# 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?

Feb 3, 2016

$\text{12.18 u}$

#### 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.

$\textcolor{b l u e}{{\text{avg. atomic mass" = sum_i ("isotope"_i xx "abundance}}_{i}}$

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 $100$ atoms with an atomic mass of $\text{12.00 u}$ and $10$ atoms with an atomic mass of $\text{14.00 u}$.

The total number of atoms in the sample will thus be

$100 + 10 = \text{110 atoms}$

The decimal abundances for the two isotopes will be

$\left(100 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atoms"))))/(110color(red)(cancel(color(black)("atoms}}}}\right) = 0.90909 \to$ for the first isotope

$\left(10 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atoms"))))/(110color(red)(cancel(color(black)("atoms}}}}\right) = 0.090909 \to$ for the second isotope

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

$\text{avg atomic mas" = "12.00 u" xx 0.90909 + "14.00 u} \times 0.090909$

$\text{avg. atomic mass " = " 12.18181 u}$

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")