The mole ratio is the ratio of the balancing numbers (coefficients) in a balanced equation; multiply the known moles by (coefficient of the unknown) / (coefficient of the known) to find any other amount.
This page walks through mole ratio from equations for SPM Chemistry, step by step: the formula you need, the units to watch, and a worked example.
When you use this
Every stoichiometry question in SPM Chemistry begins here. The mole ratio tells you how many moles of one substance react with, or are produced from, another. You read it straight from a balanced equation, and you need it before you can work out any mass, gas volume or concentration.
The formula
In a balanced chemical equation the large numbers in front of each formula (the coefficients) give the mole ratio. For a reaction A + 2B → 3C the ratio of moles is A : B : C = 1 : 2 : 3. To find an unknown amount:
moles of unknown = moles of known x (coefficient of unknown / coefficient of known)
Units. Amount of substance is measured in moles (mol). The ratio itself has no unit, it is a pure number.
Always balance the equation first; an unbalanced equation gives the wrong ratio.
Worked example 1 (easy)
Nitrogen reacts with hydrogen: N2 + 3H2 → 2NH3. If 6 mol of hydrogen react completely, how many moles of ammonia form?
- Ratio H2 : NH3 = 3 : 2.
- moles NH3 = 6 x (2 / 3) = 4 mol.
Answer: 4 mol of NH3. In the same way the nitrogen used is 6 x (1 / 3) = 2 mol.
Worked example 2 (medium)
Magnesium burns in oxygen: 2Mg + O2 → 2MgO. If 0.50 mol of magnesium is burned, how many moles of oxygen are needed and how much magnesium oxide is produced?
- Ratio Mg : O2 : MgO = 2 : 1 : 2.
- moles O2 = 0.50 x (1 / 2) = 0.25 mol.
- moles MgO = 0.50 x (2 / 2) = 0.50 mol.
Answer: 0.25 mol O2 and 0.50 mol MgO.
Worked example 3 (SPM level)
Calcium carbonate reacts with dilute hydrochloric acid: CaCO3 + 2HCl → CaCl2 + H2O + CO2. A sample contains 0.05 mol of calcium carbonate. Find the moles of hydrochloric acid that react and the moles of carbon dioxide released.
- Ratio CaCO3 : HCl : CO2 = 1 : 2 : 1.
- moles HCl = 0.05 x (2 / 1) = 0.10 mol.
- moles CO2 = 0.05 x (1 / 1) = 0.05 mol.
Answer: 0.10 mol HCl react and 0.05 mol CO2 is given off. From here you could go on to find the mass of any substance or the volume of the gas, because the mole ratio is the bridge to every other quantity.
Why the ratio works
A balanced equation counts particles, not grams. The coefficients tell you the ratio in which molecules or formula units react, and because one mole always contains the Avogadro constant of particles (6.02 x 1023 mol−1), those same numbers give the ratio in moles. That is why you can scale the ratio to any amount you like. A ratio of 2 : 1 for molecules is also 2 : 1 for moles, whether you are holding a few millimoles in a test tube or working with kilomoles in a factory reactor. Seeing the ratio as a count of particles, and never as a comparison of masses, is exactly what stops the classic mistakes listed below. It is also why the very first thing you do is check that the equation is balanced, atom by atom, before trusting any of its numbers.
Common traps
- Not balancing first. The coefficients only give the correct ratio once the equation is balanced. Check every element.
- Inverting the ratio. Multiply by (coefficient of what you want) / (coefficient of what you know), in that order.
- Reading a subscript instead of a coefficient. The small number in H2 is not part of the ratio; only the large number in front counts.
- Adding coefficients. The ratio is a multiplication factor, not a sum.
In our online one-to-one lessons we drill this until reading a ratio from an equation is automatic, because it is the one step that unlocks the rest of the calculation. Master it and mass, gas-volume and titration questions all become the same three moves: find moles, apply the ratio, convert back to the quantity the question wants.
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