# How would you find the average atomic mass of sulfur from the following data: S-32 95.002% (31.972), S-33 0.76% (32.971), S-34 4.22% (33.967), and S-36 0.014% (35.967)?

Oct 26, 2015

$\text{32.063 u}$

#### Explanation:

The average atomic mass of a chemical element is calculated by taking into account the atomic masses of its naturally occuring isotopes and their respective abundances.

color(blue)("avg. atomic mass" = sum_i("isotope"_i xx "abundance"_i))

In your case, the average atomic mass of sulfur will be calculated using the given atomic masses of its four isotopes and their respective decimal abundance, which is simply the percent abundance divided by $100$.

So, you know that you have

""^32"S: " "31.972 u" -> 95.002% abundance
""^33"S: " "32.971 u" -> 0.76% abundance
""^34"S: " "33.967 u" -> 4.22% abundance
""^36"S: " "35.967 u" -> 0.014% abundance

This means that the average atomic mass of sulfur will be

$\text{avg. atomic mass" = "31.972 u" xx 0.95002 + "32.971 u" xx 0.0076 + "33.967 u" xx 0.0422 + "35.967 u} \times 0.00014$

"avg. atomic mass" = color(green)("32.063 u")