants. The substances on the right are the products. The arrow means "makes".

A symbol equation uses formulae: H₂ + O₂ → H₂O. Now count the atoms. The left has 2 oxygen atoms. The right has only 1. An oxygen atom has gone. That cannot happen.

An equation drawn as molecules. On the left an H₂ molecule, two H circles, then a plus sign, then an O₂ molecule, two O circles. An arrow points to a water molecule, H₂O, with one O circle and two H circles. Under the left side the tally reads H 2, O 2. Under the right side it reads H 2, O 1.HHOOOHHH 2, O 2H 2, O 1
A first try that is not balanced. The tallies are not the same, so one oxygen atom has no place to go.

In a reaction, atoms are never made or destroyed. They only join in new ways. So an equation must have the same atoms on both sides. When it does, it is balanced.

We balance an equation by writing a number in front of a formula. This number is the coefficient. It multiplies the whole formula. 2H₂O means two water molecules, so 4 H atoms and 2 O atoms.

Never change the small number inside a formula to make an equation balance. H₂O₂ is not water. It is hydrogen peroxide, a different substance. A formula says what a substance is.

Draw it first

Balance hydrogen and oxygen making water

  1. Three versions of one equation, drawn in the same place. Step 1: H₂ + O₂ → H₂O, with tallies H 2, O 2 and H 2, O 1. Step 2: H₂ + O₂ → two H₂O, with tallies H 2, O 2 and H 4, O 2. Step 3: two H₂ + O₂ → two H₂O, with tallies H 4, O 2 and H 4, O 2.HHOOOHHH 2, O 2H 2, O 1

    1 Count the atoms in H₂ + O₂ → H₂O. Left: H 2, O 2. Right: H 2, O 1. The oxygen is not equal.

  2. Three versions of one equation, drawn in the same place. Step 1: H₂ + O₂ → H₂O, with tallies H 2, O 2 and H 2, O 1. Step 2: H₂ + O₂ → two H₂O, with tallies H 2, O 2 and H 4, O 2. Step 3: two H₂ + O₂ → two H₂O, with tallies H 4, O 2 and H 4, O 2.HHOOH 2, O 2OHHOHHH 4, O 2

    2 Write 2 in front of H₂O. Now the right has 2 O. But it has 4 H, and the left has only 2 H.

  3. Three versions of one equation, drawn in the same place. Step 1: H₂ + O₂ → H₂O, with tallies H 2, O 2 and H 2, O 1. Step 2: H₂ + O₂ → two H₂O, with tallies H 2, O 2 and H 4, O 2. Step 3: two H₂ + O₂ → two H₂O, with tallies H 4, O 2 and H 4, O 2.HHHHOOH 4, O 2OHHOHHH 4, O 2

    3 Write 2 in front of H₂. Now both sides have H 4 and O 2. The equation is balanced.

Here is how to balance any equation. Write the correct formula for every substance. Count each kind of atom on both sides. Change one number in front at a time, starting with an element that is in only one substance on each side. Leave an element on its own, such as O₂, for last. Then count everything again.

Worked example

Balance methane burning: CH₄ + O₂ → CO₂ + H₂O

  1. Count the atoms. Left: C 1, H 4, O 2. Right: C 1, H 2, O 3.
  2. Carbon is equal. Hydrogen is not: the left has 4 and the right has 2. Write 2 in front of H₂O.
  3. Now the right has 2 O in CO₂ and 2 O in the two H₂O, so 4 oxygen atoms. The left has 2.
  4. Write 2 in front of O₂. The left now has 2 × 2 = 4 oxygen atoms.
  5. Check both sides: C 1, H 4, O 4. The equation is balanced.

Answer: CH₄ + 2O₂ → CO₂ + 2H₂O

The balanced equation for methane burning, drawn as molecules. On the left a methane molecule, one C circle with four H circles, then a plus sign and two O₂ molecules. An arrow points to a carbon dioxide molecule, an O circle, a C circle and an O circle in a row, then a plus sign and two water molecules. The tallies under the two sides are both C 1, H 4, O 4.CHHHHOOOOC 1, H 4, O 4OCOOHHOHHC 1, H 4, O 4
Methane burning, balanced. Every circle on the left appears on the right, in new groups.

Equations also say what state each substance is in. A state symbol goes after the formula, in brackets.

A table with the columns Symbol and Means. (s) means solid. (l) means liquid. (g) means gas. (aq) means dissolved in water.SymbolMeans(s)solid(l)liquid(g)gas(aq)dissolved in water
The four state symbols. Aq is short for aqueous, which means in water.

Magnesium in acid is Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g). Solid magnesium goes into hydrochloric acid, which is HCl dissolved in water. It makes magnesium chloride dissolved in water, and hydrogen gas.

Now think about mass. Atoms are only rearranged, and each atom keeps its mass. So the total mass of the reactants equals the total mass of the products. We say that mass is conserved.

The balanced equation for magnesium burning, drawn as particles. On the left two single Mg circles, a plus sign and one O₂ molecule. An arrow points to two pairs of touching circles, each Mg²⁺ with O²⁻, which are magnesium oxide. The tallies are both Mg 2, O 2.MgMgOOMg 2, O 2Mg²⁺O²⁻Mg²⁺O²⁻Mg 2, O 2
2Mg + O₂ → 2MgO. Each pair on the right is one Mg²⁺ ion beside one O²⁻ ion.
A table with the columns Substance and Mass. Magnesium 48 g. Oxygen 32 g. Total before 80 g. Magnesium oxide 80 g.SubstanceMassmagnesium48 goxygen32 gtotal before80 gmagnesium oxide80 g
Magnesium and oxygen make magnesium oxide. The product has exactly the mass of the two reactants added together.

Worked example

In a closed flask 4 g of hydrogen reacts with 32 g of oxygen. What mass of water forms?

  1. The flask is closed, so nothing escapes. Mass is conserved.
  2. The mass of the reactants is 4 g + 32 g.
  3. The mass of the reactants is 36 g.
  4. The water has the same mass as the reactants: 36 g.

Answer: 36 g of water

Sometimes the mass seems to change. Burn magnesium in an open dish and the powder weighs more than the metal did. Oxygen from the air joined it. Heat chalk rock, which is calcium carbonate, in an open dish and the powder weighs less. Carbon dioxide gas escaped. In a closed container the mass stays the same.

See it three ways

As a picture

The balanced equation for water, drawn as molecules. On the left two H₂ molecules, a plus sign and one O₂ molecule. An arrow points to two water molecules. The tallies under both sides are H 4, O 2.HHHHOOH 4, O 2OHHOHHH 4, O 2

In words

Two hydrogen molecules and one oxygen molecule make two water molecules. The same four hydrogen atoms and two oxygen atoms are on both sides.

In symbols

2H₂ + O₂ → 2H₂O, with H 4 and O 2 on each side.

Try it

Catch a gas in a balloon

You need: a clean plastic bottle, a balloon, or a small plastic bag and string, vinegar, baking soda and a spoon, a paper funnel, made by rolling a sheet of paper.

Be safe: Use only vinegar and baking soda. Do not use a cap or cork, because pressure could push it out. Keep your face and eyes away from the balloon, and taste nothing.

  1. Pour vinegar into the bottle until it is about a quarter full.
  2. Use the paper funnel to put two spoons of baking soda into the balloon or bag.
  3. Stretch the neck of the balloon over the top of the bottle. With a bag, tie its neck tight round the bottle with string. Let it hang down, so the soda does not fall in yet.
  4. Lift the balloon or bag up so the baking soda falls into the vinegar. Watch the bottle and the balloon or bag.

What you will see: The mixture fizzes, and the balloon or bag swells. A new substance, carbon dioxide gas, is made from the two things you put in. The bottle and balloon are closed, so the gas cannot escape. It stays in the balloon or bag.

If you cannot try it, this is what happens.
A flow of three boxes joined by arrows. Baking soda meets vinegar. Carbon dioxide gas is made. The gas fills the balloon.Baking soda meets vinegarCarbon dioxide gas is madeThe gas fills the balloon

A wrong idea many people have

To balance an equation, change the small numbers in a formula. For example, change H₂O to H₂O₂.

Why it feels right: Changing a small number is the quickest way to equal the atom counts. The numbers also look like part of a puzzle.

The test that breaks it: Draw H₂O₂ as circles: it has 2 O atoms, not 1. It is hydrogen peroxide, which bleaches and is not water. The reaction in the picture makes water.

What is true: A small number inside a formula is part of what the substance is. Only the number in front, the coefficient, may be changed to balance.

Key words

reactants
the substances that react, written on the left of the arrow.
products
the substances that are made, written on the right of the arrow.
balanced
having the same atoms of every element on both sides of the equation.
coefficient
the number in front of a formula that says how many of it.
state symbol
a letter in brackets after a formula: (s), (l), (g) or (aq).
conserved
kept the same in a reaction, as the total mass is.

Back to your guess

The answer is A: It joins with oxygen from the air and becomes gases, such as carbon dioxide and water vapour.

The atoms of the wax join with oxygen from the air. They make carbon dioxide and water vapour, which are gases and drift away. No atoms are destroyed.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. The first try H₂ + O₂ → H₂O is drawn. It is not balanced. Which balanced equation makes water from hydrogen gas and oxygen gas?

    An H₂ molecule, two H circles, and an O₂ molecule, two O circles, with an arrow to a water molecule, an O circle with two H circles. Under the left side the tally reads H 2, O 2. Under the right side it reads H 2, O 1.HHOOOHHH 2, O 2H 2, O 1
    Tap your answer.

    1. Not this one. That balances the atoms by making a different substance, hydrogen peroxide. A small number inside a formula must never be changed. Try another.

    2. Not this one. Oxygen gas is made of O₂ molecules, so its formula is O₂. A formula cannot be changed to balance an equation. Try another.

    3. Yes, that is right. Two H₂O molecules hold 2 oxygen atoms and 4 hydrogen atoms. Two H₂ molecules give the 4 hydrogen atoms, and one O₂ gives the 2 oxygen atoms.

    See the answer

    2H₂ + O₂ → 2H₂O

    Two H₂O molecules hold 2 oxygen atoms and 4 hydrogen atoms. Two H₂ molecules give the 4 hydrogen atoms, and one O₂ gives the 2 oxygen atoms.

    • If you chose A: That balances the atoms by making a different substance, hydrogen peroxide. A small number inside a formula must never be changed.
    • If you chose B: Oxygen gas is made of O₂ molecules, so its formula is O₂. A formula cannot be changed to balance an equation.

  2. Which equation for making ammonia is balanced?

    Tap your answer.

    1. Yes, that is right. Two NH₃ molecules have 2 N and 6 H. The left has N₂, which is 2 N, and three H₂, which is 6 H.

    2. Not this one. The left has 4 H atoms, but two NH₃ molecules have 6. The hydrogen is not equal. Try another.

    3. Not this one. The hydrogen is not equal: 6 on the left but only 3 on the right. The nitrogen is not equal either: 2 on the left and 1 on the right. Try another.

    See the answer

    N₂ + 3H₂ → 2NH₃

    Two NH₃ molecules have 2 N and 6 H. The left has N₂, which is 2 N, and three H₂, which is 6 H.

    • If you chose B: The left has 4 H atoms, but two NH₃ molecules have 6. The hydrogen is not equal.
    • If you chose C: The hydrogen is not equal: 6 on the left but only 3 on the right. The nitrogen is not equal either: 2 on the left and 1 on the right.

  3. In Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g), what does (aq) mean?

    Tap your answer.

    1. Not this one. A pure liquid is (l). Something with (aq) is a substance mixed into water. Go to S3.5.7. Try another.

    2. Yes, that is right. Aq is short for aqueous, which means in water. HCl(aq) is hydrochloric acid, and MgCl₂(aq) is magnesium chloride dissolved in water.

    3. Not this one. A gas is (g). In this equation it is the hydrogen, H₂(g), that escapes. Try another.

    See the answer

    dissolved in water

    Aq is short for aqueous, which means in water. HCl(aq) is hydrochloric acid, and MgCl₂(aq) is magnesium chloride dissolved in water.

    • If you chose A: A pure liquid is (l). Something with (aq) is a substance mixed into water. Go to S3.5.7.
    • If you chose C: A gas is (g). In this equation it is the hydrogen, H₂(g), that escapes.

  4. Magnesium is burned in an open dish. The white powder weighs more than the metal did. Why?

    Tap your answer.

    1. Yes, that is right. Magnesium and oxygen make magnesium oxide. The oxide has the mass of the magnesium and the oxygen together. The oxygen came from the air, which an open dish does not hold back.

    2. Not this one. Matter is never made from nothing in a reaction. The extra mass came from the air. Go to S3.6.6. Try another.

    3. Not this one. Heat does not change the mass of a solid you could weigh. The extra mass came from oxygen that joined it. Try another.

    See the answer

    Oxygen from the air joined the magnesium.

    Magnesium and oxygen make magnesium oxide. The oxide has the mass of the magnesium and the oxygen together. The oxygen came from the air, which an open dish does not hold back.

    • If you chose B: Matter is never made from nothing in a reaction. The extra mass came from the air. Go to S3.6.6.
    • If you chose C: Heat does not change the mass of a solid you could weigh. The extra mass came from oxygen that joined it.

  5. Chalk rock, which is calcium carbonate, is heated strongly in an open dish, and the powder left weighs less. Why?

    Tap your answer.

    1. Not this one. The energy of the heat is far too small to change a mass you could weigh. The missing mass is in the gas. Try another.

    2. Not this one. Mass is never destroyed in a reaction. The missing mass is in the gas that left. Try another.

    3. Yes, that is right. Chalk rock, CaCO₃, breaks into CaO and CO₂. The CO₂ is a gas and leaves the dish. In a closed container the total mass would stay the same.

    See the answer

    Carbon dioxide gas escaped into the air.

    Chalk rock, CaCO₃, breaks into CaO and CO₂. The CO₂ is a gas and leaves the dish. In a closed container the total mass would stay the same.

    • If you chose A: The energy of the heat is far too small to change a mass you could weigh. The missing mass is in the gas.
    • If you chose B: Mass is never destroyed in a reaction. The missing mass is in the gas that left.

  6. From an earlier chapter

    How many hydrogen atoms are in 3Ca(OH)₂?

    Tap your answer.

