Determination of Relative Mass

This lesson covers: 

1. Interpreting mass spectra
2. Calculating relative atomic mass from mass spectra

Interpreting mass spectra

A mass spectrum plots the relative abundance of ions against their mass-to-charge ratio (m/z).

• The x-axis displays the m/z values. The m/z of each peak equals the relative mass of the ion.
• The y-axis indicates the relative abundance of each ion, either in arbitrary units or as a percentage.

For elemental samples, each peak represents a different isotope.

• The relative height of each peak shows how abundant the isotope is.
• Elements with only one stable isotope will show a single peak.

Below is the mass spectrum of an element with two stable isotopes.

For molecular samples, the peak at the highest m/z value is the molecular ion (M⁺).

• The m/z of the molecular ion peak matches the molecule's relative molecular mass (M_r).
• Peaks at lower m/z values come from fragments of the molecular ion.

Below is the mass spectrum for a compound with a molecular mass of 72.

Calculating relative atomic mass from mass spectra

To find an element's relative atomic mass (A_r) from its mass spectrum, follow these steps:

1. Multiply the relative isotopic mass by its relative abundance for each isotope.
2. Add these products together.
3. Divide the total by the sum of the relative abundances (100 if using percentages).

Worked example 1 - Calculating the relative atomic mass of copper from its mass spectrum

Calculate the relative atomic mass (A_r) of copper using the mass spectrum shown below:

Step 1: Multiply the relative isotopic mass by its relative abundance for each isotope

For ⁶³Cu: 63 x 69.2 = 4,359.6

For ⁶⁵Cu: 65 x 30.8 = 2,002.0

Step 2: Sum these values

Sum = 4,359.6 + 2,002.0 = 6,361.6

Step 3: Divide by the total relative abundance

Total relative abundance = 69.2 + 30.8 = 100.0

Ar ​=1006,361.6​=63.616

Therefore, the calculated relative atomic mass (A_r) of copper from its mass spectrum is 63.6.