Relative Mass (OCR A-Level Chemistry A): Revision Notes

Relative mass

Introduction to relative mass

Chemists need a practical system for comparing the masses of different atoms. Rather than working with the incredibly small actual masses (which would be extremely inconvenient), they use a relative mass scale. This scale allows us to express atomic masses as simple numbers by comparing them to a standard reference.

The carbon-12 standard

Subatomic particles and mass

Before understanding relative mass, let's review the masses of subatomic particles. Atoms contain three types of particle, each with different masses:

Notice that protons and neutrons have very similar masses (both approximately 1), whilst electrons are much lighter at roughly 1/2000th the mass of a proton. This means that almost all of an atom's mass comes from its nucleus.

Why we need a standard

When you try to find the mass of an isotope by adding up the masses of its particles, you hit a problem. The strong nuclear force that holds protons and neutrons together in the nucleus actually causes a tiny amount of mass to be lost – this is called the mass defect. Albert Einstein's famous work showed this over 100 years ago.

So chemists needed to establish a practical standard for measuring atomic masses that accounts for this effect.

The carbon-12 isotope

Carbon-12 has been chosen as the international standard for atomic mass measurements. This isotope contains 6 protons, 6 neutrons, and 6 electrons:

From this, we can establish:

• The atomic mass unit ($u$) is defined as $\frac{1}{12}$ of the mass of one carbon-12 atom
• On this scale, 1 $u$ is approximately the mass of one proton or one neutron

Relative isotopic mass

This is a dimensionless quantity (it has no units) because it's a ratio of two masses. For most purposes in A-Level chemistry, you can assume that the relative isotopic mass is the same as the mass number (the number of protons plus neutrons).

However, when accurate values are needed, relative isotopic masses show small deviations from whole numbers:

Relative atomic mass

Understanding weighted mean

Most elements exist naturally as a mixture of different isotopes. For example, chlorine exists as both chlorine-35 and chlorine-37. The relative atomic mass ($A_r$) takes this into account.

The key word here is weighted mean – this means we must account for:

1. The percentage abundance of each isotope
2. The relative isotopic mass of each isotope

Like relative isotopic mass, $A_r$ is dimensionless.

Finding relative atomic mass values

You can find relative atomic mass values in the periodic table. Each element box shows the atomic number (smaller number at top) and the relative atomic mass (larger number underneath):

Notice that relative atomic mass values are rarely whole numbers – this is because they represent weighted averages of isotopic masses.

Determination of relative atomic mass using mass spectrometry

How mass spectrometry works

Scientists use an instrument called a mass spectrometer to find the percentage abundances of isotopes in a sample. Although different types exist, they all work on the same basic principle.

The mass spectrometry process involves four main stages:

1. Sample introduction
   The sample is placed into the mass spectrometer.

2. Vaporisation and ionisation
   The sample is vaporised (turned into a gas) and then ionised to form positive ions.

3. Acceleration and separation
   The ions are accelerated using an electric field. Heavier ions move more slowly and are harder to deflect than lighter ions, so ions of different isotopes become separated.

4. Detection
   Ions are detected as they reach the detector. Each ion that arrives adds to the signal, so the more abundant an isotope is, the larger its signal will be.

Mass-to-charge ratio

The mass spectrometer measures the mass-to-charge ratio ($m/z$) of each ion:

For ions with a single positive charge (which is most common), this ratio equals the relative isotopic mass. The results are displayed as a mass spectrum.

Interpreting a mass spectrum

Let's look at the mass spectrum of chlorine:

This spectrum reveals two distinct isotopes:

• Chlorine-35 ($m/z = 35$): 75.78% abundance
• Chlorine-37 ($m/z = 37$): 24.22% abundance

Calculating relative atomic mass

The calculation method

Once you know the percentage abundances and isotopic masses, you can calculate relative atomic mass using:

$A_r = \frac{\sum(\text{abundance} \times \text{isotopic mass})}{100}$

For an element with two isotopes:

$A_r = \frac{(\text{abundance}_1 \times \text{mass}_1) + (\text{abundance}_2 \times \text{mass}_2)}{100}$

Worked example: chlorine

Accurate isotopic masses

If you're given accurate relative isotopic masses (like 34.968852... for $^{35}$Cl), use these instead of mass numbers for more precise calculations. However, the method remains exactly the same.

Additional notes on relative atomic mass values

Modern periodic tables sometimes show relative atomic mass as a range rather than a single value for some elements. This is because isotopic abundances can vary slightly depending on where the sample originated. The International Union of Pure and Applied Chemistry (IUPAC) reviews these values every two years.

Remember!