    1. Not this one. That is one Ca(OH)₂. The 3 in front says there are three of them. Go to S4.7.1. Try another.

    2. Yes, that is right. One Ca(OH)₂ has 2 H, because the bracket multiplies the H by 2. There are 3 of them, so 3 × 2 = 6.

    3. Not this one. There is one H in each OH, but the bracket has a 2 after it. Each Ca(OH)₂ has 2 hydrogen atoms. Go to S4.7.1. Try another.

    See the answer

    6 hydrogen atoms

    One Ca(OH)₂ has 2 H, because the bracket multiplies the H by 2. There are 3 of them, so 3 × 2 = 6.

    • If you chose A: That is one Ca(OH)₂. The 3 in front says there are three of them. Go to S4.7.1.
    • If you chose C: There is one H in each OH, but the bracket has a 2 after it. Each Ca(OH)₂ has 2 hydrogen atoms. Go to S4.7.1.

  7. Balance this equation: Mg + O₂ → MgO. What are the smallest whole numbers in front of Mg, O₂ and MgO, in that order?

    See the answer

    2, 1 and 2

    Two MgO have 2 Mg and 2 O. So write 2 in front of Mg. One O₂ has 2 O. The equation is 2Mg + O₂ → 2MgO.

  8. In a closed flask 8 g of A reacts with some B to make 20 g of C. How many grams of B reacted?

    See the answer

    12 g

    Mass is conserved, so the reactants weigh the same as the product. 20 g − 8 g = 12 g of B.

Keep it

Copy this into your exercise book.

Atoms are not made or destroyed, so both sides of an equation have the same atoms. Balance with numbers in front. Never change a formula. Mass is conserved.

Draw: The equation 2H₂ + O₂ → 2H₂O with a tally of H 4, O 2 under each side.

S4.7.3 Chapter 3

The mole

How can a chemist count atoms when they are far too small to see?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

One drop of water holds about a thousand million million million molecules. Nobody can count them one by one. Chemists use a trick: they weigh. This chapter shows how weighing can count.

Every element has a relative atomic mass. It compares the mass of its atoms with one twelfth of a carbon 12 atom. Hydrogen is 1, carbon is 12 and oxygen is 16. It has no unit. It is an average over the isotopes, which is why chlorine is 35.5.

A table with the columns Element, Symbol and Mass. Hydrogen H 1. Carbon C 12. Nitrogen N 14. Oxygen O 16. Sodium Na 23. Magnesium Mg 24. Sulfur S 32. Chlorine Cl 35.5. Calcium Ca 40. Iron Fe 56.ElementSymbolMasshydrogenH1carbonC12nitrogenN14oxygenO16sodiumNa23magnesiumMg24sulfurS32chlorineCl35.5calciumCa40ironFe56
Relative atomic masses used in this book, part 1. The column Mass is the relative atomic mass, so it has no unit. Part 2 follows.
A table with the columns Element, Symbol and Mass. Aluminium Al 27. Potassium K 39. Copper Cu 63.5. Zinc Zn 65. Bromine Br 80. Tin Sn 119. Lead Pb 207.ElementSymbolMassaluminiumAl27potassiumK39copperCu63.5zincZn65bromineBr80tinSn119leadPb207
Relative atomic masses used in this book, part 2. These are the values the questions use when they do not give them.

The relative formula mass, written Mr, is the sum of the relative atomic masses of all the atoms in a formula. For a molecule it is also called the relative molecular mass. Add the atoms one by one, and use a bracket the same way as in chapter 1.

Worked example

What is the relative formula mass of Ca(OH)₂?

  1. The atoms are Ca 1, O 2 and H 2. The bracket multiplies O and H by 2.
  2. The relative atomic masses are Ca 40, O 16 and H 1.
  3. Ca: 1 × 40 = 40. O: 2 × 16 = 32. H: 2 × 1 = 2.
  4. Mr = 40 + 32 + 2 = 74.

Answer: 74

Now the key idea. A mole is an amount of substance. One mole of anything holds 6.02 × 10²³ particles. This is 602 followed by 21 zeros. The particles may be atoms, molecules or the units of an ionic formula.

The mass of one mole, in grams, is the Mr of the substance. So 12 g of carbon is one mole of carbon atoms. 18 g of water is one mole of water molecules. 44 g of carbon dioxide is one mole of CO₂ molecules. Mr has no unit. The mass of one mole is Mr in grams.

A table with the columns Substance, Mr and 1 mol. Carbon, 12, 12 g. Water, 18, 18 g. Carbon dioxide, 44, 44 g. Table salt, 58.5, 58.5 g.SubstanceMr1 molcarbon1212 gwater1818 gcarbon dioxide4444 gtable salt58.558.5 g
The column 1 mol is the mass of one mole. Table salt is sodium chloride, NaCl. Each row holds 6.02 × 10²³ particles. The particles differ in mass, so the masses differ.

Draw it first

The triangle for mass, moles and Mr

  1. A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr. In step 2 the n (mol) cell is hatched, covered. In step 3 the mass (g) cell is hatched, covered.mass(g)n (mol)Mr

    1 Write mass on top, and moles and Mr side by side below.

  2. A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr. In step 2 the n (mol) cell is hatched, covered. In step 3 the mass (g) cell is hatched, covered.mass(g)Mr

    2 Cover moles. What is left is mass over Mr, so moles = mass ÷ Mr.

  3. A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr. In step 2 the n (mol) cell is hatched, covered. In step 3 the mass (g) cell is hatched, covered.n (mol)Mr

    3 Cover mass. What is left is moles beside Mr, so mass = moles × Mr.

A kitchen scale with water on it. The display reads 90 g.water90 g
The scale for the worked example: water, with a mass of 90 g. The scale was set to zero with the empty cup on it, so it shows the water only.

Worked example

How many moles of water are on the scale?

  1. Mr of H₂O = 2 × 1 + 16 = 18.
  2. moles = mass ÷ Mr.
  3. moles = 90 ÷ 18 = 5 mol.

Answer: 5 mol

See it three ways

As a picture

A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr.mass(g)n (mol)Mr

In words

Cover the one you want. Mass over Mr gives moles. Moles beside Mr gives mass: multiply.

In symbols

moles = mass ÷ Mr, and mass = moles × Mr.

Reactions in water use solutions. The concentration of a solution is how many moles of the solute are in 1 dm³ of the solution. A dm³ is a cubic decimetre, which is one litre. It is 1 000 cm³.

Concentration is measured in mol/dm³. Say it as "moles per cubic decimetre". The same amount of solute in less water gives a more concentrated solution.

Worked example

2 g of sodium hydroxide, NaOH, is dissolved in water to make 500 cm³ of solution. What is the concentration in mol/dm³?

  1. Mr of NaOH = 23 + 16 + 1 = 40.
  2. moles = 2 ÷ 40 = 0.05 mol.
  3. volume = 500 cm³ ÷ 1 000 = 0.5 dm³.
  4. concentration = moles ÷ volume = 0.05 ÷ 0.5 = 0.1 mol/dm³.

Answer: 0.1 mol/dm³

A beaker with a scale from 100 to 600 cm³. The liquid reaches the mark at 500 cm³. The label under it reads NaOH solution.100200300400500600cm³NaOH solution
The solution for the worked example. It is at the 500 cm³ mark.
A triangle with a line across and a line down. Moles, n (mol), is on top. Concentration, c (mol/dm³), is bottom left. Volume, V (dm³), is bottom right.n (mol)c(mol/dm³)V (dm³)
The same triangle for concentration: c = n ÷ V, n = c × V and V = n ÷ c. Volume must be in dm³.

Try it

Strong tea and weak tea

You need: cold, strong tea, three clear cups or glasses of the same size, water, a spoon and a sheet of white paper.

Be safe: An adult makes the tea and lets it cool completely. Drink none of it, and wash your hands afterwards.

  1. Put the same amount of water in each of two cups, about half full. Add 1 spoon of tea to one and 2 spoons to the other. Stir.
  2. Hold each cup against the white paper. Which looks darker?
  3. Fill the third cup with twice as much water as the others. Add 4 spoons of tea and stir.
  4. Compare this cup with the one that has 2 spoons.

What you will see: The cup with 2 spoons is darker than the cup with 1 spoon: more tea in the same amount of water. The third cup has 4 spoons in twice the water, which is 2 spoons for each cup of water. It looks like the second cup. Concentration is the amount of solute divided by the volume.

If you cannot try it, this is what happens.
A table with the columns Tea, Water and Colour. 1 spoon in 1 cup of water: lightest. 2 spoons in 1 cup of water: darker. 4 spoons in 2 cups of water: as row 2, the same colour as 2 spoons in 1 cup.TeaWaterColour1 spoon1 cuplightest2 spoons1 cupdarker4 spoons2 cupsas row 2

A wrong idea many people have

One mole of every substance has the same mass.

Why it feels right: Every mole has the same number of particles, so it seems it should weigh the same.

The test that breaks it: Look at the table of one mole. 1 mol of carbon is 12 g, but 1 mol of carbon dioxide is 44 g.

What is true: One mole always has the same number of particles, 6.02 × 10²³. The particles have different masses, so a mole of one substance is heavier than a mole of another.

Key words

relative atomic mass
the mass of an atom compared with one twelfth of a carbon 12 atom.
relative formula mass
Mr, the sum of the relative atomic masses in a formula.
mole
an amount of substance: 6.02 × 10²³ particles.
concentration
the moles of solute in 1 dm³ of solution.

Back to your guess

The answer is C: By weighing them, because the mass of a pile tells how many atoms it holds.

Chemists weigh. Each kind of atom has its own mass, so a known mass of a substance holds a known number of particles. The mole is the name for that number.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. What is the relative formula mass of CO₂? Use C 12 and O 16.

    Tap your answer.

    1. Not this one. That is 12 + 16, for CO with one oxygen. CO₂ has two oxygen atoms. Try another.

    2. Not this one. That is 2 × 16, the two oxygen atoms. The carbon atom must be added too. Try another.

    3. Yes, that is right. CO₂ has 1 carbon and 2 oxygen atoms. 12 + 2 × 16 = 12 + 32 = 44.

    See the answer

    44

    CO₂ has 1 carbon and 2 oxygen atoms. 12 + 2 × 16 = 12 + 32 = 44.

    • If you chose A: That is 12 + 16, for CO with one oxygen. CO₂ has two oxygen atoms.
    • If you chose B: That is 2 × 16, the two oxygen atoms. The carbon atom must be added too.

  2. The scale shows 36 g of water. It was set to zero with the empty cup on it. Mr of water is 18. How many moles of water is that?

    A kitchen scale with water on it. The display reads 36 g.water36 g
    Tap your answer.

    1. Yes, that is right. moles = mass ÷ Mr = 36 ÷ 18 = 2 mol.

    2. Not this one. That is 18 ÷ 36, the wrong way round. Moles are mass divided by Mr. Try another.

    3. Not this one. That is the Mr itself. Divide the mass by it: moles = mass ÷ Mr. Try another.

    See the answer

    2 mol

    moles = mass ÷ Mr = 36 ÷ 18 = 2 mol.

    • If you chose B: That is 18 ÷ 36, the wrong way round. Moles are mass divided by Mr.
    • If you chose C: That is the Mr itself. Divide the mass by it: moles = mass ÷ Mr.

  3. What is the mass of 2 mol of calcium carbonate, CaCO₃?

    Tap your answer.

    1. Not this one. That is 100 ÷ 2. To go from moles to mass, multiply by Mr. Try another.

    2. Yes, that is right. Mr of CaCO₃ = 40 + 12 + 3 × 16 = 100. mass = moles × Mr = 2 × 100 = 200 g.

    3. Not this one. That is the mass of 1 mol. There are 2 mol, so multiply by 2. Try another.

    See the answer

    200 g

    Mr of CaCO₃ = 40 + 12 + 3 × 16 = 100. mass = moles × Mr = 2 × 100 = 200 g.

    • If you chose A: That is 100 ÷ 2. To go from moles to mass, multiply by Mr.
    • If you chose C: That is the mass of 1 mol. There are 2 mol, so multiply by 2.

  4. A 100 cm³ sample of solution holds 0.2 mol of sodium chloride. What is its concentration?

    Tap your answer.

    1. Not this one. That divides by 100 as if the volume were in dm³. 100 cm³ is 0.1 dm³ first. Try another.

    2. Not this one. That multiplies by 100. To change cm³ into dm³ divide by 1 000, which gives 0.1 dm³. Try another.

    3. Yes, that is right. 100 cm³ = 0.1 dm³. concentration = moles ÷ volume = 0.2 ÷ 0.1 = 2 mol/dm³.

    See the answer

    2 mol/dm³

    100 cm³ = 0.1 dm³. concentration = moles ÷ volume = 0.2 ÷ 0.1 = 2 mol/dm³.

    • If you chose A: That divides by 100 as if the volume were in dm³. 100 cm³ is 0.1 dm³ first.
    • If you chose B: That multiplies by 100. To change cm³ into dm³ divide by 1 000, which gives 0.1 dm³.

  5. Which sample holds the most particles: 12 g of carbon, 18 g of water or 44 g of carbon dioxide?

    Tap your answer.

    1. Not this one. More mass does not mean more particles. Each particle of carbon dioxide has more mass than a carbon atom. Try another.

    2. Yes, that is right. Each sample is one mole, because its mass in grams equals its Mr: 12, 18 and 44. One mole always has the same number of particles.

    3. Not this one. The size of a particle does not decide it. Count the moles instead: 12 g of carbon is one mole. Try another.

    See the answer

    All three hold the same number of particles.

    Each sample is one mole, because its mass in grams equals its Mr: 12, 18 and 44. One mole always has the same number of particles.

    • If you chose A: More mass does not mean more particles. Each particle of carbon dioxide has more mass than a carbon atom.
    • If you chose C: The size of a particle does not decide it. Count the moles instead: 12 g of carbon is one mole.

  6. One mole holds 6.02 × 10²³ particles. How many carbon atoms are in 0.5 mol of carbon?

    Tap your answer.

    1. Yes, that is right. Half a mole holds half the particles. 0.5 × 6.02 × 10²³ = 3.01 × 10²³ atoms.

    2. Not this one. That is the number in a whole mole. Here there is only half a mole, so half as many atoms. Try another.

    3. Not this one. Half of 6.02 is 3.01, but the power of ten stays at 23. A power of 22 would be ten times too small. Try another.

