Chemistry 1.12 - Calculating relative atomic mass

Calculating relative atomic mass

Relative atomic mass is a weighted mean: the most abundant isotope has the greatest influence. Recall that isotope masses are measured relative to one twelfth of the mass of a carbon-12 atom, so the resulting relative atomic mass has no unit.

To calculate $A_r$, each isotope's relative mass must be weighted by how abundant that isotope is. The abundances may be percentages, decimals or relative counts.

If percentage abundances add to 100, the denominator is 100. If decimal proportions add to 1, either use the general formula or add the weighted contributions directly. For relative counts such as $4:1$, divide by $4+1$, not by 100.

Worked example 1: percentage abundances

Element M has three isotopes. Calculate its relative atomic mass and give the answer to 1 decimal place.

1. Weight every isotope:

2. Add the contributions:

3. Divide by the total abundance:

4. Round only at the end:

5. Sense-check: 24.3 lies between 24 and 26 and is much closer to 24, the isotope with 79% abundance. No unit is written because $A_r$ is a ratio.

Worked example 2: relative counts

Another element has isotope masses 84 and 86 in the ratio $4:1$. A typical group of five atoms therefore contains four atoms of mass 84 and one of mass 86: