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# Atomic and molecular mass

## Atomic mass

The relative atomic mass (A${_r}$) is defined relative to the mass of carbon-12. It is a dimensionless number (it has no units) listed on the periodic table.

Carbon-12 is an isotope of carbon defined to have a mass of 12.

The proportions of the different isotopes of an element are taken into account when calculating the relative atomic mass.

Magnesium has a relative atomic mass of around 24.3. About 79% of magnesium atoms have a weight of 24, 10% have a weight of 25 and 11% have a weight of 26.

$$24\times0.79 + 25\times0.1 + 26\times0.11 \approx 24.3$$
Hydrogen has 3 isotopes and 99.99% of it is $\ce{^1_1H}$

The relative atomic mass is approximately equal to the number of nucleons in an atom, but this is not the definition and not how the mass is calculated. In reality, the mass is measured using apparatus called a mass spectrometer.

## Relative molecular mass

Relative molecular mass (M${_r}$) is a dimensionless quantity determined by adding the relative atomic masses of all atoms within a molecule.

Remember that the relative atomic mass is defined relative to the mass of carbon-12.

The M${_r}$ is approximately equal to the total number of nucleons within a molecule.

A water molecule, made up of one large oxygen atom (in red) and two smaller hydrogen atoms (in white).

Water ($\ce{H2O}$) has an estimated relative molecular mass of 18 because hydrogen and oxygen have relative atomic masses of around 1 and 16 respectively.

A${_r}$ of hydrogen = 1

A${_r}$ of oxygen = 16

Therefore, M${_r}$ of water = 2 $\times$ 1 + 16 = 18