    See the answer

    3.01 × 10²³ atoms

    Half a mole holds half the particles. 0.5 × 6.02 × 10²³ = 3.01 × 10²³ atoms.

    • If you chose B: That is the number in a whole mole. Here there is only half a mole, so half as many atoms.
    • If you chose C: Half of 6.02 is 3.01, but the power of ten stays at 23. A power of 22 would be ten times too small.

  7. Why is the relative atomic mass of chlorine 35.5, and not a whole number?

    Tap your answer.

    1. Not this one. Protons are never split. Every chlorine atom has 17 whole protons. Go to S4.6.1. Try another.

    2. Not this one. It is measured carefully. The value is 35.45, which school tables round to 35.5. It is not whole because chlorine is a mixture of two isotopes with different masses, and 35.5 is their average. Go to S4.6.3. Try another.

    3. Yes, that is right. Chlorine atoms with 18 neutrons are about three times as common as those with 20. The average mass lies between 35 and 37, closer to 35, at 35.5.

    See the answer

    It is the average of the masses of its isotopes, weighted by how common each is.

    Chlorine atoms with 18 neutrons are about three times as common as those with 20. The average mass lies between 35 and 37, closer to 35, at 35.5.

    • If you chose A: Protons are never split. Every chlorine atom has 17 whole protons. Go to S4.6.1.
    • If you chose B: It is measured carefully. The value is 35.45, which school tables round to 35.5. It is not whole because chlorine is a mixture of two isotopes with different masses, and 35.5 is their average. Go to S4.6.3.

  8. From an earlier chapter

    Calcium burns in oxygen to make calcium oxide, CaO. Which is the balanced equation for this?

    Tap your answer.

    1. Yes, that is right. Two CaO have 2 Ca and 2 O. So 2 Ca on the left, and one O₂ for 2 O.

    2. Not this one. This is balanced, but CaO₂ is not calcium oxide. The formula of the product must stay CaO. Only the number in front may change. Go to S4.7.2. Try another.

    3. Not this one. The left has 2 O atoms and the right has 1. The oxygen is not equal. Go to S4.7.2. Try another.

    See the answer

    2Ca + O₂ → 2CaO

    Two CaO have 2 Ca and 2 O. So 2 Ca on the left, and one O₂ for 2 O.

    • If you chose B: This is balanced, but CaO₂ is not calcium oxide. The formula of the product must stay CaO. Only the number in front may change. Go to S4.7.2.
    • If you chose C: The left has 2 O atoms and the right has 1. The oxygen is not equal. Go to S4.7.2.

  9. What is the relative formula mass of Na₂CO₃?

    See the answer

    106

    Na₂CO₃ has 2 Na, 1 C and 3 O. 2 × 23 + 12 + 3 × 16 = 46 + 12 + 48 = 106.

  10. How many moles are in 22 g of carbon dioxide?

    See the answer

    0.5 mol

    Mr of CO₂ is 44. moles = mass ÷ Mr = 22 ÷ 44 = 0.5 mol.

  11. A solution of volume 250 cm³ holds 0.5 mol of solute. What is its concentration in mol/dm³?

    See the answer

    2 mol/dm³

    250 cm³ ÷ 1 000 = 0.25 dm³. concentration = 0.5 ÷ 0.25 = 2 mol/dm³.

Keep it

Copy this into your exercise book.

Mr is the sum of the relative atomic masses. One mole is Mr grams and 6.02 × 10²³ particles. moles = mass ÷ Mr. concentration = moles ÷ volume in dm³.

Draw: The triangle with mass on top and moles and Mr below. Add a second triangle for n, c and V.

S4.7.4 Chapter 4

Reacting masses and yield

If I burn 12 g of magnesium, how much magnesium oxide can I make?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

A balanced equation is a recipe. In 2Mg + O₂ → 2MgO, two magnesium atoms and one oxygen molecule make two units of magnesium oxide. A chemist wants to know how much of each to weigh.

The numbers in front of the formulae count particles. So they also count moles. 2 mol of Mg and 1 mol of O₂ make 2 mol of MgO. They are not masses. A mole of each substance has its own mass.

Draw it first

From the equation to the masses

  1. The balanced equation drawn as particles: two Mg circles, a plus sign and an O₂ molecule, then an arrow to two pairs of touching circles, each Mg²⁺ with O²⁻, which are magnesium oxide. Under it, in step 2, the line 2 mol : 1 mol : 2 mol. In step 3, under that, the line 48 g : 32 g : 80 g.MgMgOOMg²⁺O²⁻Mg²⁺O²⁻

    1 Write the balanced equation: 2Mg + O₂ → 2MgO.

  2. The balanced equation drawn as particles: two Mg circles, a plus sign and an O₂ molecule, then an arrow to two pairs of touching circles, each Mg²⁺ with O²⁻, which are magnesium oxide. Under it, in step 2, the line 2 mol : 1 mol : 2 mol. In step 3, under that, the line 48 g : 32 g : 80 g.MgMgOOMg²⁺O²⁻Mg²⁺O²⁻2 mol : 1 mol : 2 mol

    2 The numbers in front are moles: 2 mol of Mg and 1 mol of O₂ make 2 mol of MgO.

  3. The balanced equation drawn as particles: two Mg circles, a plus sign and an O₂ molecule, then an arrow to two pairs of touching circles, each Mg²⁺ with O²⁻, which are magnesium oxide. Under it, in step 2, the line 2 mol : 1 mol : 2 mol. In step 3, under that, the line 48 g : 32 g : 80 g.MgMgOOMg²⁺O²⁻Mg²⁺O²⁻2 mol : 1 mol : 2 mol48 g : 32 g : 80 g

    3 Change moles into grams with Mr. 2 × 24 = 48 g, 1 × 32 = 32 g and 2 × 40 = 80 g.

To find the mass of a product, work in three steps. Change the mass you know into moles, with mass ÷ Mr. Use the equation to find the moles of the substance you want. Change those moles into mass, with moles × Mr.

Four boxes joined by arrows, from top to bottom. Mass of the substance you know. Moles of it: mass ÷ Mr. Moles of the other substance: use the equation ratio. Mass of the other substance: moles × Mr.Mass of the substance youknowMoles of it: mass ÷ MrMoles of the other substance:use the equation ratioMass of the other substance:moles × Mr
The method for every reacting mass question.

Worked example

What mass of magnesium oxide forms when 12 g of magnesium burns? Use 2Mg + O₂ → 2MgO.

  1. The ratio of Mg to MgO in the equation is 2 to 2, which is 1 to 1.
  2. Moles of Mg = 12 ÷ 24 = 0.5 mol.
  3. Moles of MgO = 0.5 mol, from the 1 to 1 ratio.
  4. Mr of MgO = 24 + 16 = 40.
  5. Mass of MgO = 0.5 × 40 = 20 g.

Answer: 20 g

Worked example

What mass of hydrogen chloride, HCl, reacts with 12 g of magnesium? Use Mg + 2HCl → MgCl₂ + H₂.

  1. The ratio of Mg to HCl in the equation is 1 to 2.
  2. Moles of Mg = 12 ÷ 24 = 0.5 mol.
  3. Moles of HCl = 2 × 0.5 = 1 mol.
  4. Mr of HCl = 1 + 35.5 = 36.5.
  5. Mass of HCl = 1 × 36.5 = 36.5 g.

Answer: 36.5 g

A graph. The bottom is labelled magnesium (g) and runs from 0 to 24. The side is labelled magnesium oxide (g) and runs from 0 to 40. A straight line starts at 0 and 0 and rises to 24 and 40.036912151821240510152025303540magnesium (g)magnesium oxide (g)
More magnesium makes more oxide, in a fixed ratio. Double the magnesium and the oxide doubles. The line is straight and starts at 0.

The amount a perfect reaction would make is the theoretical yield. The amount we really collect is the actual yield. The actual yield is nearly always smaller.

The percentage yield compares them. percentage yield = actual yield ÷ theoretical yield × 100.

A bar chart labelled magnesium oxide (g), with two bars. The bar labelled theory reaches 20. The bar labelled actual reaches 18.0510152025theoryactualmagnesium oxide (g)
The theory says 20 g. A student collects 18 g.

Worked example

The theoretical yield of magnesium oxide is 20 g. A student collects 18 g. What is the percentage yield?

  1. percentage yield = actual yield ÷ theoretical yield × 100.
  2. Actual yield = 18 g. Theoretical yield = 20 g.
  3. 18 ÷ 20 = 0.9.
  4. 0.9 × 100 = 90%.

Answer: 90%

Why is the yield below 100%? Atoms are not lost. The product is somewhere, but not all of it reaches the scale. Some stays on the glass or the filter paper when it is moved. Another reaction may make a different product. The reaction may stop before all the reactants are used. Some product may stay dissolved.

A yield over 100% would be a mistake. The product may be wet or mixed with another substance, so it weighs too much.

See it three ways

As a picture

A straight line graph. The bottom is labelled magnesium (g) and runs from 0 to 24. The side is labelled magnesium oxide (g) and runs from 0 to 40. The line rises from 0 and 0.036912151821240510152025303540magnesium (g)magnesium oxide (g)

In words

The oxide is always 40 for every 24 of magnesium, which is 5 for every 3. A straight line through zero shows that the two masses are in a fixed ratio.

In symbols

mass of MgO = mass of Mg × 40 ÷ 24

Try it

Where does the yield go?

You need: four cups, or two that you wash and dry, a spoon, water, cooking oil, paper and a pencil.

Be safe: Taste nothing. Wipe up any oil that spills, because it makes the floor slippery.

  1. Count out 10 level spoons of water into one cup.
  2. Pour all of it into the second, dry cup. Pour slowly, and wait until the last drop falls.
  3. Use the same spoon to lift the water out of the second cup. Count the spoons, until you can lift no more.
  4. Do the same with 10 spoons of cooking oil, using two clean, dry cups.

What you will see: You get back a little less than you put in, and the oil loses more than the water. The liquid clings to the cup, so it never all arrives. Real reactions lose product the same way, so the actual yield is below the theoretical yield. Your own counts may differ from the picture.

If you cannot try it, this is what happens.
A table with the columns Liquid, In and Out. Water: 10 spoons in, 9 spoons out. Oil: 10 spoons in, 8 spoons out. These are an example, not a fixed result.LiquidInOutwater10 spoons9 spoonsoil10 spoons8 spoons

A wrong idea many people have

In 2Mg + O₂ → 2MgO the numbers say that 2 g of Mg reacts with 1 g of O₂.

Why it feels right: The numbers are in the equation, and they look like quantities to weigh out.

The test that breaks it: Work out the masses of 2 mol of Mg and 1 mol of O₂. They are 48 g and 32 g, which is not a ratio of 2 to 1.

What is true: The numbers in front are moles, or numbers of particles. To get masses, multiply the moles by Mr.

Key words

theoretical yield
the mass of product a perfect reaction would make.
actual yield
the mass of product really collected.
percentage yield
the actual yield divided by the theoretical yield, times 100.

Back to your guess

The answer is B: More than 12 g, and the equation shows how much more.

The product is 20 g. Oxygen from the air joins the magnesium, so the oxide weighs more than the metal. The equation, with Mr, tells us how much.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. The graph shows magnesium oxide made from magnesium. Read it. How many grams of magnesium oxide form from 15 g of magnesium?

    A graph. The bottom is labelled magnesium (g) and runs from 0 to 24. The side is labelled magnesium oxide (g) and runs from 0 to 40. A straight line starts at 0 and 0 and rises to 24 and 40.036912151821240510152025303540magnesium (g)magnesium oxide (g)
    Tap your answer.

    1. Not this one. That is the mass of magnesium. The oxide weighs more, because oxygen joins the magnesium. Go to S4.7.2. Try another.

    2. Yes, that is right. Go up from 15 g of magnesium to the line, then across to 25 on the side. The calculation agrees: 15 ÷ 24 × 40 = 25 g.

    3. Not this one. That is the top of the line, for 24 g of magnesium. Go up from 15 on the bottom scale to the line, and then across. Try another.

    See the answer

    25 g

    Go up from 15 g of magnesium to the line, then across to 25 on the side. The calculation agrees: 15 ÷ 24 × 40 = 25 g.

    • If you chose A: That is the mass of magnesium. The oxide weighs more, because oxygen joins the magnesium. Go to S4.7.2.
    • If you chose C: That is the top of the line, for 24 g of magnesium. Go up from 15 on the bottom scale to the line, and then across.

  2. In N₂ + 3H₂ → 2NH₃, how many moles of NH₃ form from 3 mol of H₂?

    Tap your answer.

    1. Not this one. The numbers in front are 3 for H₂ and 2 for NH₃. They are not equal. Go to S4.7.2. Try another.

    2. Not this one. That multiplies by 2, but the ratio is 3 H₂ to 2 NH₃. 3 mol of H₂ is one lot of the recipe. Try another.

    3. Yes, that is right. The ratio of H₂ to NH₃ is 3 to 2. So 3 mol of H₂ make 2 mol of NH₃.

    See the answer

    2 mol

    The ratio of H₂ to NH₃ is 3 to 2. So 3 mol of H₂ make 2 mol of NH₃.

    • If you chose A: The numbers in front are 3 for H₂ and 2 for NH₃. They are not equal. Go to S4.7.2.
    • If you chose B: That multiplies by 2, but the ratio is 3 H₂ to 2 NH₃. 3 mol of H₂ is one lot of the recipe.

  3. Calcium carbonate breaks down: CaCO₃ → CaO + CO₂. What mass of calcium oxide, CaO, forms from 10 g of calcium carbonate?

    Tap your answer.

    1. Yes, that is right. Mr of CaCO₃ is 100, so 10 g is 0.1 mol. The ratio is 1 to 1, so 0.1 mol of CaO forms. Mr of CaO is 56, so the mass is 0.1 × 56 = 5.6 g.

    2. Not this one. That is the mass of the carbon dioxide, 0.1 × 44. The question asks for the calcium oxide. Try another.

    3. Not this one. The product has less mass, because carbon dioxide gas leaves. Use moles: 10 g is 0.1 mol. Try another.

    See the answer

    5.6 g

    Mr of CaCO₃ is 100, so 10 g is 0.1 mol. The ratio is 1 to 1, so 0.1 mol of CaO forms. Mr of CaO is 56, so the mass is 0.1 × 56 = 5.6 g.

