Balancing Chemical Equations – Chemical Reactions (Senior 1 Chemistry) | Ganzaa

Chemical Reactions

Lessons

Senior 1 · Chemistry

Chemical Reactions

5 lessons

Lesson 4 of 5

Balancing Chemical Equations

25 min

Where did the oxygen atom go?

Hydrogen burns in oxygen to give water, and nothing else. Hydrogen fuel-cell buses use this reaction to run on hydrogen, with only water coming out of the exhaust. In Lesson 3 you wrote its skeleton equation:

$\mathrm{H_2(g) + O_2(g) \rightarrow H_2O(l)} \qquad \text{(skeleton)}$

There are two oxygen atoms on the left and only one on the right. Taken at face value, one oxygen atom has vanished, which the law of conservation of mass says cannot happen. The formulae are correct, so we must change the number of molecules of each substance until every atom is accounted for. This is called balancing the equation.

Definition

Balanced equation: a chemical equation with the same number of atoms of each element on both sides. Example: $\mathrm{2H_2(g) + O_2(g) \rightarrow 2H_2O(l)}$ has 4 H and 2 O on each side.

Definition

Coefficient: the large number written in front of a formula in an equation. It multiplies the whole formula: $\mathrm{2H_2O}$ means two molecules of water, containing 4 H atoms and 2 O atoms. A coefficient of 1 is not written.

The method

Write the word equation, then the correct formula of every substance. These formulae must never be changed from now on.
Count the atoms of each element on each side, in a small table.
Pick an element that is not balanced. Start with one that appears in only one substance on each side, and leave elements that appear on their own, such as $\mathrm{O_2}$ or $\mathrm{H_2}$ , until last.
Put a coefficient in front of a formula to balance that element. Recount everything, because a coefficient changes every atom in that formula.
Repeat until every element balances. Use the smallest whole numbers.
Add the state symbols and do a final check.

Figure 4.1: The balanced equation drawn as particles: the atoms are the same on both sides, only rearranged.

Worked example

Problem. Balance $\mathrm{H_2(g) + O_2(g) \rightarrow H_2O(l)}$ .

Solution. Count:

Atom	Left	Right
H	2	2
O	2	1

Oxygen is short on the right. Put 2 in front of water: $\mathrm{H_2 + O_2 \rightarrow 2H_2O}$ . Recount: the right now has H = 4 and O = 2.

Atom	Left	Right
H	2	4
O	2	2

Now hydrogen is short on the left. Put 2 in front of $\mathrm{H_2}$ :

$\mathrm{2H_2(g) + O_2(g) \rightarrow 2H_2O(l)}$

Check: H 4 = 4, O 2 = 2. Balanced.

Worked example

Problem. Magnesium burns in oxygen to form magnesium oxide. Write the balanced equation.

Solution. Skeleton: $\mathrm{Mg + O_2 \rightarrow MgO}$ . Mg: 1 and 1; O: 2 and 1. Put 2 in front of $\mathrm{MgO}$ to give 2 O on the right; that makes 2 Mg on the right, so put 2 in front of Mg:

$\mathrm{2Mg(s) + O_2(g) \rightarrow 2MgO(s)}$

Check: Mg 2 = 2, O 2 = 2.

Worked example

Problem. Many Kigali kitchens cook with LPG, which is mostly propane, $\mathrm{C_3H_8}$ . Balance the equation for propane burning completely in air to give carbon dioxide and water.

Solution. Skeleton: $\mathrm{C_3H_8 + O_2 \rightarrow CO_2 + H_2O}$ . Oxygen appears on its own, so leave it until last.

Carbon: 3 on the left, so write $\mathrm{3CO_2}$ .
Hydrogen: 8 on the left; each water has 2 H, so write $\mathrm{4H_2O}$ .
Oxygen: right side $3 \times 2 + 4 \times 1 = 10$ atoms, so the left needs $\mathrm{5O_2}$ .

$\mathrm{C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(l)}$

Atom	Left	Right
C	3	3
H	8	8
O	$5 \times 2 = 10$	$6 + 4 = 10$

Worked example

Problem. Aluminium reacts with oxygen to form the protective layer of aluminium oxide, $\mathrm{Al_2O_3}$ , on cooking pots. Balance the equation.

