Mass to moles

This is the commonest calculation of all: a mass in grams is given, and the number of moles is asked for. Every time it is n = m ÷ M.

Example 1 — 10 g of carbon

Problem

The molar mass of carbon is 12 g mol^-1. Find the amount of carbon, in moles, contained in 10 g of it.

Solution

n = m ÷ M

= 10 g ÷ 12 g mol^-1

= 0.83 mol

Example 2 — 22 g of carbon dioxide

Problem

Calculate the amount of CO₂, in moles, contained in 22 g of carbon dioxide. (The molar mass of carbon dioxide is 44 g mol^-1.)

Solution

n = m ÷ M

= 22 g ÷ 44 g mol^-1

= 0.5 mol

22 is half of 44, so the answer is half a mole. You can see that without a calculator.

Example 3 — 20 g of water

Problem

The molar mass of water is 18 g mol^-1. Find the amount of water, in moles, contained in 20 g of it.

Solution

n = m ÷ M

= 20 g ÷ 18 g mol^-1

= 1.11 mol

Is the answer reasonable?

If the mass is less than the molar mass the answer must be less than 1 mole; if it is more, the answer must be more than 1. Getting 0.83 for 10 g of carbon and 1.11 for 20 g of water both pass that check. An answer that fails it means the division went the wrong way round.