    • If you chose B: That is the mass of the carbon dioxide, 0.1 × 44. The question asks for the calcium oxide.
    • If you chose C: The product has less mass, because carbon dioxide gas leaves. Use moles: 10 g is 0.1 mol.

  4. A reaction should make 40 g of product. It makes 30 g. What is the percentage yield?

    Tap your answer.

    1. Not this one. That divides the wrong way round. The actual yield goes on top: 30 ÷ 40. Try another.

    2. Yes, that is right. percentage yield = actual ÷ theoretical × 100 = 30 ÷ 40 × 100 = 75%.

    3. Not this one. That is the percentage lost, 10 ÷ 40. The yield is the percentage collected. Try another.

    See the answer

    75%

    percentage yield = actual ÷ theoretical × 100 = 30 ÷ 40 × 100 = 75%.

    • If you chose A: That divides the wrong way round. The actual yield goes on top: 30 ÷ 40.
    • If you chose C: That is the percentage lost, 10 ÷ 40. The yield is the percentage collected.

  5. The bars show a theoretical yield and an actual yield. What is the percentage yield?

    A bar chart labelled product (g) with two bars. The bar labelled theory reaches 50. The bar labelled actual reaches 40.0102030405060theoryactualproduct (g)
    Tap your answer.

    1. Yes, that is right. percentage yield = actual ÷ theoretical × 100 = 40 ÷ 50 × 100 = 80%.

    2. Not this one. That divides the theoretical yield by the actual yield. The actual yield goes on top. Try another.

    3. Not this one. That is the difference in grams, 10 g, not a percentage of the theoretical yield. Try another.

    See the answer

    80%

    percentage yield = actual ÷ theoretical × 100 = 40 ÷ 50 × 100 = 80%.

    • If you chose B: That divides the theoretical yield by the actual yield. The actual yield goes on top.
    • If you chose C: That is the difference in grams, 10 g, not a percentage of the theoretical yield.

  6. A student works out a yield of more than 100%. What is the most likely reason?

    Tap your answer.

    1. Not this one. Atoms are never made in a reaction. The product must have weighed more for another reason. Go to S4.7.2. Try another.

    2. Not this one. Losing product makes the yield smaller, not larger. Try another.

    3. Yes, that is right. Water or an impurity adds mass, so the product weighs more than it should. The mistake is in the weighing, not in the chemistry.

    See the answer

    The product was still wet or mixed with another substance.

    Water or an impurity adds mass, so the product weighs more than it should. The mistake is in the weighing, not in the chemistry.

    • If you chose A: Atoms are never made in a reaction. The product must have weighed more for another reason. Go to S4.7.2.
    • If you chose B: Losing product makes the yield smaller, not larger.

  7. From an earlier chapter

    How many moles are in 11 g of carbon dioxide, CO₂?

    Tap your answer.

    1. Not this one. That is 44 ÷ 11, upside down. Moles are mass divided by Mr. Go to S4.7.3. Try another.

    2. Yes, that is right. Mr of CO₂ is 44. moles = mass ÷ Mr = 11 ÷ 44 = 0.25 mol.

    3. Not this one. Mr of CO₂ is 12 + 2 × 16 = 44, so 11 g is a quarter of a mole, not a half. Go to S4.7.3. Try another.

    See the answer

    0.25 mol

    Mr of CO₂ is 44. moles = mass ÷ Mr = 11 ÷ 44 = 0.25 mol.

    • If you chose A: That is 44 ÷ 11, upside down. Moles are mass divided by Mr. Go to S4.7.3.
    • If you chose C: Mr of CO₂ is 12 + 2 × 16 = 44, so 11 g is a quarter of a mole, not a half. Go to S4.7.3.

  8. Magnesium burns: 2Mg + O₂ → 2MgO. What mass of magnesium oxide forms from 6 g of magnesium?

    See the answer

    10 g

    6 ÷ 24 = 0.25 mol of Mg. The ratio is 1 to 1, so 0.25 mol of MgO forms. Its mass is 0.25 × 40 = 10 g.

  9. The theoretical yield is 40 g. The actual yield is 34 g. What is the percentage yield?

    See the answer

    85%

    percentage yield = actual ÷ theoretical × 100 = 34 ÷ 40 × 100 = 85%.

Keep it

Copy this into your exercise book.

Numbers in an equation are moles. Mass to moles with Mr, moles to moles with the ratio, moles to mass with Mr. Percentage yield = actual ÷ theoretical × 100.

Draw: The flow of four boxes: mass, moles, other moles, other mass, with the three operations on the arrows.

S4.7.5 Chapter 5

Acids, bases and salts

Why does vinegar fizz when I add baking soda?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Lemon juice, vinegar and the juice in your stomach are acids. Soap and baking soda solution are alkalis. This chapter shows what they have in common, and what they make when they react.

An acid is a substance that makes hydrogen ions, H⁺, when it dissolves in water. Hydrochloric acid, HCl, splits into H⁺ and Cl⁻ ions. Sulfuric acid is H₂SO₄ and nitric acid is HNO₃.

A base is a substance that reacts with an acid and cancels it. Metal oxides and metal hydroxides are bases. An alkali is a base that dissolves in water. It makes hydroxide ions, OH⁻. Sodium hydroxide, NaOH, makes Na⁺ and OH⁻ ions.

When an acid reacts, it makes a salt. A salt is a compound. It is made from the metal (or ammonium) part of the other substance and the negative ion of the acid. Hydrochloric acid makes chlorides. Sulfuric acid makes sulfates. Nitric acid makes nitrates.

A table with the columns Acid and Salt. Hydrochloric acid makes a chloride. Sulfuric acid makes a sulfate. Nitric acid makes a nitrate.AcidSalthydrochloricchloridesulfuricsulfatenitricnitrate
The name of the acid gives the end of the name of the salt. Zinc and hydrochloric acid make zinc chloride.

There are three kinds of reaction to know. An acid with a metal makes a salt and hydrogen. An acid with a base makes a salt and water. An acid with a carbonate makes a salt, water and carbon dioxide.

A table with the columns Acid with and Makes. A metal makes salt + H₂. A base makes salt + H₂O. A carbonate makes salt + H₂O + CO₂.Acid withMakesmetalsalt + H₂basesalt + H₂Ocarbonatesalt + H₂O + CO₂
The three reactions. H₂ is hydrogen, H₂O is water and CO₂ is carbon dioxide.

Worked example

Write a balanced equation for zinc reacting with hydrochloric acid.

  1. Word equation: zinc + hydrochloric acid → zinc chloride + hydrogen.
  2. Formulae: Zn + HCl → ZnCl₂ + H₂. Zinc chloride is ZnCl₂, because Zn²⁺ needs two Cl⁻.
  3. Count Cl: 1 on the left and 2 on the right. Write 2 in front of HCl.
  4. Now H is 2 on each side. The equation is balanced.

Answer: Zn + 2HCl → ZnCl₂ + H₂

Three discs in a row. A hatched disc is Zn²⁺. Two plain discs are Cl⁻. Under them the sum reads +2 −1 −1 = 0, and the formula ZnCl₂.Zn²⁺Cl⁻Cl⁻+2 −1 −1 = 0ZnCl₂
The salt zinc chloride. One Zn²⁺ ion goes with two Cl⁻ ions.

Worked example

Write a balanced equation for magnesium hydroxide reacting with hydrochloric acid.

  1. Word equation: magnesium hydroxide + hydrochloric acid → magnesium chloride + water.
  2. Formulae: Mg(OH)₂ + HCl → MgCl₂ + H₂O.
  3. Count Cl: 1 on the left and 2 on the right. Write 2 in front of HCl.
  4. Count H: 2 in Mg(OH)₂ and 2 in 2HCl, so 4 on the left. Write 2 in front of H₂O to make 4 on the right.
  5. Check O: 2 on each side. The equation is balanced.

Answer: Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O

Worked example

Write a balanced equation, with state symbols, for calcium carbonate reacting with hydrochloric acid.

  1. Word equation: calcium carbonate + hydrochloric acid → calcium chloride + water + carbon dioxide.
  2. Formulae: CaCO₃ + HCl → CaCl₂ + H₂O + CO₂.
  3. Count Cl: 1 on the left and 2 on the right. Write 2 in front of HCl.
  4. Now H is 2 on the left, from the 2HCl, and 2 on the right, in H₂O.
  5. C is 1 on each side. O is 3 in CaCO₃ on the left and 1 + 2 = 3 on the right.
  6. Add state symbols. The carbonate is a solid. The acid and the salt are dissolved. The water is a liquid, and the carbon dioxide is a gas.

Answer: CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)

Now think about what makes a solution acid or alkaline. It is the number of H⁺ ions. The pH scale measures it. A solution of pH 7 is neutral, at room temperature. Below 7 is acid, and above 7 is alkaline.

A lower pH means more H⁺ ions in each dm³. Each step of 1 on the scale means 10 times as many H⁺ ions, or 10 times fewer. A solution of pH 3 has 10 times more H⁺ than one of pH 4.

The pH scale stood upright, from 0 at the top to 14 at the bottom, with acid, neutral and alkali regions. The marks read stomach acid, 1 to 2; lemon juice, about 2; vinegar, about 3; pure water, 7; baking soda solution, about 8; and soap, about 10.neutralacidalkali01234567891011121314pHstomach acid,1 to 2lemon juice,about 2vinegar, about 3pure water, 7baking sodasolution,about 8soap, about 10
The pH scale with some things from a home. The values are about, because they change with the brand and the strength.
A table with the columns pH and Times more H⁺, compared with pure water at pH 7. pH 6 has 10 times as many H⁺. pH 5 has 100 times as many. pH 4 has 1 000 times as many. pH 3 has 10 000 times as many.pHTimes more H⁺610 times5100 times41 000 times310 000 times
Compared with pure water, at pH 7. Each step down is 10 times more H⁺. Vinegar, at about pH 3, has about ten thousand times as many H⁺ ions as pure water.

Draw it first

An acid and an alkali meet

  1. Three steps, drawn in the same place. Step 1: a hatched disc H⁺ with the charge +1. Step 2: a plain disc OH⁻ is added and the sum reads +1 −1 = 0. Step 3: the formula H₂O appears under the sum.H⁺+1

    1 An acid supplies H⁺ ions. Each has a charge of +1.

  2. Three steps, drawn in the same place. Step 1: a hatched disc H⁺ with the charge +1. Step 2: a plain disc OH⁻ is added and the sum reads +1 −1 = 0. Step 3: the formula H₂O appears under the sum.H⁺OH⁻+1 −1 = 0

    2 An alkali supplies OH⁻ ions, each with a charge of −1. One of each makes a total charge of 0.

  3. Three steps, drawn in the same place. Step 1: a hatched disc H⁺ with the charge +1. Step 2: a plain disc OH⁻ is added and the sum reads +1 −1 = 0. Step 3: the formula H₂O appears under the sum.H⁺OH⁻+1 −1 = 0H₂O

    3 They join to make a water molecule, H₂O. This is neutralisation: H⁺ + OH⁻ → H₂O.

See it three ways

As a picture

A pH scale with the acid, neutral and alkali regions, and one mark, vinegar, about 3.neutralacidalkali01234567891011121314pHvinegar, about 3

In words

Lower pH, more H⁺. Every step down the scale is ten times more H⁺ ions in the same volume.

In symbols

pH 3 has 10 × more H⁺ than pH 4, and 100 × more than pH 5.

Try it

Red cabbage tells acid from alkali

You need: a few leaves of red cabbage, hot water, poured by an adult, six clear cups, or four if you wash and dry two, vinegar, water, baking soda and a spoon.

Be safe: An adult pours the hot water and lets the cabbage liquid cool. Vinegar and baking soda are the strongest acid and alkali to use. Taste nothing, keep the liquids away from your eyes, and wash your hands after.

  1. Tear the cabbage into small pieces in a cup. An adult pours hot water over them. Leave it for 15 minutes, then pour off the purple liquid into a second cup.
  2. Stir a spoon of baking soda into half a cup of cold water, in a third cup, to make baking soda solution.
  3. Put an equal amount of purple liquid into three clean cups.
  4. Add 2 spoons of vinegar to the first cup. Add 2 spoons of plain water to the second. Add 2 spoons of baking soda solution to the third.
  5. Look at the three colours.

What you will see: The vinegar turns the purple liquid pink or red. The water leaves it purple. The baking soda solution turns it blue, or blue green. The cabbage juice is an indicator. Its colour changes with the number of H⁺ ions.

If you cannot try it, this is what happens.
A table with the columns Added and Colour. Vinegar: pink or red. Water: purple. Baking soda solution: blue green.AddedColourvinegarpink or redwaterpurplebaking sodablue green

A wrong idea many people have

The pH scale goes in equal steps, so pH 3 is only a little more acidic than pH 4.

Why it feels right: The numbers 3 and 4 are close together, like 3 cm and 4 cm on a ruler.

The test that breaks it: Take a strong acid, such as hydrochloric acid, at pH 3. Add water until it has 10 times the volume. Its pH rises by 1, to 4, because the H⁺ ions are spread through ten times the space. A weak acid such as vinegar changes less.

What is true: Each step of 1 on the pH scale is a change of 10 times in the H⁺ ions. A solution of pH 3 has 10 times more H⁺ than one of pH 4.

Key words

acid
a substance that makes H⁺ ions in water.
base
a substance that reacts with an acid and cancels it.
alkali
a base that dissolves in water and makes OH⁻ ions.
salt
a compound made when an acid reacts, such as zinc chloride.
pH
a scale that measures the H⁺ ions in a solution.
neutralisation
the reaction of H⁺ and OH⁻ to make water.

Back to your guess

The answer is A: The acid in the vinegar reacts with the baking soda and makes a new gas.

Vinegar is an acid. It reacts with baking soda, sodium hydrogencarbonate, which reacts like a carbonate, and makes a new gas, carbon dioxide. The fizz is that gas leaving the liquid.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Zinc is added to hydrochloric acid and bubbles form. What gas is in the bubbles?

    Tap your answer.

    1. Yes, that is right. An acid with a metal makes a salt and hydrogen. Here zinc chloride and hydrogen gas form.

    2. Not this one. There is no oxygen to release. An acid with a metal makes a salt and hydrogen. Try another.

    3. Not this one. Carbon dioxide comes from a carbonate. Zinc is a metal, so it makes hydrogen. Go to S3.6.7. Try another.

