# How would you find the molecular weight of an unknown gas?

Aug 19, 2016

I would determine the mass of a fixed volume of the gas at a known temperature and pressure and then use the Ideal Gas Law to calculate the molar mass.

#### Explanation:

EXAMPLE

The mass of an evacuated 255 mL flask is 143.187 g. The mass of the flask filled with an unknown gas at 25.0 °C and 265 Torr is 143.289 g.

Solution

The Ideal Gas Law is

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Since $n = \text{mass"/"molar mass} = \frac{m}{M}$, we can write the Ideal Gas Law as

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P V = \frac{m}{M} R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange this to get

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

$m = \text{143.289 g - 143.187 g" = "0.102 g}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{(25.0 + 273.15) K" = "298.75 K}$
P = 265 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.3487 atm"
$V = \text{0.255 L}$

M = ("0.102 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 298.15 color(red)(cancel(color(black)("K"))))/("0.3487" color(red)(cancel(color(black)("atm"))) × 0.255 color(red)(cancel(color(black)("L")))) = "28.1 g/mol"

The molar mass is 28.1 g/mol.

∴ The molecular mass is 28.1 u.