# A 248 mL gas sample has a mass of 0.433 g at a pressure of 745 mmHg and a temperature of 28°C. What is the molar mass of the gas?

Oct 30, 2016

The molar mass of the gas is 44.0 g/mol.

#### Explanation:

We can use the Ideal Gas Law to solve this problem.

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

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

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

$m = \text{0.433 g}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{28 °C" = "301.15 K}$
P = 745 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg"))))= "0.9803 atm"
$V = \text{248 mL" = "0.248 L}$
M = ("0.433 g"× "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 301.15 color(red)(cancel(color(black)("K"))))/(0.9803 color(red)(cancel(color(black)("atm")))× 0.248 color(red)(cancel(color(black)("L")))) = "44.0 g/mol"