# How do you calculate the molar mass of a gas?

Jan 4, 2015

The molar mass of a gas can be derived from the ideal gas law, $P V = n R T$, by using the definition of molar mass to replace $n$, the number of moles.

Molar mass is defined as the mass of a substance occupied by exactly $6.022 \cdot {10}^{23}$ of that respective gas' atoms (or molecules). Since we know that $6.022 \cdot {10}^{23}$ represents Avogadro's number, and is the equivalent of 1 mole, we can describe molar mass as being equal to

$M = \frac{m}{n}$, where

$m$ - the gas' mass in grams;
$n$ - the number of moles of gas;

We can therefore write that $n = \frac{m}{M}$, which can be used in the ideal gas law equation to get the value of the gas' molar mass

$P V = \frac{m}{M} \cdot R T \implies M = \frac{m R T}{P V}$, so

$M = m \cdot \frac{R T}{P V}$

Here's an example of how this would look in a problem:

An unknown gas has a mass of 153 g and occupies 15.0 L at a temperature of 300.0 K and a pressure of 2.00 atm. What is its molar mass?

$M = 153 g \cdot \frac{0.082 \frac{L \cdot a t m}{K \cdot m o l} \cdot 300.0 K}{2.00 a t m \cdot 15.0 L} = 125$ $\text{g/mol}$