Relative Atomic Mass

Atoms are incredibly small, and their actual masses are also very small. Therefore, we compare the masses of atoms using a relative scale, known as relative atomic mass (Ar). This allows us to compare the masses of different atoms in a more meaningful way.

To standardise this comparison, we use the carbon-12 atom as a reference point. The relative atomic mass of an atom is expressed as a ratio, with one atomic mass unit being equal to 1/12th of the mass of a carbon-12 atom. As the relative atomic mass is a ratio, it has no units.

For example, the relative atomic mass of hydrogen is 1. This means that 12 hydrogen atoms have the same mass as 1 carbon atom. Similarly, magnesium has a relative atomic mass of 24, which means that magnesium atoms are twice as heavy as carbon atoms.

Calculating Relative Atomic Mass

The equation to calculate the relative atomic mass of an isotope is:

Relative atomic mass = [(mass number of isotope 1 multiplied by the percentage of isotope 1) plus (mass number of isotope 2 multiplied by the percentage of isotope 2)] divided by 100.

Example

Let’s consider the two isotopes of chlorine:

  • \mathrm{}^{17}_{35}Cl chlorine-35
  • \mathrm{}^{17}_{37}Cl chlorine-37

The abundance of chlorine-35 is 75% and the abundance of chlorine-37 is 25%. So, to calculate this:

A_{r}=\frac{(35\times75)+(37\times25)}{100}

A_{r}=\frac{2625+925}{100}

=35.5

Example

The element magnesium has three natural isotopes:

  • magnesium-24
  • magnesium-25
  • magnesium-26

Let’s assume that 78.99% of all magnesium atoms are magnesium-24, 10% are magnesium-25, and 11.01% are magnesium-26.

Calculate the relative atomic mass of magnesium to three significant figures

The atomic masses of these isotopes are 24, 25 and 26 respectively.

We can now use this information to calculate the relative atomic mass of magnesium:

A_{r}=\frac{(24\times78.99)+(25\times10)+(26\times11.01)}{100}A_{r}=\frac{(24\times78.99)+(25\times10)+(26\times11.01)}{100}

A_{r}=\frac{1895.76+250+286.26}{100}A_{r}=\frac{1895.76+250+286.26}{100}

= 24.3

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