D. Quantities in Chemical Reactions · Quantities in Chemical Reactions

Mole Ratios in Balanced Chemical Equations

D3.4 D2.5 D2.1 A1.12About 70 minutes

Learning goals

I can read a balanced equation in terms of particles, moles and masses.
I can explain why mass is conserved in a reaction but the number of moles may change.
I can write mole ratios from a balanced equation.
I can use a mole ratio to find the amount of any reactant or product from the amount of another.

Words to know

coefficient
The number in front of a formula in a balanced equation. It gives the relative number of particles, and of moles, of that substance.

mole ratio
The ratio of the coefficients of two substances in a balanced equation, such as 3 mol H₂ : 2 mol NH₃.

stoichiometry
The study of the quantitative relationships (amounts, masses, numbers of particles) between reactants and products in a chemical reaction.

state symbols
(s) solid, (l) liquid, (g) gas, (aq) dissolved in water.

An equation is a recipe

A pancake recipe might say: 2 cups flour + 1 egg + 1.5 cups milk → 8 pancakes. If you want 24 pancakes, you triple everything. You do not need to know how much an egg weighs; the recipe works in counts.

A balanced chemical equation is a recipe too. It works in particles, and therefore in moles. This is the key idea of stoichiometry (stoy-kee-OM-uh-tree), from Greek words meaning "element" and "measure".

Remember from Grade 10

In Grade 10 you balanced equations by changing coefficients, never subscripts, until each kind of atom was equal on both sides. You also learned the law of conservation of mass: the total mass of the products equals the total mass of the reactants. Now you will use the coefficients to calculate amounts.

Three ways to read one equation

Take the reaction used to make ammonia for fertilizer:

N₂(g) + 3H₂(g) → 2NH₃(g)

Particles: 1 molecule of N₂ reacts with 3 molecules of H₂ to make 2 molecules of NH₃.
Moles: multiply every count by 6.02 × 10²³. 1 mol N₂ reacts with 3 mol H₂ to make 2 mol NH₃.
Mass: multiply each amount by its molar mass. 28.02 g N₂ + 6.06 g H₂ → 34.08 g NH₃.

The coefficients are the ratio of particles and of moles, never of grams.

N₂ + 3H₂ → 2NH₃ drawn with particles. The atoms are rearranged, not created or destroyed, so mass is conserved. The number of molecules, and so the number of moles, changes from 4 to 2.

Reading the same balanced equation as molecules, moles and masses. Only the mass row adds up the same on both sides.

Moles are not conserved, mass is

In the ammonia reaction, 4 mol of reactant molecules become 2 mol of product molecules. That is fine: molecules are rearranged into new, bigger molecules. What is conserved is every atom, and so the total mass (34.08 g on each side). Never add up moles on each side and expect them to match.

Mole ratios as conversion factors

Any two substances in a balanced equation are linked by a mole ratio. From N₂ + 3H₂ → 2NH₃ you can write:

1 mol N₂ : 3 mol H₂ · 1 mol N₂ : 2 mol NH₃ · 3 mol H₂ : 2 mol NH₃

To find the amount of a wanted substance from the amount of a given substance, multiply by the ratio of their coefficients, wanted over given:

The mole ratio: put the coefficient of the substance you want on top and the coefficient of the substance you know on the bottom.

Worked example

Example 1: Reactant to product

Propane burns in a barbecue: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g). What amount of oxygen is needed to burn 2.50 mol of propane, and what amount of carbon dioxide is produced?

The equation is already balanced. Given: 2.50 mol C₃H₈.
O₂: n = 2.50 mol C₃H₈ × (5 mol O₂ ÷ 1 mol C₃H₈) = 12.5 mol O₂.
CO₂: n = 2.50 mol C₃H₈ × (3 mol CO₂ ÷ 1 mol C₃H₈) = 7.50 mol CO₂.
Check: units of mol C₃H₈ cancel, leaving the wanted substance.

12.5 mol O₂ is needed and 7.50 mol CO₂ is produced.

Worked example

Example 2: Balance first

Aluminium reacts with oxygen: Al(s) + O₂(g) → Al₂O₃(s). What amount of aluminium oxide forms from 0.600 mol of aluminium?

Balance: 4Al(s) + 3O₂(g) → 2Al₂O₃(s). (Al: 4 = 4; O: 6 = 6.)
n(Al₂O₃) = 0.600 mol Al × (2 mol Al₂O₃ ÷ 4 mol Al) = 0.300 mol.

0.300 mol Al₂O₃. Always balance the equation before using a mole ratio; an unbalanced equation gives a wrong ratio.

Worked example

Example 3: Particles instead of moles

In 2H₂(g) + O₂(g) → 2H₂O(g), how many oxygen molecules react with 3.01 × 10²³ hydrogen molecules?

The coefficients are particle ratios too: 2 molecules H₂ : 1 molecule O₂.
N(O₂) = 3.01 × 10²³ × (1 ÷ 2) = 1.505 × 10²³.
(Or convert to moles: 0.500 mol H₂ × ½ = 0.250 mol O₂ = 1.505 × 10²³ molecules.)

1.51 × 10²³ O₂ molecules.

