# How do you find the molar mass of argon?

Aug 12, 2016

Grab a periodic table!

#### Explanation:

The thing to remember about the molar mass of an element is that it's actually given to you in the Periodic Table of Elements.

Every element listed in the periodic table has its relative atomic mass added to the bottom of its element box. An element's relative atomic mass, ${A}_{r}$, tells you the ratio that exists between the average mass of the atoms that make up an element and $\frac{1}{12} \text{th}$ of the mass of a single, unbound carbon-12 atom, i.e. one unified atomic mass unit, $\text{u}$.

Grab a periodic table and look for argon, $\text{Ar}$. You'll find it located in period 3, group 18. Notice the number added to the bottom of the element box. In this case, you have $39.948$, which means that the relative atomic mass of argon is

${A}_{r} = 39.948$

Here comes the cool part -- this value is also the element's molar mass! Here's why.

You get the relative atomic mass by dividing the atomic mass, ${m}_{a}$, by $\text{u}$, which means that you can get the atomic mass by multiplying the relative atomic mass by $\text{u}$

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{m}_{a} = {A}_{r} \cdot \text{1 u}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This means that the atomic mass of argon is equal to

${m}_{a} = 39.948 \cdot \text{1 u" = "39.948 u}$

By definition, a unified atomic mass unit, $\text{u}$, is equal to ${\text{1 g mol}}^{- 1}$.

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\text{1 u " = " 1 g mol}}^{- 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Therefore, the molar mass of argon, which is simply the mass of one mole of atoms of argon, is equal to

39.948 color(red)(cancel(color(black)("u"))) * "1 g mol"^(-1)/(1color(red)(cancel(color(black)("u")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("39.948 g mol"^(-1))color(white)(a/a)|)))

Long story short, the molar mass of an element can be found by taking its relative atomic mass listed in the periodic table and tagging along the units that correspond to molar mass, i.e. ${\text{g mol}}^{- 1}$.