Atomic and molecular masses

Dalton's atomic theory

In 1808, John Dalton put the laws together into one picture.

1. Matter is made of tiny particles called atoms, which cannot be divided.
2. All atoms of one element are the same, with the same mass. Atoms of different elements differ in mass.
3. Compounds form when atoms of different elements join in a fixed ratio of small whole numbers.
4. A chemical reaction only rearranges atoms. Atoms are neither made nor destroyed.

Each law follows. Atoms are not destroyed, so mass is conserved. A compound always has the same ratio of atoms of fixed mass, so its make-up is definite. An oxide with one or two oxygen atoms for each nitrogen atom holds oxygen in the ratio $1 : 2$, which is multiple proportions.

What has changed since

Two of Dalton's ideas needed repair.

• Atoms can be divided. They are made of electrons, protons and neutrons, as the next chapter shows.
• Atoms of one element can differ in mass. These are isotopes: atoms with the same number of protons but different numbers of neutrons. Chlorine, for example, has atoms of two masses.

The heart of the theory still stands. In every chemical reaction, atoms keep their identity and are only rearranged. Idea 2 now speaks of average masses, as you will see.

A unit for tiny masses

One atom of hydrogen has a mass of about $1.67 \times 10^{-24}\ \text{g}$. Numbers like this are awkward, so chemists compare atoms with a standard atom instead.

Today the standard is the most common atom of carbon, carbon-12.

One atomic mass unit, 1 u, is one twelfth of the mass of one carbon-12 atom. $1\ \text{u} = 1.66056 \times 10^{-24}\ \text{g}$.

So a carbon-12 atom has a mass of exactly $12$ u. On this scale, an atom of hydrogen-1 is $1.0078$ u and an atom of oxygen-16 is $15.995$ u. The older name for the unit is amu; the symbol in use now is u, sometimes called the dalton.

Average atomic mass

Boron in nature is a mixture of two isotopes. A balance cannot pick out single atoms, so the atomic mass of boron is the average over all its atoms, with each isotope counted by how common it is.

This is the $10.81$ in the periodic table. It is not the mass of any single boron atom; no atom of boron has a mass of $10.81$ u. It is the mass of an average atom. In general:

The average always lies between the lightest and the heaviest isotope, and nearest to the most common one.

Set both sliders to $0$. The average becomes $23.985$ u, the mass of magnesium-24 alone. Now raise magnesium-26 and watch the dashed line move to the right.

Molecular mass

The molecular mass of a substance is the sum of the atomic masses of all the atoms in one molecule. Take glucose, $\text{C}_6\text{H}_{12}\text{O}_6$, with $\text{C} = 12.011$ u, $\text{H} = 1.008$ u and $\text{O} = 16.00$ u:

Formula mass

Ionic compounds such as sodium chloride have no separate molecules. Their crystals are a regular pattern of ions. For them we use the formula mass: the sum of the atomic masses in one formula unit. For calcium fluoride, $\text{CaF}_2$, with $\text{Ca} = 40.08$ u and $\text{F} = 19.00$ u:

The arithmetic is the same as for a molecular mass; only the name changes.

Practise with new numbers

Try it in Python

The program finds the average atomic mass of three elements from their isotopes. It also checks that the shares add up to $100\%$.

Common mistakes

• Using mass numbers for isotope masses. Boron-11 has a mass of $11.009$ u, not exactly $11$. For careful work, use the measured masses.
• Taking a plain average. Two isotopes are seldom equally common. Weight each mass by its share.
• Shares that do not add up to $100\%$. Check them first. A missing isotope makes the average wrong.
• Thinking 1 u is 1 g. One u is about $1.66 \times 10^{-24}$ g, the scale of a single atom.
• Calling the formula mass of an ionic solid a molecular mass. Sodium chloride has no molecules, so use formula mass.

Remember these

• Dalton: atoms of fixed mass join in small whole-number ratios and are only rearranged in reactions.
• Atoms can be divided, and one element can have isotopes of different mass.
• $1\ \text{u}$ is one twelfth of the mass of a carbon-12 atom, $1.66056 \times 10^{-24}\ \text{g}$.
• Average atomic mass = (sum of each isotope's mass times its share in percent) divided by 100.
• Molecular mass, or formula mass for an ionic compound, is the sum of the atomic masses in the formula.

Check yourself

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

1. Which idea of Dalton's did the discovery of isotopes change?

2. Why is the mass of a carbon-12 atom exactly $12$ u?

3. An element has two isotopes, and its average atomic mass is $79.90$ u. One isotope is $78.92$ u and the other $80.92$ u. Which is more common?

4. What is the formula mass of potassium bromide, $\text{KBr}$, with $\text{K} = 39.10$ u and $\text{Br} = 79.90$ u?

5. Why do we say formula mass, not molecular mass, for potassium bromide?