## Relative Atomic Mass

Relative Atomic Mass In chemistry, it is important to quantify particles. For the fact that the size of an atom is too small to be weighed practically, relative atomic mass is therefore used to represent the mass or weight of an atom of an element.

Definition: The relative atomic mass (symbol: Ar) of an element is the mass of one atom of the element compared with the mass of an atom of the carbon-12 isotope whose mass is exactly 12.

For naturally occurring elements with isotopes, the above definition is a little bit adjusted to accommodate the fact that each isotope of the element has a different mass.

The relative atomic mass of a naturally occurring element with isotopes can be defined as the weighted average of the masses of its isotopes compared with the mass of an atom of the carbon-12 isotope whose mass is taken to be exactly 12.

Note:

Relative atomic mass is a dimensionless quantity and so does not have a unit. It is measured using an instrument called mass spectrometer.

Isotopes of an element are atoms of the element with different masses. The atoms have the same number of protons but different neutrons.

Relative atomic mass is also called atomic weight.

The carbon-12 isotope is also known as the unified atomic mass unit - its atomic mass is exactly 12.

The relative atomic masses of elements are usually published by the International Union of Pure and Applied Chemistry (IUPAC) and are reprinted in a wide varieties of materials, including textbooks, commercial catalogues, periodic table, and wallcharts.

### Calculating Relative Atomic Mass of Elements with Isotopes

Some elements have been found to contain isotopes. The relative atomic mass of such element is determined by the masses of all the isotopes, and is closer to the mass of the more abundant isotope.

The relative atomic mass of these elements can be calculated using the formula:

Relative atomic mass = (A/100 x a) + (B/100 x b) + (C/100 x c)

Where A/100 (or A%) is the abundance of one of the isotopes with relative atomic mass a; B/100 is the abundance of another isotope with relative atomic mass b; C/100 is the abundance of the third isotope with relative atomic mass c.

Example 1: Oxygen has three isotopes 16O, 17O, and 18O with relative abundance 99.76%, 0.04%, and 0.20% respectively, calculate the relative atomic mass of oxygen.

Solution:

Relative atomic mass of 16O is 16 and its relative abundance is 99.76%; 17O – atomic mass 17, abundance 0.04%; 18O – atomic mass 18, abundance 0.20%.

Relative atomic mass of oxygen = (99.76/100 x 16) + (0.04/100 x 17) + (0.20/100 x 18)

= 15.9616 + 0.0068 + 0.036 = 16.0044

By tweaking the formula above you can also calculate the relative abundance of the isotopes if the relative atomic mass of the element and the atomic masses of the respective isotopes are known.

Example 2: Chlorine with relative atomic mass of 35.5 contains two isotopes 35Cl and 37Cl, what is the relative abundance of each isotope in a sample of chlorine?

Solution:

35.5 = (A/100 x 35) + ((100 – A)/100 x 37)

Note that if the abundance of the isotope of atomic mass 35 is A%, the abundance of the isotope of mass 37 will be (100 – A)%.

35.5 = 0.35A + (100 – A) x 0.37 35.5

= 0.35A + 37 – 0.37A 0.37A – 0.35A

= 37 – 35.5 0.02A = 1.5 A

= 1.5/0.02 = 75

Therefore, the abundance of the isotope of relative atomic mass 35.5 is 75% while that for the isotope 17Cl is 100 – 75 = 25%.