# (8.000x10^-1) g of a gas is collected in the lab and found to have a volume of (8.9000x10^-1) L when the pressure is (9.600x10^1) kPa and the temperature is (3.00x10^2) K. According to this collected data what is the molar mass of the gas?

May 6, 2017

According to these data, the molar mass of the gas is 23.4 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 $n = \frac{m}{M}$, we can rearrange this equation to get

$P V = \left(\frac{m}{M}\right) R T$

And we can solve this equation to get

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

m = 8.000 × 10^"-1"color(white)(l) "g"
$R = \text{8.314 kPa·L·K"^"-1""mol"^"-1}$
T = 3.00 × 10^2color(white)(l) "K"
P = 9.600 × 10^1 color(white)(l) "kPa "
V = 8.9000 × 10^"-1"color(white)(l) "L "
M = (8.000 × 10^"-1"color(white)(l)"g" × 8.314 color(red)(cancel(color(black)("kPa·L·K"^"-1")))"mol"^"-1" × 3.00 × 10^2 color(red)(cancel(color(black)("K"))))/(9.600 × 10^1 color(red)(cancel(color(black)("kPa"))) ×8.900 × 10^"-1" color(red)(cancel(color(black)("L")))) = "23.4 g/mol"