Chapter 2 of 8

All 8 chapters
  1. 1Chemical formulae, readunderstood
  2. 2Balancing equations, readunderstood
  3. 3The mole, readunderstood
  4. 4Reacting masses and yield, readunderstood
  5. 5Acids, bases and salts, readunderstood
  6. 6The reactivity series, readunderstood
  7. 7Electrolysis, readunderstood
  8. 8Energy changes and rates, readunderstood

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

  • Balance symbol equations and add state symbols
  • Explain why mass is conserved in a reaction

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.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (907 KB). It opens on any phone.