How to Calculate Relative Atomic Mass: Nerd Guide

Relative atomic mass (Ar) is a way of expressing the average mass of atoms of an element, taking into account the different isotopes and their abundances. It’s calculated based on the weighted average of the atomic masses of all the naturally occurring isotopes of that element.

This value is not always a whole number, because it’s an average.

Step-by-Step: How to Calculate Relative Atomic Mass

To calculate the relative atomic mass, use this formula:

Relative atomic mass = (isotope mass × abundance) + (isotope mass × abundance) ÷ 100

Here’s how to do it step by step.

Example: Chlorine

Chlorine has two main isotopes:

• Chlorine-35 with a mass of 35 and an abundance of 75%

• Chlorine-37 with a mass of 37 and an abundance of 25%

Step 1: Multiply each isotope’s mass by its percentage abundance

• (35 × 75) = 2625

• (37 × 25) = 925

Step 2: Add the results together

• 2625 + 925 = 3550

Step 3: Divide by 100

• 3550 ÷ 100 = 35.5

So, the relative atomic mass of chlorine is 35.5

Key Things to Remember

• Use actual percentage abundances (not decimals) when using the divide-by-100 method

• Always round your final answer to a suitable number of decimal places (usually 1 or 2)

• Units are atomic mass units (u) but you don’t usually need to write the unit for relative atomic mass in school exams

• This calculation only applies when an element has more than one isotope

Final Thought

Calculating relative atomic mass is all about working out the weighted average of the isotopes that make up an element. Once you know the masses and abundances, it’s a simple bit of multiplication and division. Practice with a few elements and it’ll become second nature — just remember the formula and work step by step.