    See the answer

    Hydrogen

    An acid with a metal makes a salt and hydrogen. Here zinc chloride and hydrogen gas form.

    • If you chose B: There is no oxygen to release. An acid with a metal makes a salt and hydrogen.
    • If you chose C: Carbon dioxide comes from a carbonate. Zinc is a metal, so it makes hydrogen. Go to S3.6.7.

  2. Which is the balanced equation for magnesium reacting with hydrochloric acid?

    Tap your answer.

    1. Not this one. The Cl is not equal: 1 on the left and 2 on the right. A number in front of HCl is missing. Try another.

    2. Yes, that is right. MgCl₂ has 2 Cl, so we need 2HCl. Then H is 2 on each side.

    3. Not this one. MgCl is not a formula that works: Mg²⁺ needs two Cl⁻, so the salt is MgCl₂. Go to S4.7.1. Try another.

    See the answer

    Mg + 2HCl → MgCl₂ + H₂

    MgCl₂ has 2 Cl, so we need 2HCl. Then H is 2 on each side.

    • If you chose A: The Cl is not equal: 1 on the left and 2 on the right. A number in front of HCl is missing.
    • If you chose C: MgCl is not a formula that works: Mg²⁺ needs two Cl⁻, so the salt is MgCl₂. Go to S4.7.1.

  3. An acid reacts with a carbonate. What does it make?

    Tap your answer.

    1. Not this one. That is what a metal makes. A carbonate makes carbon dioxide too. Try another.

    2. Not this one. That is what a base makes. A carbonate also gives off carbon dioxide gas, which is the fizz. Try another.

    3. Yes, that is right. The carbonate ion, CO₃²⁻, is changed by the acid into water and carbon dioxide. The rest makes the salt.

    See the answer

    A salt, water and carbon dioxide

    The carbonate ion, CO₃²⁻, is changed by the acid into water and carbon dioxide. The rest makes the salt.

    • If you chose A: That is what a metal makes. A carbonate makes carbon dioxide too.
    • If you chose B: That is what a base makes. A carbonate also gives off carbon dioxide gas, which is the fizz.

  4. How many times more H⁺ ions does a solution of pH 3 have than a solution of pH 5?

    Tap your answer.

    1. Yes, that is right. pH 3 and pH 5 are 2 steps apart. Each step is 10 times, so 10 × 10 = 100.

    2. Not this one. That is the difference between the two pH numbers, 5 − 3. Each step is 10 times, so the answer is bigger. Try another.

    3. Not this one. That would be 3 steps. 3 and 5 are 2 steps apart. Try another.

    See the answer

    100 times

    pH 3 and pH 5 are 2 steps apart. Each step is 10 times, so 10 × 10 = 100.

    • If you chose B: That is the difference between the two pH numbers, 5 − 3. Each step is 10 times, so the answer is bigger.
    • If you chose C: That would be 3 steps. 3 and 5 are 2 steps apart.

  5. A sample is at pH 9 on the scale. What is true of it?

    The pH scale stood upright, from 0 at the top to 14 at the bottom. One mark, labelled sample X, is at pH 9.01234567891011121314pHsample X
    Tap your answer.

    1. Not this one. Acids are below 7. Sample X is above 7, so it has few H⁺ ions. Try another.

    2. Not this one. Only pH 7 is neutral, with as many H⁺ ions as OH⁻ ions. Try another.

    3. Yes, that is right. A pH above 7 is alkaline. Higher pH means fewer H⁺ ions and more OH⁻ ions.

    See the answer

    It is alkaline, with fewer H⁺ ions than pure water.

    A pH above 7 is alkaline. Higher pH means fewer H⁺ ions and more OH⁻ ions.

    • If you chose A: Acids are below 7. Sample X is above 7, so it has few H⁺ ions.
    • If you chose B: Only pH 7 is neutral, with as many H⁺ ions as OH⁻ ions.

  6. What happens when an acid and an alkali neutralise each other?

    Tap your answer.

    1. Not this one. They cancel each other. The H⁺ ions and the OH⁻ ions are used up. Go to S3.6.8. Try another.

    2. Yes, that is right. The equation is H⁺ + OH⁻ → H₂O. The other ions stay in the solution as the salt.

    3. Not this one. Hydrogen comes from a metal and an acid. Acid and alkali make a salt and water. Try another.

    See the answer

    H⁺ and OH⁻ ions join to make water.

    The equation is H⁺ + OH⁻ → H₂O. The other ions stay in the solution as the salt.

    • If you chose A: They cancel each other. The H⁺ ions and the OH⁻ ions are used up. Go to S3.6.8.
    • If you chose C: Hydrogen comes from a metal and an acid. Acid and alkali make a salt and water.

  7. From an earlier chapter

    How many moles of hydrochloric acid, HCl, neutralise 4 g of sodium hydroxide, NaOH? Use NaOH + HCl → NaCl + H₂O. Mr of NaOH is 40.

    Tap your answer.

    1. Not this one. That is 40 ÷ 4, upside down. Moles are mass divided by Mr. Go to S4.7.3. Try another.

    2. Not this one. The 4 is the mass in grams, not moles. Divide by Mr first. Go to S4.7.3. Try another.

    3. Yes, that is right. Moles of NaOH = 4 ÷ 40 = 0.1 mol. The ratio of NaOH to HCl is 1 to 1, so 0.1 mol of HCl is needed.

    See the answer

    0.1 mol

    Moles of NaOH = 4 ÷ 40 = 0.1 mol. The ratio of NaOH to HCl is 1 to 1, so 0.1 mol of HCl is needed.

    • If you chose A: That is 40 ÷ 4, upside down. Moles are mass divided by Mr. Go to S4.7.3.
    • If you chose B: The 4 is the mass in grams, not moles. Divide by Mr first. Go to S4.7.3.

  8. Balance this equation: Mg + H₂SO₄ → MgSO₄ + H₂. What are the smallest whole numbers in front of each formula, in order?

    See the answer

    1, 1, 1 and 1

    Mg is 1 on each side. SO₄ is 1 on each side. H₂ is 2 on each side. No change is needed.

  9. How many times more H⁺ ions does a solution of pH 2 have than a solution of pH 3?

    See the answer

    10 times

    The two are 1 step apart. Each step is 10 times.

Keep it

Copy this into your exercise book.

Acid + metal makes salt and hydrogen. Acid + base makes salt and water. Acid + carbonate makes salt, water and carbon dioxide. Each pH step is ten times the H⁺.

Draw: The pH scale from 0 to 14 with vinegar, water and soap marked, and H⁺ + OH⁻ → H₂O underneath.

S4.7.6 Chapter 6

The reactivity series

Why is gold found shining in the ground, but iron is found as dull red rock?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Some metals react at once with water or air. Others hardly change in a thousand years. The reactivity of a metal is how easily it takes part in reactions. We can find it by watching what a metal does with cold water and with dilute acid.

A table with the columns Metal and In cold water. Potassium: very violent. Sodium: violent. Lithium: fizzes fast. Calcium: fizzes steadily.MetalIn cold waterpotassiumvery violentsodiumviolentlithiumfizzes fastcalciumfizzes steadily
These four metals react with cold water. They make hydrogen and a metal hydroxide.
A table with the columns Metal and In dilute acid. Magnesium: fizzes fast. Zinc: fizzes steadily. Iron: fizzes slowly. Copper: no change.MetalIn dilute acidmagnesiumfizzes fastzincfizzes steadilyironfizzes slowlycopperno change
These metals react little or not at all with cold water. In dilute acid they make a salt and hydrogen. The faster the fizz, the more reactive the metal.

Put the results together and the metals fall into a list. It is called the reactivity series. Carbon and hydrogen are not metals, but they have a place in the list, because they take part in the same reactions.

A column of boxes with an arrow up the side, most reactive at the top and least reactive at the bottom. From the top: potassium (K), sodium (Na), lithium (Li), calcium (Ca), magnesium (Mg), aluminium (Al), carbon (C), zinc (Zn), iron (Fe), hydrogen (H), copper (Cu), gold (Au). Carbon and hydrogen have a dashed border and dots, and a key says they are not a metal.most reactivepotassium (K)sodium (Na)lithium (Li)calcium (Ca)magnesium (Mg)aluminium (Al)carbon (C)zinc (Zn)iron (Fe)hydrogen (H)copper (Cu)gold (Au)least reactivemetalnot a metal
Part of the reactivity series. A metal above hydrogen reacts with dilute acid. A metal below hydrogen does not.

Aluminium seems to break the rule, because it reacts little with water and acid although it is high in the list. It is covered by a thin, tough skin of aluminium oxide, which forms within seconds in air. The skin keeps the acid and water away from the metal below.

The series also tells us about displacement. A more reactive metal pushes a less reactive metal out of its compound. Iron put into copper sulfate solution takes the place of the copper: Fe + CuSO₄ → FeSO₄ + Cu. Copper is left as a solid. Copper put into iron sulfate does nothing, because copper is below iron.

Most metals are found in rocks as compounds, mixed with other minerals. A rock with enough of a metal compound to be worth mining is an ore. Iron ore is mostly iron oxide, Fe₂O₃. To get the metal, we must take the oxygen away.

Taking oxygen away is reduction. Adding oxygen is oxidation. Carbon is more reactive than iron. So carbon can take the oxygen from iron oxide and leave the iron. Metals above carbon, such as aluminium, hold their oxygen too tightly for carbon to take it.

See it three ways

As a picture

A column of boxes with an arrow up the side, labelled most reactive at the top and least reactive at the bottom. From the top: aluminium (Al), carbon (C), zinc (Zn), iron (Fe). Carbon has a dashed border and dots. Carbon and iron have a thick border and hatching. A key says that carbon is not a metal.most reactivealuminium (Al)carbon (C)zinc (Zn)iron (Fe)least reactivemetalnot a metal

In words

Carbon is above iron in the series. So carbon wins the oxygen from iron oxide and the iron is left. Carbon is below aluminium, so it cannot do the same for aluminium oxide.

In symbols

Fe₂O₃ + 3CO → 2Fe + 3CO₂

Iron is made in a blast furnace, a tower about 30 metres tall. Iron ore, coke and limestone go in at the top. Coke is nearly pure carbon. Hot air is blown in near the bottom.

A tall furnace. Iron ore, coke and limestone go in at the top. Waste gases leave at the top. Hot air is blasted in near the bottom. At the bottom there are two layers of liquid: molten slag on top, which has the higher tap, and molten iron below it.iron ore, cokeand limestonewaste gaseshot airmolten ironmolten slag
The blast furnace. The slag floats on the iron, because it is less dense.

Three things happen in the furnace. The coke burns in the hot air and makes heat: C + O₂ → CO₂. Then the carbon dioxide meets more hot coke and makes carbon monoxide: CO₂ + C → 2CO. The carbon monoxide takes the oxygen from the ore: Fe₂O₃ + 3CO → 2Fe + 3CO₂.

Three boxes joined by arrows, from top to bottom. Coke burns: C + O₂ → CO₂. Carbon dioxide meets hot coke: CO₂ + C → 2CO. Carbon monoxide removes oxygen from the ore: Fe₂O₃ + 3CO → 2Fe + 3CO₂.Coke burns: C + O₂ → CO₂Carbon dioxide meets hotcoke: CO₂ + C → 2COCarbon monoxide removesoxygen from the ore: Fe₂O₃ +3CO → 2Fe + 3CO₂
The three reactions. In the last, the iron oxide is reduced and the carbon monoxide is oxidised.

Worked example

Balance the main reaction in the furnace: Fe₂O₃ + CO → Fe + CO₂

  1. Count Fe: 2 on the left. Write 2 in front of Fe.
  2. Fe₂O₃ gives away its oxygen atoms. Each CO takes one and becomes CO₂. Fe₂O₃ has 3 oxygen atoms, so 3 CO are needed.
  3. Write 3 in front of CO and 3 in front of CO₂.
  4. Check: C is 3 and 3. O is 3 + 3 = 6 on the left and 3 × 2 = 6 on the right.

Answer: Fe₂O₃ + 3CO → 2Fe + 3CO₂

Rock has impurities. The main one is sand, which is silicon dioxide. The limestone breaks down in the heat: CaCO₃ → CaO + CO₂. The calcium oxide then joins the sand and makes calcium silicate, called slag. Slag melts and floats on the iron. It is tapped off and used to make roads.

Metals above carbon cannot be extracted this way. They are extracted with electricity. That is the topic of the next chapter.

Try it

Which metal fizzes in vinegar?

You need: two plain iron nails, or a small pad of plain steel wool, a short piece of bare copper wire, if you have one; if not, do the iron cup only, two clear cups, vinegar and a spoon, a hand lens, if you have one.

Be safe: Nails and steel wool can cut skin, so use the spoon for steel wool. Keep vinegar away from your eyes. Taste nothing, and wash your hands afterwards.

  1. Pour vinegar into the cups, about a hand deep.
  2. Put the nails into one cup. If you use steel wool, push it in with the spoon and do not touch it with your fingers.
  3. If you have copper wire, put it into the other cup.
  4. Look closely at both after a few minutes, and again after some hours.

What you will see: Tiny bubbles of hydrogen gather on the iron. The copper wire, if you used it, stays bare. Iron is above hydrogen in the series, so it makes hydrogen with an acid. Copper is below hydrogen, so it does not. The bubbles are small and slow, because vinegar is a weak acid.

If you cannot try it, this is what happens.
A table with the columns Metal and In vinegar. Iron: tiny bubbles. Copper wire: no change.MetalIn vinegarirontiny bubblescopper wireno change

A wrong idea many people have

Aluminium does not seem to react, so it must be low in the reactivity series.

Why it feels right: Aluminium pans and foil last for years and do not rust. A metal that does not change looks unreactive.

The test that breaks it: Aluminium is found in rock only as a compound, never as a metal. It is very hard to extract. A really unreactive metal, such as gold, is found as a pure metal.

What is true: Aluminium is high in the series. A thin tough oxide skin forms at once and protects the metal under it.

Key words

reactivity
how easily a metal takes part in reactions.
displacement
a more reactive metal pushing a less reactive one out of its compound.
ore
a rock with enough of a metal compound to be worth mining.
reduction
the loss of oxygen by a substance.
oxidation
the gain of oxygen by a substance.
blast furnace
a tall furnace that makes iron from iron ore, coke and limestone.
slag
the waste that floats on the molten iron, mostly calcium silicate.

