Relative masses compare to carbon-12

Atoms have tiny absolute masses that are impractical to measure directly. Instead, the mass of one atom is compared to 1/12^th the mass of a carbon-12 atom. This is the atom's relative mass.

Key definitions:

Relative isotopic mass - The mass of an atom of an isotope compared to 1/12 the mass of a carbon-12 atom.

• Relative isotopic mass is specific to a particular isotope of an element.
• It is usually very close to being a whole number.
• At A level, relative isotopic masses are rounded to one decimal place.
• E.g. The relative isotopic masses of the two main chlorine isotopes (³⁵Cl and ³⁷Cl) are 35.0 and 37.0 respectively.

Relative atomic mass (A_r_) - The weighted mean mass of an atom of an element compared to 1/12 the mass of a carbon-12 atom.

• A_r is an average of the masses of all the isotopes of an element, weighted according to their natural abundances.
• Since it's an average, A_r_ is not usually a whole number.
• The next section explains how to calculate relative atomic mass from isotopic abundances.

Relative molecular mass (M_r_) - The average mass of a molecule compared to 1/12 the mass of a carbon-12 atom.

• For simple covalent molecules, M_r is calculated by adding up the A_r values of all the atoms in one molecule.
• E.g. For ethanol (C₂H₅OH): M_r(C₂H₅OH) = (2 × A_r of C) + (6 × A_r of H) + (1 × A_r of O) = (2 × 12.0) + (6 × 1.0) + (1 × 16.0) = 24.0 + 6.0 + 16.0 = 46.0

Relative formula mass - Used for ionic compounds. It is calculated by adding up the A_r_ values of all the ions in one formula unit.

• E.g. For calcium fluoride (CaF₂): M_r(CaF₂) = (1 × A_r of Ca) + (2 × A_r of F) = (1 × 40.1) + (2 × 19.0) = 40.1 + 38.0 = 78.1

Calculating A_r_ from isotopic abundances

To calculate the relative atomic mass (A_r_) from isotopic abundances, use this formula:

$A_r=\frac{\text{ sum of (isotopic mass }\times \text{ isotopic abundance) }}{\text{ sum of abundance of all isotopes }}$

Worked example 1 - Calculating the relative atomic mass of chlorine from its isotopic abundances

Chlorine has two main isotopes, ³⁵Cl with an abundance of 75% and ³⁷Cl with an abundance of 25%.

Calculate the relative atomic mass (A_r_) of chlorine.

Step 1: For each isotope, multiply its relative mass by its percentage abundance.

• For ³⁵Cl: 35.0 × 75 = 2,625
• For ³⁷Cl: 37.0 × 25 = 925

Step 2: Add up all the values from step 1 to get the numerator of the fraction.

2,625 + 925 = 3,550

Step 3: Add up the abundances of all isotopes to get the denominator of the fraction. If abundances are percentages, this will be 100.

75 + 25 = 100

Step 4: Divide numerator by denominator to get A_r_.

${\text{A}}_{\text{r }}=\frac{\mathrm{3,550}}{100}=35.5$

Therefore, the relative atomic mass of chlorine is 35.5.

Worked example 2 - Calculating the relative atomic mass of magnesium from its isotopic abundances

Magnesium has three main isotopes: ²⁴Mg with an abundance of 79%, ²⁵Mg with an abundance of 10%, and ²⁶Mg with an abundance of 11%.

Calculate the relative atomic mass (A_r_) of magnesium.

Step 1: For each isotope, multiply its relative mass by its percentage abundance.

• For ²⁴Mg: 24.0 × 79 = 1,896
• For ²⁵Mg: 25.0 × 10 = 250
• For ²⁶Mg: 26.0 × 11 = 286

Step 2: Add up all the values from step 1 to get the numerator of the fraction.

1,896 + 250 + 286 = 2,432

Step 3: Add up the abundances of all isotopes to get the denominator of the fraction. If abundances are percentages, this will be 100.

79 + 10 + 11 = 100

Step 4: Divide numerator by denominator to get A_r_.

${\text{A}}_{\text{r }}=\frac{\mathrm{2,432}}{100}=24.32$

Therefore, the relative atomic mass of magnesium is 24.3.