# A sample of element X contains 100 atoms with a mass of 12.00 and 10 atoms with a mass of 14.00. What is the average atomic mass (in amu) of element X?

##### 1 Answer

#### Explanation:

The **average atomic mass** of an element is calculated by taking the **weighted average** of the atomic masses of its stable isotopes.

In other words, each stable isotope will contribute to the average mass of the element **proportionally** to its *abundance*.

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

To calculate an isotope's *decimal abundance*, you need to divide the number of atoms of that isotope by the **total number of atoms** present in the sample.

In your case, you know that the sample contains

The total number of atoms in the sample will thus be

#100 + 10 = "110 atoms"#

The decimal abundances for the two isotopes will be

#(100 color(red)(cancel(color(black)("atoms"))))/(110color(red)(cancel(color(black)("atoms")))) = 0.90909 -># for the first isotope

#(10color(red)(cancel(color(black)("atoms"))))/(110color(red)(cancel(color(black)("atoms")))) = 0.090909 -># for the second isotope

This means that the average atomic mass of the element will be equal to

#"avg atomic mas" = "12.00 u" xx 0.90909 + "14.00 u" xx 0.090909#

#"avg. atomic mass " = " 12.18181 u"#

I think I'll leave this rounded off to four sig figs, the number of sig figs you have for the atomic masses of the two isotopes

#"avg. atomic mass " = color(green)(" 12.18 u")#