If you have ever wondered how we end up with strange decimal values like 35.5 for chlorine on the periodic table, you are not alone. This article will show you how to calculate relative atomic mass from isotopic data, step-by-step. This key concept is covered in Module 2: Foundations in Chemistry (2.1.1.d) of the OCR specification as well as in the equivalent modules of other exam boards.

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What Is Relative Atomic Mass?

Relative atomic mass (Ar) is a weighted average of the masses of all the isotopes of an element, based on their abundance.

Because most elements exist as a mix of isotopes, the Ar is usually not a whole number.

Just as a reminder, isotopes are atoms of the same element that have the same number of protons but a different number of neutrons.

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Key Formula

To calculate relative atomic mass:

Relative atomic mass=∑(isotopic mass×percentage abundance)/100

Note: This formula assumes the abundances are given as percentages. If given as ratios or decimals, adjust accordingly.

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Worked Example: Calculate the relative atomic mass of chlorine

Chlorine has two isotopes:

• Chlorine-35 (mass = 35, abundance = 75%)
• Chlorine-37 (mass = 37, abundance = 25%)

Step 1: Multiply each mass by its abundance

(35×75)=2625

(37×25)=925

Step 2: Add the results 2625+925=3550

Step 3: Divide by 100 3550/100=35.5

Answer: The relative atomic mass of chlorine is 35.5

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Common Mistakes to Avoid

• Mixing up the masses and abundances

• Forgetting to divide by 100 (if using %)

• Rounding too early – always round at the end

Exam Questions

Typical exam questions include:

• Using mass spectrometry data to determine the relative abundance of the isotopes. This can then be used to calculate relative isotopic masses using the formula above.
• Finding the percentage abundance of two isotopes when the relative atomic mass is known. See below an example.

Example: Bromine has two stable isotopes:

• Br-79 (relative mass = 78.918)
• Br-81 (relative mass = 80.916)

The relative atomic mass of bromine is 79.90.

Calculate the percentage abundances of the two isotopes. Give your answers to 2 decimal places.

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