Back to your guess

The answer is C: Gold hardly reacts with anything, but iron reacts with oxygen and is found joined to it.

Gold is very unreactive, so it stays a pure metal. Iron reacts with oxygen, so in the ground it is found as a compound, iron oxide, and has to be extracted.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Which list shows the metals in order of reactivity, with the most reactive first?

    Tap your answer.

    1. Yes, that is right. Sodium reacts with cold water. Magnesium reacts with acid but hardly with cold water. Copper does not react with either.

    2. Not this one. Sodium is more reactive than magnesium. It reacts violently with cold water, and magnesium hardly reacts with cold water. Try another.

    3. Not this one. This is the order of least reactive first. Copper is the least reactive of the three. Try another.

    See the answer

    sodium, magnesium, copper

    Sodium reacts with cold water. Magnesium reacts with acid but hardly with cold water. Copper does not react with either.

    • If you chose B: Sodium is more reactive than magnesium. It reacts violently with cold water, and magnesium hardly reacts with cold water.
    • If you chose C: This is the order of least reactive first. Copper is the least reactive of the three.

  2. Which of these mixtures will react?

    Tap your answer.

    1. Not this one. Copper is below zinc, so it cannot push zinc out of its compound. Try another.

    2. Yes, that is right. Zinc is above copper in the series. It displaces copper: Zn + CuSO₄ → ZnSO₄ + Cu.

    3. Not this one. Copper is much lower than magnesium, so it cannot take its place. Try another.

    See the answer

    zinc in copper sulfate solution

    Zinc is above copper in the series. It displaces copper: Zn + CuSO₄ → ZnSO₄ + Cu.

    • If you chose A: Copper is below zinc, so it cannot push zinc out of its compound.
    • If you chose C: Copper is much lower than magnesium, so it cannot take its place.

  3. Carbon can extract iron from its ore, but not aluminium from its ore. Why?

    Tap your answer.

    1. Yes, that is right. A more reactive element takes oxygen from a less reactive one. Carbon is above iron, so it takes the oxygen from iron oxide. It is below aluminium, so it cannot.

    2. Not this one. Melting is not the reason. Aluminium holds its oxygen too tightly for carbon to take it. Try another.

    3. Not this one. It does: Al₂O₃ has 3 oxygen atoms. Carbon cannot take them because it is below aluminium in the series. Try another.

    See the answer

    Carbon is more reactive than iron but less reactive than aluminium.

    A more reactive element takes oxygen from a less reactive one. Carbon is above iron, so it takes the oxygen from iron oxide. It is below aluminium, so it cannot.

    • If you chose B: Melting is not the reason. Aluminium holds its oxygen too tightly for carbon to take it.
    • If you chose C: It does: Al₂O₃ has 3 oxygen atoms. Carbon cannot take them because it is below aluminium in the series.

  4. In Fe₂O₃ + 3CO → 2Fe + 3CO₂, which substance is reduced?

    Tap your answer.

    1. Not this one. CO gains oxygen and becomes CO₂. Gaining oxygen is oxidation. Try another.

    2. Not this one. CO₂ is a product, the result of the oxidation of CO. It is not the substance that loses oxygen. Try another.

    3. Yes, that is right. Fe₂O₃ loses its oxygen and becomes iron. Losing oxygen is reduction.

    See the answer

    Fe₂O₃

    Fe₂O₃ loses its oxygen and becomes iron. Losing oxygen is reduction.

    • If you chose A: CO gains oxygen and becomes CO₂. Gaining oxygen is oxidation.
    • If you chose B: CO₂ is a product, the result of the oxidation of CO. It is not the substance that loses oxygen.

  5. What does the limestone do in the blast furnace?

    Tap your answer.

    1. Not this one. The carbon comes from the coke. Limestone is a carbonate of calcium. Try another.

    2. Not this one. Coke burns to heat the furnace. Limestone does not burn. Try another.

    3. Yes, that is right. Limestone breaks down to calcium oxide, which joins the sand in the ore and makes slag. The slag floats on the iron and is tapped off.

    See the answer

    It reacts with sand and makes slag.

    Limestone breaks down to calcium oxide, which joins the sand in the ore and makes slag. The slag floats on the iron and is tapped off.

    • If you chose A: The carbon comes from the coke. Limestone is a carbonate of calcium.
    • If you chose B: Coke burns to heat the furnace. Limestone does not burn.

  6. Aluminium is above iron in the series, but aluminium foil does not react with air or water. Why?

    Tap your answer.

    1. Not this one. It is above iron. That is why aluminium is so hard to extract from its ore. Try another.

    2. Yes, that is right. The aluminium reacts with oxygen at once and makes a skin of aluminium oxide. The skin keeps air and water away from the metal below.

    3. Not this one. It reacts with oxygen at once. The oxide skin that forms is the reason it then stops. Try another.

    See the answer

    A thin tough oxide skin covers it and protects it.

    The aluminium reacts with oxygen at once and makes a skin of aluminium oxide. The skin keeps air and water away from the metal below.

    • If you chose A: It is above iron. That is why aluminium is so hard to extract from its ore.
    • If you chose C: It reacts with oxygen at once. The oxide skin that forms is the reason it then stops.

  7. From an earlier chapter

    Zinc reacts with sulfuric acid. What does it make?

    Tap your answer.

    1. Not this one. Water is made from an acid and a base. A metal makes hydrogen. Go to S4.7.5. Try another.

    2. Not this one. The salt of sulfuric acid is a sulfate. An oxide is not made. Go to S4.7.5. Try another.

    3. Yes, that is right. An acid with a metal makes a salt and hydrogen. Sulfuric acid makes a sulfate, so the salt is zinc sulfate.

    See the answer

    Zinc sulfate and hydrogen

    An acid with a metal makes a salt and hydrogen. Sulfuric acid makes a sulfate, so the salt is zinc sulfate.

    • If you chose A: Water is made from an acid and a base. A metal makes hydrogen. Go to S4.7.5.
    • If you chose B: The salt of sulfuric acid is a sulfate. An oxide is not made. Go to S4.7.5.

  8. How many moles of carbon monoxide react with 2 mol of iron oxide? Use Fe₂O₃ + 3CO → 2Fe + 3CO₂.

    See the answer

    6 mol

    The ratio of Fe₂O₃ to CO is 1 to 3. So 2 mol of Fe₂O₃ need 2 × 3 = 6 mol of CO.

  9. Carbon is heated with copper(II) oxide: 2CuO + C → 2Cu + CO₂. What mass of copper forms from 159 g of copper oxide? Use Mr of CuO = 79.5 and Cu = 63.5.

    See the answer

    127 g

    Moles of CuO = 159 ÷ 79.5 = 2 mol. The ratio of CuO to Cu is 1 to 1, so 2 mol of Cu form. Mass = 2 × 63.5 = 127 g.

Keep it

Copy this into your exercise book.

A more reactive metal displaces a less reactive one. Carbon is above iron, so it removes the oxygen from iron oxide: reduction. Aluminium is above carbon.

Draw: The column of metals from potassium to gold with carbon and hydrogen in place, and Fe₂O₃ + 3CO → 2Fe + 3CO₂ underneath.

S4.7.7 Chapter 7

Electrolysis

Carbon cannot take the oxygen from aluminium oxide. So how is aluminium made?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

In the last chapter, carbon took the oxygen from iron oxide. Aluminium is above carbon in the series. Carbon cannot take its oxygen. The way out is a flow of electricity.

Electrolysis is the splitting of a compound by passing an electric current through it. The liquid that is split is the electrolyte. The current enters and leaves it by two electrodes, made of a material that conducts, such as graphite.

An ionic compound must be molten for this. In the solid, the ions are held in fixed places, so no charge can flow. When the compound is melted, the ions can move. Moving ions carry the current.

A model of an ionic solid in one flat layer. Small hatched circles with a plus sign are metal ions and larger white circles with a minus sign are non-metal ions. They alternate in rows and columns. A key says metal ion and non-metal ion.metal ionnon-metal ion
A solid ionic compound. Each ion is held in its place, so the solid does not conduct.

Think of the cell for lead bromide, PbBr₂. It melts at 371 °C. The melted compound has two kinds of ion, Pb²⁺ and Br⁻. Two electrodes dip into it and are joined to a cell, or battery.

One electrode is joined to the negative end of the battery. It is the cathode. The other is joined to the positive end. It is the anode. Opposite charges attract.

See it three ways

As a picture

A crucible of molten lead bromide, with heat arrows and the word heat. Two electrodes dip into it, joined to a cell symbol. The short thick plate (−) of the cell symbol is wired to the left electrode, labelled cathode (−). The long thin plate (+) of the cell symbol is wired to the right electrode, labelled anode (+). Pb²⁺ ions, hatched, move to the cathode and Br⁻ ions, plain, move to the anode. Lead forms at the cathode and bromine forms at the anode. A key names both ions.−+molten leadbromidePb²⁺Br⁻cathode (−)leadanode (+)bromineheat

In words

The positive Pb²⁺ ions go to the negative cathode. There each gains two electrons and becomes a lead atom. The negative Br⁻ ions go to the positive anode. There each loses an electron, and pairs of bromine atoms join to make Br₂. Each disc in the picture shows the sign of the charge, and the key gives the size.

In symbols

PbBr₂ → Pb + Br₂

So the rule is short. Positive ions go to the cathode. A metal forms there. Negative ions go to the anode. A non-metal forms there. The charges of the ions tell you which way each one moves.

A table with the columns Compound, Cathode and Anode. PbBr₂: Pb at the cathode, Br₂ at the anode. NaCl: Na and Cl₂. ZnCl₂: Zn and Cl₂. Al₂O₃: Al and O₂. MgO: Mg and O₂.CompoundCathodeAnodePbBr₂PbBr₂NaClNaCl₂ZnCl₂ZnCl₂Al₂O₃AlO₂MgOMgO₂
Products of electrolysis of five molten compounds. Br₂, Cl₂ and O₂ are bromine, chlorine and oxygen gas, made of two-atom molecules.
Five discs in a row. Two hatched discs are Al³⁺. Three plain discs are O²⁻. Under them the sum reads +3 +3 −2 −2 −2 = 0, and under the sum is the formula Al₂O₃.Al³⁺Al³⁺O²⁻O²⁻O²⁻+3 +3 −2 −2 −2 = 0Al₂O₃
Aluminium oxide has 2 Al³⁺ ions for each 3 O²⁻ ions.

Aluminium is the most common metal in the Earth's crust, but it is always combined. The ore is bauxite. It is purified to make aluminium oxide, Al₂O₃. Aluminium oxide melts above 2 000 °C, which is too hot to be practical.

The trick is to dissolve the oxide in molten cryolite, another aluminium compound. The oxide dissolves in the molten cryolite, so the mixture is liquid at about 950 °C. It is still very hot, but far lower. Cryolite does not split.

A crucible of molten aluminium oxide, with heat arrows and the word heat. Two electrodes dip into it, joined to a cell symbol. The short thick plate (−) of the cell symbol is wired to the left electrode, labelled cathode (−). The long thin plate (+) of the cell symbol is wired to the right electrode, labelled anode (+). Al³⁺ ions, hatched, move to the cathode and O²⁻ ions, plain, move to the anode. Aluminium forms at the cathode and oxygen forms at the anode. A key names both ions.−+moltenaluminiumoxideAl³⁺O²⁻cathode (−)aluminiumanode (+)oxygenheat
The same idea for aluminium. Two Al³⁺ ions to three O²⁻ ions balance the charges. In a real cell the oxide is dissolved in molten cryolite. Each disc shows the sign of the charge; the key gives the size.

At the cathode, Al³⁺ ions gain electrons and make molten aluminium, which sinks to the bottom and is tapped off. At the anode, O²⁻ ions lose electrons and make oxygen gas. The anodes are made of carbon. The hot oxygen burns the carbon and makes carbon dioxide, so the anodes wear away and must be replaced.

Worked example

Balance the equation for the electrolysis of aluminium oxide: Al₂O₃ → Al + O₂

  1. Count the atoms. Left: Al 2, O 3. Right: Al 1, O 2.
  2. O is 3 on the left and 2 on the right. The smallest number that both go into is 6. Write 2 in front of Al₂O₃ and 3 in front of O₂.
  3. Now Al is 2 × 2 = 4 on the left. Write 4 in front of Al.
  4. Check: Al is 4 and 4. O is 6 and 6. The equation is balanced.

Answer: 2Al₂O₃ → 4Al + 3O₂

Worked example

What mass of aluminium is made from 204 g of aluminium oxide? Use 2Al₂O₃ → 4Al + 3O₂.

  1. Mr of Al₂O₃ = 2 × 27 + 3 × 16 = 102.
  2. Moles of Al₂O₃ = 204 ÷ 102 = 2 mol.
  3. The ratio of Al₂O₃ to Al is 2 to 4, which is 1 to 2. So 2 mol of Al₂O₃ make 4 mol of Al.
  4. Mass of Al = 4 × 27 = 108 g.

Answer: 108 g

Four boxes joined by arrows, from top to bottom. Bauxite is purified to aluminium oxide. The oxide is dissolved in molten cryolite at about 950 °C. A current splits it: aluminium at the cathode and oxygen at the anode. The aluminium is tapped off and the carbon anodes are replaced.Bauxite is purified toaluminium oxideThe oxide is dissolved inmolten cryolite at about 950°CA current splits it:aluminium at the cathode andoxygen at the anodeThe aluminium is tapped offand the carbon anodes arereplaced
Making aluminium. The step with the current needs a great deal of electricity. A smelter is built where there is plenty of electricity, often from water power. Recycled aluminium needs far less energy.

Try it

Move the ions on paper

You need: a sheet of paper and a pencil, three small torn pieces of paper.

Be safe: Use only paper and a pencil. Do not try any of this with real electricity or real salts.

  1. Draw a box in the middle of the sheet. Write a minus sign on the left side for the cathode. Write a plus sign on the right side for the anode.
  2. Write Pb²⁺ on one torn piece and Br⁻ on the other two. Lay them in a row in the box. In the solid they cannot move.
  3. Now melt the compound. Slide the pieces about freely.
  4. Send the Pb²⁺ piece to the minus side. Send both Br⁻ pieces to the plus side.
  5. At the minus side, write "lead" on the back of the Pb²⁺ piece. At the plus side, join the two Br⁻ pieces and write "bromine, Br₂".