Ions count too

When an ionic compound dissolves, the formula tells you the mole ratio of the ions:

CaCl₂(s) → Ca²⁺(aq) + 2Cl⁻(aq)

So 0.10 mol of CaCl₂ gives 0.10 mol of Ca²⁺ ions and 0.20 mol of Cl⁻ ions. You will use this often in the unit Solutions and Solubility.

Just for fun

Why does a balanced equation never lose an argument?

It always sees both sides.

Hands-on activity

Bean molecules

You need: dried beans or buttons in two colours (about 20 of each), and a sheet of paper. Keep beans and buttons away from small children (choking hazard).

Let one colour be hydrogen atoms and the other oxygen atoms. Draw a big arrow across the middle of the paper.
On the left, build 2 H₂ molecules (pairs of H) and 1 O₂ molecule (a pair of O).
Take them apart and rebuild them on the right as H₂O molecules. How many can you make? Is anything left over?
Now start with 6 H₂ and 3 O₂. How many H₂O can you make?
Count molecules and atoms on each side both times.

What to look for: 2 H₂ + 1 O₂ make exactly 2 H₂O, and 6 H₂ + 3 O₂ make exactly 6 H₂O, with nothing left over. The number of molecules goes down (3 → 2, or 9 → 6), but the number of atoms of each colour never changes. That is why mass is conserved but moles are not. Scaling the recipe (×3) keeps the same 2 : 1 : 2 ratio, just as any number of moles does.

Your turn

Write all three mole ratios for 2H₂(g) + O₂(g) → 2H₂O(g).

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g). What amount of oxygen is needed to burn 3.00 mol of methane?

N₂(g) + 3H₂(g) → 2NH₃(g). What amount of ammonia forms from 0.450 mol of hydrogen?

Balance KClO₃(s) → KCl(s) + O₂(g). Then find the amount of oxygen made from 0.500 mol of KClO₃.

2Na(s) + Cl₂(g) → 2NaCl(s). How many chlorine molecules react with 1.20 × 10²⁴ sodium atoms?

Show that mass is conserved in CH₄ + 2O₂ → CO₂ + 2H₂O, using molar masses.

In 2H₂ + O₂ → 2H₂O, there are 3 mol of reactants and 2 mol of products. Does this break the law of conservation of mass? Explain.

More practice: warm-up

What do the coefficients in a balanced equation tell you?

In N₂ + 3H₂ → 2NH₃, what is the mole ratio of N₂ to NH₃?

2Mg(s) + O₂(g) → 2MgO(s). What amount of MgO forms from 4.0 mol of Mg?

In the same reaction, what amount of O₂ reacts with 4.0 mol of Mg?

What does the word stoichiometry mean?

More practice: on your own

In a blast furnace, Fe₂O₃(s) + 3CO(g) → 2Fe(l) + 3CO₂(g). What amount of iron is produced from 1.50 mol of Fe₂O₃, and what amount of CO is needed?

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O. What amount of CO₂ is made from 0.250 mol of glucose? How many O₂ molecules are used?

Balance C₂H₆(g) + O₂(g) → CO₂(g) + H₂O(g). What amount of O₂ is needed for 1.00 mol of ethane?

Pb(NO₃)₂(aq) + 2KI(aq) → PbI₂(s) + 2KNO₃(aq). What amount of KI reacts with 0.0200 mol of lead(II) nitrate, and what amount of PbI₂ precipitate forms?

What amount of chloride ions is released when 0.300 mol of AlCl₃ dissolves?

Challenge

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. How many CO₂ molecules does a plant need to make 1.00 g of glucose?

Gasoline is mostly octane: 2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O. What amount of CO₂ is produced by burning 5.00 mol of octane? What amount of O₂ is used per mole of octane?

Hydrogen and oxygen react in a 2 : 1 mole ratio to make water. Find the mass ratio of hydrogen to oxygen, and explain why it is not 2 : 1.

Check your understanding

Quiz

In 2SO₂(g) + O₂(g) → 2SO₃(g), what amount of SO₃ forms from 3.0 mol of O₂?

What do the coefficients in a balanced equation represent?

In N₂ + 3H₂ → 2NH₃, which quantity is the same on both sides?

C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. What amount of water forms from 0.50 mol of propane?

Before using a mole ratio, you must…

4Fe + 3O₂ → 2Fe₂O₃. What amount of O₂ reacts with 2.0 mol of Fe?

For parents and teachers

Big idea: The coefficients in a balanced equation are a recipe in particles and moles. A mole ratio ("wanted over given") converts the amount of one substance into the amount of another. Mass is conserved; moles are not necessarily. This lesson addresses D3.4 (quantitative relationships in a balanced equation) and starts D2.5.

How to help: Use cooking: "If 2 eggs make 12 cookies, how many eggs for 30 cookies?" That is exactly a mole-ratio calculation. Ask your teen to read an equation aloud in molecules, then in moles.

Common difficulties:

Using an unbalanced equation.
Flipping the ratio (given over wanted). Writing units such as "mol O₂ / mol C₃H₈" shows when it is upside down.
Treating coefficients as mass ratios.
Expecting moles to be equal on both sides of an equation.