Mole calculations

A method for every problem

Most mole problems go in the same steps.

1. Write the formula and find the molar mass $M$ in g/mol.
2. Find the number of moles: $n = m \div M$ (or $m = n \times M$ if we want the mass).
3. Find the number of particles: $N = n \times N_A$.
4. If we want atoms and not molecules, multiply by the number of atoms in one molecule.

Example 1: the mass of some moles

What is the mass of $0.5\ \text{mol}$ of $\text{CO}_2$?

$M = 44\ \text{g/mol}$. We want $m$, so $m = n \times M = 0.5\ \text{mol} \times 44\ \text{g/mol} = 22\ \text{g}$.

Example 2: molecules and atoms

How many molecules, and how many atoms, are there in $90\ \text{g}$ of water?

• $M = 18\ \text{g/mol}$, so $n = 90\ \text{g} \div 18\ \text{g/mol} = 5\ \text{mol}$.
• Molecules: $5\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 3.011 \times 10^{24}$.
• Each molecule of $\text{H}_2\text{O}$ has $3$ atoms, so the atoms are $3 \times 3.011 \times 10^{24} = 9.033 \times 10^{24}$.

Example 3: the mass of one molecule

What is the mass of one molecule of water, in grams?

One mole of water has a mass of $18\ \text{g}$ and has $6.022 \times 10^{23}$ molecules. So one molecule has

Example 4: the percentage of an element

The percentage by mass of an element in a compound is

For $\text{CaCO}_3$ (molecular mass $100\ \text{u}$): calcium is $\dfrac{40\ \text{u}}{100\ \text{u}} \times 100 = 40\ \%$, carbon is $\dfrac{12\ \text{u}}{100\ \text{u}} \times 100 = 12\ \%$, and oxygen is $\dfrac{48\ \text{u}}{100\ \text{u}} \times 100 = 48\ \%$. The three add up to $100\ \%$.

You should find that urea is nearly half nitrogen, while ammonium sulphate is barely a fifth.

Practise with new numbers

Try it in Python

This program changes masses to moles and to the number of particles.

The next program finds the percentage of each element in $\text{CaCO}_3$.

Remember these

• Steps: formula, molar mass, moles ($n = m \div M$), particles ($N = n \times N_A$), then atoms if needed.
• The mass of one molecule is $M \div N_A$.
• The percentage of an element is its mass in the formula, divided by the molecular mass, times $100$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the mass of $3\ \text{mol}$ of methane, $\text{CH}_4$?

2. How many atoms are there in $0.1\ \text{mol}$ of ammonia, $\text{NH}_3$?

3. What percentage of water is hydrogen by mass?

4. What is the mass of one molecule of nitrogen gas, $\text{N}_2$?