What you will see: The ions of opposite charge go to opposite sides. One Pb²⁺ is paired with two Br⁻, because +2 and −1 −1 add to zero. The metal forms at the negative side and the non-metal at the positive side.

If you cannot try it, this is what happens.
Three discs in a row. A hatched disc is Pb²⁺. Two plain discs are Br⁻. Under them the sum reads +2 −1 −1 = 0, and under the sum is the formula PbBr₂.Pb²⁺Br⁻Br⁻+2 −1 −1 = 0PbBr₂

A wrong idea many people have

In electrolysis the current in the liquid is a flow of electrons.

Why it feels right: In a copper wire the current is a flow of electrons, so it seems the same in a liquid.

The test that breaks it: Look at the cell. Ions move through the liquid, and lead and bromine are made where they arrive. Free electrons would not make new substances.

What is true: Electrons flow in the wires. In the liquid, the ions carry the charge. Electrons are gained and lost only at the electrodes.

Key words

electrolysis
splitting a compound by passing an electric current through it.
electrolyte
the molten or dissolved compound that is split.
electrodes
the two conductors that carry the current into and out of the liquid.
cathode
the negative electrode, where positive ions go.
anode
the positive electrode, where negative ions go.
cryolite
a molten compound that aluminium oxide dissolves in, so it is liquid at a lower temperature.

Back to your guess

The answer is B: Electricity splits aluminium oxide into aluminium and oxygen.

Aluminium is above carbon in the reactivity series, so carbon cannot remove its oxygen at any temperature we use. A current of electricity does it instead. That is electrolysis.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Molten lead bromide is electrolysed. At which electrode does the lead form?

    Tap your answer.

    1. Not this one. Pb²⁺ is positive, so it is attracted to the negative electrode. The positive electrode attracts the Br⁻ ions. Try another.

    2. Yes, that is right. Pb²⁺ ions are positive and go to the negative electrode, the cathode. There they gain electrons and become lead.

    3. Not this one. Each kind of ion goes to one electrode only. Lead forms at one and bromine at the other. Try another.

    See the answer

    The cathode, the negative electrode

    Pb²⁺ ions are positive and go to the negative electrode, the cathode. There they gain electrons and become lead.

    • If you chose A: Pb²⁺ is positive, so it is attracted to the negative electrode. The positive electrode attracts the Br⁻ ions.
    • If you chose C: Each kind of ion goes to one electrode only. Lead forms at one and bromine at the other.

  2. Why does solid lead bromide not conduct electricity, but molten lead bromide does?

    Tap your answer.

    1. Not this one. The solid is made of ions. They are fixed in a lattice and cannot move. Go to S4.6.6. Try another.

    2. Not this one. It is ions that move in the liquid, not electrons. The heat only frees the ions from the lattice. Try another.

    3. Yes, that is right. A current needs charged particles that can move. The ions are fixed in the solid and free in the liquid.

    See the answer

    The ions are free to move when it is molten.

    A current needs charged particles that can move. The ions are fixed in the solid and free in the liquid.

    • If you chose A: The solid is made of ions. They are fixed in a lattice and cannot move. Go to S4.6.6.
    • If you chose B: It is ions that move in the liquid, not electrons. The heat only frees the ions from the lattice.

  3. Molten zinc chloride, ZnCl₂, is electrolysed. What forms at each electrode?

    Tap your answer.

    1. Yes, that is right. Zn²⁺ goes to the cathode and becomes zinc. Cl⁻ goes to the anode and becomes chlorine, Cl₂.

    2. Not this one. Zn²⁺ is positive and goes to the negative cathode. Cl⁻ is negative and goes to the positive anode. Try another.

    3. Not this one. Ions of opposite charge go to opposite electrodes. Chlorine forms at the anode. Try another.

    See the answer

    Zinc at the cathode and chlorine at the anode

    Zn²⁺ goes to the cathode and becomes zinc. Cl⁻ goes to the anode and becomes chlorine, Cl₂.

    • If you chose B: Zn²⁺ is positive and goes to the negative cathode. Cl⁻ is negative and goes to the positive anode.
    • If you chose C: Ions of opposite charge go to opposite electrodes. Chlorine forms at the anode.

  4. Why is aluminium made by electrolysis and not by heating its oxide with carbon?

    Tap your answer.

    1. Not this one. Heat is not the problem. Carbon is below aluminium in the series, so in a furnace it cannot take the oxygen. Go to S4.7.6. Try another.

    2. Yes, that is right. A less reactive element cannot take oxygen from a more reactive one. Carbon is below aluminium in the series, so electricity is used instead.

    3. Not this one. It is not about hardness. Carbon cannot take oxygen from aluminium oxide in a furnace. Go to S4.7.6. Try another.

    See the answer

    Carbon is less reactive than aluminium, so it cannot take the oxygen.

    A less reactive element cannot take oxygen from a more reactive one. Carbon is below aluminium in the series, so electricity is used instead.

    • If you chose A: Heat is not the problem. Carbon is below aluminium in the series, so in a furnace it cannot take the oxygen. Go to S4.7.6.
    • If you chose C: It is not about hardness. Carbon cannot take oxygen from aluminium oxide in a furnace. Go to S4.7.6.

  5. What is the job of cryolite in the aluminium cell?

    Tap your answer.

    1. Not this one. Cryolite does not react. The current splits the oxide. Try another.

    2. Not this one. The aluminium comes from aluminium oxide. Cryolite only dissolves it. Try another.

    3. Yes, that is right. Aluminium oxide melts above 2 000 °C. Dissolved in molten cryolite, it can be electrolysed at about 950 °C, which saves energy.

    See the answer

    It dissolves the aluminium oxide, so it is liquid at a much lower temperature.

    Aluminium oxide melts above 2 000 °C. Dissolved in molten cryolite, it can be electrolysed at about 950 °C, which saves energy.

    • If you chose A: Cryolite does not react. The current splits the oxide.
    • If you chose B: The aluminium comes from aluminium oxide. Cryolite only dissolves it.

  6. Why must the carbon anodes in the aluminium cell be replaced from time to time?

    Tap your answer.

    1. Yes, that is right. O²⁻ ions become oxygen at the anode. Oxygen and hot carbon make carbon dioxide, so the carbon is used up.

    2. Not this one. The aluminium forms at the cathode. The anodes are where the oxygen is made. Try another.

    3. Not this one. A current does not wear a conductor away like that. The carbon burns in the hot oxygen. Try another.

    See the answer

    The hot oxygen made at the anode burns the carbon away.

    O²⁻ ions become oxygen at the anode. Oxygen and hot carbon make carbon dioxide, so the carbon is used up.

    • If you chose B: The aluminium forms at the cathode. The anodes are where the oxygen is made.
    • If you chose C: A current does not wear a conductor away like that. The carbon burns in the hot oxygen.

  7. From an earlier chapter

    Which of these metals can be made by heating its oxide with carbon?

    Tap your answer.

    1. Not this one. Aluminium is above carbon in the series. Carbon cannot take its oxygen. Go to S4.7.6. Try another.

    2. Not this one. Sodium is far above carbon in the series, so it is also made by electrolysis. Go to S4.7.6. Try another.

    3. Yes, that is right. Iron is below carbon in the series, so carbon removes the oxygen from iron oxide in the blast furnace.

    See the answer

    Iron

    Iron is below carbon in the series, so carbon removes the oxygen from iron oxide in the blast furnace.

    • If you chose A: Aluminium is above carbon in the series. Carbon cannot take its oxygen. Go to S4.7.6.
    • If you chose B: Sodium is far above carbon in the series, so it is also made by electrolysis. Go to S4.7.6.

  8. What mass of aluminium is made from 102 g of aluminium oxide? Use 2Al₂O₃ → 4Al + 3O₂. Mr of Al₂O₃ is 102 and the relative atomic mass of Al is 27.

    See the answer

    54 g

    102 ÷ 102 = 1 mol of Al₂O₃. The ratio of Al₂O₃ to Al is 1 to 2, so 2 mol of Al form. Mass = 2 × 27 = 54 g.

  9. Molten lead bromide has Pb²⁺ ions and Br⁻ ions. How many Br⁻ ions are there for each Pb²⁺ ion?

    See the answer

    2 bromide ions

    The charges must add to zero. Pb²⁺ is +2 and each Br⁻ is −1, so 2 ÷ 1 = 2 bromide ions.

Keep it

Copy this into your exercise book.

A molten ionic compound conducts because its ions move. Positive ions go to the cathode and make a metal. Negative ions go to the anode. Aluminium needs electrolysis.

Draw: A cell with a cathode and anode, Pb²⁺ moving to the cathode and Br⁻ to the anode, and PbBr₂ → Pb + Br₂.

S4.7.8 Chapter 8

Energy changes and rates

Why does a fire warm a room, but baking soda in vinegar makes the cup feel cold?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Every reaction moves energy. To react, bonds between the atoms of the reactants must break, and that takes energy in. Then new bonds form in the products, and that gives energy out.

If more energy is given out than was taken in, the reaction is exothermic. The extra goes to the surroundings, which get warmer. Burning, neutralisation and respiration in our cells are exothermic. Some hand warmers use iron rusting fast.

If more energy is taken in than is given out, the reaction is endothermic. The energy comes from the surroundings, which get cooler. Thermal decomposition and photosynthesis are endothermic. So is baking soda with vinegar, which is why the cup feels colder.

An energy profile of an exothermic reaction. A line labelled energy goes up the side and a line labelled progress of reaction goes along the bottom. The reactants are a flat line high on the left. A hump rises and falls to the products, a flat line lower on the right. An arrow up to the hump is labelled activation energy. An arrow down between the two levels is labelled energy given out, and under the products is ΔH negative.energyactivation energyenergygiven outΔH negativereactantsproductsprogress of reaction
An exothermic reaction. The products are lower in energy than the reactants. The difference is given out.
An energy profile of an endothermic reaction. A line labelled energy goes up the side and a line labelled progress of reaction goes along the bottom. The reactants are a flat line low on the left. A hump rises and falls to the products, a flat line higher on the right. An arrow up to the hump is labelled activation energy. An arrow up between the two levels is labelled energy taken in, and over the products is ΔH positive.energyactivation energyenergytaken inΔH positivereactantsproductsprogress of reaction
An endothermic reaction. The products are higher in energy than the reactants. The difference is taken in.

Both graphs have a hump. Particles must have a minimum energy to react. This is the activation energy. It is the height from the reactants to the top of the hump.

See it three ways

As a picture

An energy profile with an axis labelled energy (kJ) and a line along the bottom labelled progress of reaction. The reactants are at 350, the products at 150 and the top of the hump at 450. An arrow up to the hump is labelled activation energy. An arrow between the levels is labelled energy given out and the change is ΔH = −200 kJ.0100200300400500600energy (kJ)activation energyenergygiven outΔH = −200 kJreactantsproductsprogress of reaction

In words

The reactants are at 350 kJ and the products at 150 kJ, so 200 kJ is given out. The energy change is written ΔH. It is negative when energy is given out.

In symbols

ΔH = 150 − 350 = −200 kJ, so 200 kJ is given out.

Now think about speed. The rate of reaction is how fast reactants are used up or products are made. We can measure it by collecting a gas and timing it.

A conical flask with a delivery tube to a gas syringe. The plunger has been pushed out by the gas collected. The parts are labelled conical flask, delivery tube and gas syringe.020406080100cm³conical flaskdelivery tubegas syringe
Collecting a gas in a gas syringe. Read the volume every 10 seconds.

Worked example

A reaction makes 24 cm³ of gas in 8 seconds. What is the mean rate of reaction?

  1. mean rate = amount of product ÷ time taken.
  2. mean rate = 24 ÷ 8 = 3 cm³/s.

Answer: 3 cm³/s

A graph of gas collected against time. The bottom is labelled time (s) and runs from 0 to 60. The side is labelled gas (cm³) and runs from 0 to 70. The line rises steeply at first, then more gently, and is flat from 50 seconds at 65 cm³.0102030405060010203040506070time (s)gas (cm³)
The line is steepest at the start, so the reaction is fastest then. It flattens when a reactant is used up.

Worked example

Use the graph. What is the mean rate of reaction between 10 s and 30 s?

  1. At 10 s the graph reads 30 cm³. At 30 s it reads 58 cm³.
  2. Gas made = 58 − 30 = 28 cm³.
  3. Time taken = 30 − 10 = 20 s.
  4. mean rate = 28 ÷ 20 = 1.4 cm³/s.

Answer: 1.4 cm³/s

Reactions happen when particles collide with enough energy. A faster reaction has more successful collisions each second. Three things raise the number.

Temperature: warmer particles move faster. They collide more often, and more of the collisions have enough energy. The reaction goes faster. Concentration: more particles in the same volume collide more often. Surface area: a finer solid exposes more of its particles to the other reactant.

Draw it first

Three ways to make more collisions

  1. A box of particles drawn three times in the same place. Step 1: few particles moving slowly, shown with short trails. Step 2: three times as many particles, still slow. Step 3: the same number of particles moving fast, shown with long trails.

    1 A few particles of two kinds, open circles and dark dots, move slowly in the box. Short trails show slow movement. They collide rarely.

  2. A box of particles drawn three times in the same place. Step 1: few particles moving slowly, shown with short trails. Step 2: three times as many particles, still slow. Step 3: the same number of particles moving fast, shown with long trails.

    2 Put in three times as many particles in the same volume. This is a higher concentration, and there are more collisions.

  3. A box of particles drawn three times in the same place. Step 1: few particles moving slowly, shown with short trails. Step 2: three times as many particles, still slow. Step 3: the same number of particles moving fast, shown with long trails.

    3 Keep them, and make them move faster. This is a higher temperature. A longer trail means a faster particle. There are even more collisions.

A cube drawn whole and labelled side 2 cm, 1 cube and surface area 24 cm². Beside it the same cube cut into small cubes, labelled side 1 cm, 8 pieces and total surface area 48 cm².side 2 cm1 cubesurface area24 cm²side 1 cm8 piecestotal surfacearea 48 cm²
Cutting a cube into 8 pieces doubles the surface area. A reaction can happen only at a surface.

Worked example

A cube has sides of 2 cm. It is cut into 8 small cubes. What is the total surface area of the 8 small cubes?

