Average Atomic Mass

Calculating the Average Atomic Mass

To calculate the average atomic mass (often referred to as the average atomic weight or simply atomic weight) of an element like carbon, you need to consider the natural abundance of its isotopes and their respective atomic masses. The average atomic mass is calculated as the weighted average of the atomic masses of the naturally occurring isotopes of the element.

Example: Calculating the Average Atomic Mass of Carbon

Carbon has two stable isotopes: carbon-12 (C-12) and carbon-13 (C-13). The atomic mass and natural abundance of these isotopes are as follows:

• Carbon-12 (C-12): Atomic mass ≈ 12.00 amu, Natural abundance ≈ 98.93%
• Carbon-13 (C-13): Atomic mass ≈ 13.003 amu, Natural abundance ≈ 1.07%

To calculate the average atomic mass of carbon, we use the formula:

$\text{Average atomic mass}=\left(\text{fractional abundance of isotope 1}\times \text{atomic mass of isotope 1}\right)+\left(\text{fractional abundance of isotope 2}\times \text{atomic mass of isotope 2}\right)+\dots$

For carbon:

$\text{Average atomic mass of carbon}=(0.9893\times 12.00\text{ amu})+(0.0107\times 13.003\text{ amu})$ $\text{Average atomic mass of carbon}=11.8664\text{ amu}+0.1391\text{ amu}$ $\text{Average atomic mass of carbon}\approx 12.01\text{ amu}$

Conclusion

The average atomic mass of carbon is approximately 12.01 amu.