Solution. Skeleton: $\mathrm{Al + O_2 \rightarrow Al_2O_3}$ . Oxygen is 2 on the left and 3 on the right, an even number against an odd one. The smallest number that both 2 and 3 divide into is 6, so aim for 6 oxygen atoms on each side: $\mathrm{3O_2}$ and $\mathrm{2Al_2O_3}$ . Now there are $2 \times 2 = 4$ Al on the right, so write 4Al on the left:

$\mathrm{4Al(s) + 3O_2(g) \rightarrow 2Al_2O_3(s)}$

Check: Al 4 = 4, O 6 = 6.

Warning

Never change a formula to balance an equation. Changing $\mathrm{H_2O}$ into $\mathrm{H_2O_2}$ would balance the oxygen, but $\mathrm{H_2O_2}$ is hydrogen peroxide, a bleach, not water. Only the coefficients in front of formulae may be changed.

Tip

Leave single elements until last ( $\mathrm{O_2}$ , $\mathrm{H_2}$ , $\mathrm{Fe}$ ): putting a coefficient in front of them changes nothing else. If a radical such as $\mathrm{SO_4}$ appears unchanged on both sides, balance it as one unit.

Try it yourself

Open the Balancing Chemical Equations simulation. Change the coefficients and watch the molecules and the balance scales: the equation is balanced only when every scale is level. Then try the game.

Tyler DeWitt: Introduction to Balancing Chemical Equations (12 min). Watch how he draws the molecules to show why only coefficients, never subscripts, can change.

✦

Practice

Why must a chemical equation be balanced?
Balance: $\mathrm{Na + Cl_2 \rightarrow NaCl}$ .
Balance: $\mathrm{N_2 + H_2 \rightarrow NH_3}$ (making ammonia for fertilisers).
Balance: $\mathrm{CH_4 + O_2 \rightarrow CO_2 + H_2O}$ (methane from Lake Kivu burning).
Balance: $\mathrm{Fe + O_2 \rightarrow Fe_2O_3}$ .
Balance: $\mathrm{Ca(OH)_2 + HCl \rightarrow CaCl_2 + H_2O}$ .
How many atoms of each element are in $\mathrm{3Al_2(SO_4)_3}$ ?
Uwase balances $\mathrm{H_2 + Cl_2 \rightarrow HCl}$ by writing $\mathrm{H_2 + Cl_2 \rightarrow H_2Cl_2}$ . Explain her mistake and give the correct equation.

Show answersHide answers

Atoms are neither created nor destroyed in a reaction (conservation of mass), so there must be the same number of atoms of each element on both sides.
$\mathrm{2Na + Cl_2 \rightarrow 2NaCl}$
$\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$
$\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$
$\mathrm{4Fe + 3O_2 \rightarrow 2Fe_2O_3}$
$\mathrm{Ca(OH)_2 + 2HCl \rightarrow CaCl_2 + 2H_2O}$
Al: $3 \times 2 = 6$ ; S: $3 \times 3 = 9$ ; O: $3 \times 3 \times 4 = 36$ .
She changed the formula of the product; $\mathrm{H_2Cl_2}$ is not hydrogen chloride. The correct equation keeps the formula and adds a coefficient: $\mathrm{H_2 + Cl_2 \rightarrow 2HCl}$ .

Sources and credits

Physical Sciences Grade 10, 14.2: Balancing chemical equations (the step-by-step method for balancing and the aluminium and oxygen example), Siyavula Education and volunteers, Siyavula, licensed under CC BY 3.0. Adapted by Ganzaa.
Interactive: Balancing Chemical Equations (version 2.0.2). Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC BY 4.0 (https://phet.colorado.edu)
Video: Introduction to Balancing Chemical Equations, Tyler DeWitt, embedded from YouTube.
The particle diagram, worked examples, Practice items and exercises were written and drawn by Ganzaa.

1Where did the oxygen atom go?

2The method

Try it yourself

Where did the oxygen atom go?

The method