  1. The whole cube has 6 faces of 2 × 2 = 4 cm². Its surface area is 6 × 4 = 24 cm².
  2. Each small cube has a side of 1 cm. One face is 1 cm², so one small cube has 6 cm².
  3. There are 8 small cubes. Their total surface area is 8 × 6 = 48 cm².
  4. The area is twice as big, 48 cm² instead of 24 cm².

Answer: 48 cm²

A catalyst speeds up a reaction and is not used up. It gives the particles an easier path, so more collisions are successful. The enzymes in your body are catalysts.

Try it

Warm and cold vinegar

You need: two cups, two bowls, vinegar and baking soda, cold tap water, and tap water that is warm but not hot, a spoon, and a clock or watch with a seconds hand.

Be safe: Use only tap water, never hot water from a kettle. Keep your face and eyes away from the cups, and taste nothing.

  1. Put the same amount of vinegar in each cup, about a finger deep.
  2. Stand one cup in a bowl of cold tap water, and the other in a bowl of warm tap water. Wait 5 minutes.
  3. Add one level spoon of baking soda to each cup at the same moment. Do not stir.
  4. Time how long each cup takes to stop fizzing.

What you will see: The warm cup usually fizzes faster and stops sooner. The same amount of gas is made in both, but the warmer particles collide harder and more often. You may also feel that the cups get cooler, because the reaction is endothermic.

If you cannot try it, this is what happens.
A table with the columns Vinegar and Fizzing stops. Cold: later. Warm: sooner.VinegarFizzing stopscoldlaterwarmsooner

Try it

A whole piece and a powder

You need: two pieces of eggshell of the same size, or chalk that fizzes in vinegar, vinegar and two cups, paper and a spoon.

Be safe: Crush the eggshell or chalk on paper and do not breathe the dust. Keep your face and eyes away from the cups, and taste nothing.

  1. Put a whole piece of eggshell, or chalk, into the first cup. Pour in vinegar.
  2. Wrap the second piece in paper. Press it with the back of the spoon until it is a powder. Tip the powder into the second cup and pour in the same amount of vinegar.
  3. Watch both cups for a minute. Look at the bubbles.

What you will see: The powder makes bubbles much faster than the whole piece. Eggshell, and some chalk, is calcium carbonate. Vinegar is an acid, so they make carbon dioxide. Some chalk is calcium sulfate and does not fizz: use eggshell then. The powder has far more surface in contact with the acid, so there are more collisions.

If you cannot try it, this is what happens.
A table with the columns Solid and Bubbles. Whole piece: slowly. Powder: quickly.SolidBubbleswhole pieceslowlypowderquickly

A wrong idea many people have

In an exothermic reaction energy is made, and in an endothermic reaction energy is destroyed.

Why it feels right: A fire seems to make heat from nothing, and a cold cup seems to lose it.

The test that breaks it: Think of a hand warmer. It gets warm, and when it is finished it cannot warm you again. The energy came from the store in the chemicals, and moved to your hand.

What is true: Energy is never made or destroyed. A reaction moves it between the chemicals and the surroundings.

Key words

exothermic
a reaction that gives out energy and warms its surroundings.
endothermic
a reaction that takes in energy and cools its surroundings.
activation energy
the least energy that particles need to react.
rate of reaction
how fast reactants are used up or products are made.
collide
to hit one another.
catalyst
a substance that speeds up a reaction and is not used up.

Back to your guess

The answer is A: Some reactions give energy to their surroundings, and some take it in from them.

A reaction that gives out energy warms its surroundings. A reaction that takes energy in cools them. Energy is moved, never made or destroyed.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Which of these reactions is endothermic?

    Tap your answer.

    1. Not this one. Burning gives out energy as heat and light. It is exothermic. Try another.

    2. Not this one. Neutralisation warms the mixture. It is exothermic. Go to S3.6.8. Try another.

    3. Yes, that is right. The reaction takes in energy from its surroundings, so the cup gets colder. A reaction that takes energy in is endothermic.

    See the answer

    Baking soda and vinegar making the cup feel cold

    The reaction takes in energy from its surroundings, so the cup gets colder. A reaction that takes energy in is endothermic.

    • If you chose A: Burning gives out energy as heat and light. It is exothermic.
    • If you chose B: Neutralisation warms the mixture. It is exothermic. Go to S3.6.8.

  2. The profile shows a reaction. How much energy does the reaction give out?

    An energy profile with an axis labelled energy (kJ) and a line along the bottom labelled progress of reaction. The reactants are at 350, the products at 150 and the top of the hump at 450. An arrow up to the hump is labelled activation energy. An arrow between the levels is labelled energy given out, and under the products is ΔH negative.0100200300400500600energy (kJ)activation energyenergygiven outΔH negativereactantsproductsprogress of reaction
    Tap your answer.

    1. Yes, that is right. The reactants are at 350 kJ and the products at 150 kJ. 350 − 150 = 200 kJ is given out.

    2. Not this one. That is the top of the hump. The energy given out is the difference between reactants and products. Try another.

    3. Not this one. That is the activation energy, the height from the reactants to the top of the hump. The energy given out is between the two levels. Try another.

    See the answer

    200 kJ

    The reactants are at 350 kJ and the products at 150 kJ. 350 − 150 = 200 kJ is given out.

    • If you chose B: That is the top of the hump. The energy given out is the difference between reactants and products.
    • If you chose C: That is the activation energy, the height from the reactants to the top of the hump. The energy given out is between the two levels.

  3. Why does a reaction go faster when the temperature is raised?

    Tap your answer.

    1. Not this one. The particles stay the same size. Heat makes them move faster. Go to S3.5.4. Try another.

    2. Yes, that is right. Faster particles collide more often, and more of the collisions have at least the activation energy. So more collisions are successful.

    3. Not this one. Some reactions do, but a cold reaction goes faster when it is warmed from outside, and that is because of the particles. Try another.

    See the answer

    The particles move faster, so they collide more often and with more energy.

    Faster particles collide more often, and more of the collisions have at least the activation energy. So more collisions are successful.

    • If you chose A: The particles stay the same size. Heat makes them move faster. Go to S3.5.4.
    • If you chose C: Some reactions do, but a cold reaction goes faster when it is warmed from outside, and that is because of the particles.

  4. Powdered eggshell reacts faster with vinegar than a whole piece of eggshell of the same mass. Why?

    Tap your answer.

    1. Not this one. The same mass has the same number of atoms. The difference is how much surface the acid can reach. Try another.

    2. Not this one. Both start at the same temperature. The difference is surface area. Try another.

    3. Yes, that is right. Acid particles can hit only the surface of the eggshell. Powder has a much larger surface area than a whole piece, so there are more collisions each second.

    See the answer

    More of the eggshell is exposed to the acid, so there are more collisions.

    Acid particles can hit only the surface of the eggshell. Powder has a much larger surface area than a whole piece, so there are more collisions each second.

    • If you chose A: The same mass has the same number of atoms. The difference is how much surface the acid can reach.
    • If you chose B: Both start at the same temperature. The difference is surface area.

  5. Vinegar is mixed with an equal amount of water, and then poured onto eggshell. What happens to the rate of the reaction?

    Tap your answer.

    1. Not this one. There is more liquid, but the acid particles are spread through it. Fewer of them hit the chalk each second. Try another.

    2. Yes, that is right. The concentration of the acid is halved, so acid particles meet the eggshell less often. Fewer collisions mean a slower rate.

    3. Not this one. The amount of acid is the same, but the volume doubled. The concentration halved, so there are fewer collisions. Try another.

    See the answer

    It is slower, because there are fewer acid particles in the same volume.

    The concentration of the acid is halved, so acid particles meet the eggshell less often. Fewer collisions mean a slower rate.

    • If you chose A: There is more liquid, but the acid particles are spread through it. Fewer of them hit the chalk each second.
    • If you chose C: The amount of acid is the same, but the volume doubled. The concentration halved, so there are fewer collisions.

  6. The graph shows gas collected from a reaction. At what time did the reaction stop?

    A graph of gas collected against time. The bottom is labelled time (s) and runs from 0 to 60. The side is labelled gas (cm³) and runs from 0 to 70. The line rises steeply at first, then more gently, and then goes flat.0102030405060010203040506070time (s)gas (cm³)
    Tap your answer.

    1. Yes, that is right. The line stops rising at 50 s, and stays at 65 cm³. No more gas is made, so the reaction has stopped.

    2. Not this one. At 10 s the line is steepest, so the reaction is fastest, not finished. Try another.

    3. Not this one. The graph ends at 60 s, but the line has been flat since 50 s. No more gas was made after 50 s. Try another.

    See the answer

    50 s

    The line stops rising at 50 s, and stays at 65 cm³. No more gas is made, so the reaction has stopped.

    • If you chose B: At 10 s the line is steepest, so the reaction is fastest, not finished.
    • If you chose C: The graph ends at 60 s, but the line has been flat since 50 s. No more gas was made after 50 s.

  7. What does a catalyst do?

    Tap your answer.

    1. Yes, that is right. A catalyst gives the particles an easier path, so more collisions are successful. It is not changed, so a little can be used over and over.

    2. Not this one. A catalyst changes the speed, not the amount of product that can be made. Try another.

    3. Not this one. A catalyst is not used up. It is there at the end, just as it was at the start. Try another.

    See the answer

    It speeds up a reaction, and is not used up.

    A catalyst gives the particles an easier path, so more collisions are successful. It is not changed, so a little can be used over and over.

    • If you chose B: A catalyst changes the speed, not the amount of product that can be made.
    • If you chose C: A catalyst is not used up. It is there at the end, just as it was at the start.

  8. From an earlier chapter

    A reaction should make 50 g of product, but it makes 45 g. What is the percentage yield?

    Tap your answer.

    1. Not this one. That divides the theoretical yield by the actual yield. The actual yield goes on top. Go to S4.7.4. Try another.

    2. Yes, that is right. percentage yield = actual ÷ theoretical × 100 = 45 ÷ 50 × 100 = 90%.

    3. Not this one. That is the percentage lost, 5 ÷ 50. The yield is the percentage that was collected. Go to S4.7.4. Try another.

    See the answer

    90%

    percentage yield = actual ÷ theoretical × 100 = 45 ÷ 50 × 100 = 90%.

    • If you chose A: That divides the theoretical yield by the actual yield. The actual yield goes on top. Go to S4.7.4.
    • If you chose C: That is the percentage lost, 5 ÷ 50. The yield is the percentage that was collected. Go to S4.7.4.

  9. A reaction makes 30 cm³ of gas in 6 seconds. What is the mean rate of reaction in cm³/s?

    See the answer

    5 cm³/s

    mean rate = amount of product ÷ time = 30 ÷ 6 = 5 cm³/s.

  10. A cube with sides of 4 cm is cut into 8 equal small cubes. What is the total surface area of the small cubes, in cm²?

    See the answer

    192 cm²

    Each small cube has a side of 2 cm, so one face is 4 cm². One cube has 6 × 4 = 24 cm², and 8 cubes have 8 × 24 = 192 cm².

Keep it

Copy this into your exercise book.

Exothermic gives out energy and warms. Endothermic takes in energy and cools. Higher temperature, higher concentration and more surface area give more collisions, so a faster rate.

Draw: Two energy profiles, one for an exothermic and one for an endothermic reaction, with the energy change marked.

Key words, A to Z

Every key word in this book, what it means, and the chapter that teaches it.

acid
a substance that makes H⁺ ions in water. S4.7.5
activation energy
the least energy that particles need to react. S4.7.8
actual yield
the mass of product really collected. S4.7.4
alkali
a base that dissolves in water and makes OH⁻ ions. S4.7.5
anode
the positive electrode, where negative ions go. S4.7.7
balanced
having the same atoms of every element on both sides of the equation. S4.7.2
base
a substance that reacts with an acid and cancels it. S4.7.5
blast furnace
a tall furnace that makes iron from iron ore, coke and limestone. S4.7.6
catalyst
a substance that speeds up a reaction and is not used up. S4.7.8
cathode
the negative electrode, where positive ions go. S4.7.7
coefficient
the number in front of a formula that says how many of it. S4.7.2
collide
to hit one another. S4.7.8
concentration
the moles of solute in 1 dm³ of solution. S4.7.3
conserved
kept the same in a reaction, as the total mass is. S4.7.2
cryolite
a molten compound that aluminium oxide dissolves in, so it is liquid at a lower temperature. S4.7.7
displacement
a more reactive metal pushing a less reactive one out of its compound. S4.7.6
electrodes
the two conductors that carry the current into and out of the liquid. S4.7.7
electrolysis
splitting a compound by passing an electric current through it. S4.7.7
electrolyte
the molten or dissolved compound that is split. S4.7.7
endothermic
a reaction that takes in energy and cools its surroundings. S4.7.8
exothermic
a reaction that gives out energy and warms its surroundings. S4.7.8
formula
symbols and small numbers that show what a substance is made of. S4.7.1
ion
an atom, or a group of atoms, with an electric charge. S4.7.1
mole
an amount of substance: 6.02 × 10²³ particles. S4.7.3
neutralisation
the reaction of H⁺ and OH⁻ to make water. S4.7.5
ore
a rock with enough of a metal compound to be worth mining. S4.7.6
oxidation
the gain of oxygen by a substance. S4.7.6
percentage yield
the actual yield divided by the theoretical yield, times 100. S4.7.4
pH
a scale that measures the H⁺ ions in a solution. S4.7.5
polyatomic ion
a group of atoms that carries one charge together, such as OH⁻. S4.7.1
products
the substances that are made, written on the right of the arrow. S4.7.2
rate of reaction
how fast reactants are used up or products are made. S4.7.8
reactants
the substances that react, written on the left of the arrow. S4.7.2
reactivity
how easily a metal takes part in reactions. S4.7.6
reduction
the loss of oxygen by a substance. S4.7.6
relative atomic mass
the mass of an atom compared with one twelfth of a carbon 12 atom. S4.7.3
relative formula mass
Mr, the sum of the relative atomic masses in a formula. S4.7.3
salt
a compound made when an acid reacts, such as zinc chloride. S4.7.5
slag
the waste that floats on the molten iron, mostly calcium silicate. S4.7.6
state symbol
a letter in brackets after a formula: (s), (l), (g) or (aq). S4.7.2
theoretical yield
the mass of product a perfect reaction would make. S4.7.4