Molecular mass and formula unit mass

The mass of a molecule

Water is $\text{H}_2\text{O}$. How heavy is one molecule of it? We add up the masses of the atoms in the molecule.

The mass of one atom is a very small number in grams. A hydrogen atom has a mass of only $1.67 \times 10^{-24}\ \text{g}$. So chemists use a smaller unit, the atomic mass unit, with the symbol u. One u is about the mass of one proton or one neutron. In this unit, hydrogen is about $1\ \text{u}$, carbon is $12\ \text{u}$ and oxygen is $16\ \text{u}$.

Molecular mass

The molecular mass of a substance is the sum of the atomic masses of all the atoms in one molecule of the substance. It is measured in u.

Water, $\text{H}_2\text{O}$. Two atoms of hydrogen, and one atom of oxygen.

Carbon dioxide, $\text{CO}_2$. One atom of carbon, and two of oxygen.

Ammonia, $\text{NH}_3$. $14\ \text{u} + 3 \times 1\ \text{u} = 17\ \text{u}$.

Sulphuric acid, $\text{H}_2\text{SO}_4$. $2 \times 1\ \text{u} + 32\ \text{u} + 4 \times 16\ \text{u} = 98\ \text{u}$.

Glucose, $\text{C}_6\text{H}_{12}\text{O}_6$. $6 \times 12\ \text{u} + 12 \times 1\ \text{u} + 6 \times 16\ \text{u} = 180\ \text{u}$.

Oxygen gas, $\text{O}_2$. The molecule has two atoms: $2 \times 16\ \text{u} = 32\ \text{u}$. Notice that for an element, we use the molecule and not the atom. So the molecular mass of oxygen gas is $32\ \text{u}$, and the atomic mass of oxygen is $16\ \text{u}$.

Formula unit mass

An ionic compound, such as common salt, has no separate molecules. It is a large number of ions in a pattern. The smallest group of the ions that the formula shows is a formula unit. The formula unit mass is the sum of the atomic masses of the atoms in the formula unit. We calculate it in the same way as the molecular mass.

Sodium chloride, NaCl. $23\ \text{u} + 35.5\ \text{u} = 58.5\ \text{u}$.

Calcium carbonate, $\text{CaCO}_3$. $40\ \text{u} + 12\ \text{u} + 3 \times 16\ \text{u} = 100\ \text{u}$.

Calcium hydroxide, $\text{Ca(OH)}_2$. $40\ \text{u} + 2 \times (16\ \text{u} + 1\ \text{u}) = 74\ \text{u}$.

Sodium carbonate, $\text{Na}_2\text{CO}_3$. $2 \times 23\ \text{u} + 12\ \text{u} + 3 \times 16\ \text{u} = 106\ \text{u}$.

Ammonium sulphate, $(\text{NH}_4)_2\text{SO}_4$. The bracket holds $1$ nitrogen and $4$ hydrogen, and there are two such groups: $2 \times (14\ \text{u} + 4\ \text{u}) + 32\ \text{u} + 4 \times 16\ \text{u} = 132\ \text{u}$.

Aluminium sulphate, $\text{Al}_2(\text{SO}_4)_3$. $2 \times 27\ \text{u} + 3 \times (32\ \text{u} + 4 \times 16\ \text{u}) = 54\ \text{u} + 288\ \text{u} = 342\ \text{u}$.

You should find that glucose, $\text{C}_6\text{H}_{12}\text{O}_6$, comes to $180\ \text{u}$, and that its twelve hydrogen atoms add only $12\ \text{u}$ of it.

A way to remember

1. Write the formula.
2. Count the atoms of each element, using the numbers and the brackets.
3. Multiply each count by the atomic mass.
4. Add the results.

Write the working in a small table, and you will not make mistakes with the brackets.

The molecular mass is a number without a unit if we call it the relative molecular mass. In this course we give it in $\text{u}$.

What the molecular mass tells us

The molecular mass lets us compare how heavy molecules are. A molecule of carbon dioxide ($44\ \text{u}$) is more than twice as heavy as a molecule of water ($18\ \text{u}$). This is why carbon dioxide gas is heavier than air (average $29\ \text{u}$), and it sinks and collects at the bottom of a pit or a well. And the molecular mass is the first step to the mole, in the next lesson.

Practise with new numbers

Try it in Python

This program finds the molecular mass of six substances.

Common mistakes

• Forgetting the bracket multiplies. In $\text{Ca(OH)}_2$, there are $2$ oxygen and $2$ hydrogen atoms, and not $1$ of each.
• Adding the number of atoms and not the masses. Multiply by the atomic mass first.
• Using the atomic mass of an element in place of its molecular mass. For $\text{O}_2$ the answer is $32\ \text{u}$, not $16\ \text{u}$.
• Using the wrong atomic mass. Chlorine is $35.5\ \text{u}$, not $35\ \text{u}$.

Remember these

• Molecular mass is the sum of the atomic masses of the atoms in one molecule, in u.
• For an ionic compound, the same sum is called the formula unit mass.
• $\text{H}_2\text{O}$ is $18\ \text{u}$, $\text{CO}_2$ is $44\ \text{u}$, and NaCl is $58.5\ \text{u}$.
• Count the atoms carefully. A bracket multiplies everything inside it.

Check yourself

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

1. Find the molecular mass of ethane, $\text{C}_2\text{H}_6$.

2. Find the formula unit mass of potassium carbonate, $\text{K}_2\text{CO}_3$. Use $\text{K} = 39\ \text{u}$.

3. Which molecule is heavier: $\text{CO}$ or $\text{N}_2$?

4. Find the formula unit mass of magnesium nitrate, $\text{Mg(NO}_3)_2$.