# What is the average atomic mass of an element if, out of 100 atoms, 5 have a mass of 176 amu, 19 have a mass of 177 amu, 27 have a mass of 178 amu, 14 have a mass of 179 amu, and 35 have a mass of 180 amu?

Jul 3, 2018

$\text{Average Atomic Mass" = 178.55 color(white)(l) "amu}$

#### Explanation:

The $\text{Average Atomic Mass}$ of an element is defined as "the weighted average mass of all naturally-occurring (occasionally radioactive) isotopes of the element." (and hence the name "average") [1]

Dividing the sum of the product of the $\textcolor{p u r p \le}{\text{relative atomic mass of each of the isotope}}$ and $\textcolor{g r e y}{\text{the occasion of their presence in the sample}}$ by $\text{the sum of atoms in the sample}$ gives the weighted average of the relative atomic mass.

$\text{Average Atomic Weight}$
$= \frac{\textcolor{g r e y}{5} \times \textcolor{p u r p \le}{176} + \textcolor{g r e y}{19} \times \textcolor{p u r p \le}{177} + \textcolor{g r e y}{27} \times \textcolor{p u r p \le}{178} + \textcolor{g r e y}{14} \times \textcolor{p u r p \le}{179} + \textcolor{g r e y}{35} \times \textcolor{p u r p \le}{180}}{\textcolor{b l a c k}{100}}$
$= 178.55 \textcolor{w h i t e}{l} \text{amu}$

Reference
[1] Vitz, Ed, et al. “4.13: Average Atomic Weights.” Chemistry LibreTexts, Libretexts, 5 Sept. 2017,
chem.libretexts.org/Textbook_Maps/General_Chemistry/Book:_ChemPRIME_(Moore_et_al.)/04The_Structure_of_Atoms/4.13:_Average_Atomic_Weights.