# An experiment shows that a 252 mL gas sample has a mass of 0.433 g at a pressure of 760 mm Hg and a temperature of 34 degrees C. What is the molar mass of the gas?

Dec 2, 2016

Molar mass is $43.3 \textcolor{w h i t e}{.} g \cdot m o {l}^{- 1}$.

#### Explanation:

Gas law's shows that:

$p \cdot V = n \cdot R \cdot T$,

where $p$ is the pressure of gas, $V$ it's volume, $n$ the amount of gas, in mols, $R$ is the constant of gases, and $T$ is the absolute temperature of the gas.

In I.S. units, $R \approx 8.31 \textcolor{w h i t e}{.} J \cdot m o {l}^{- 1} \cdot {K}^{- 1}$.

Done molar mass is given by:

${M}_{r} = \frac{m}{n}$

we can write gas law's in the next form:

$p \cdot V = \frac{m}{M} _ r \cdot R \cdot T$,

and we obtain:

${M}_{r} = \frac{m \cdot R \cdot T}{p \cdot V} = \frac{0.433 g \cdot 8.31 J \cdot m o {l}^{- 1} \cdot {K}^{- 1} \cdot \left(34 + 273 , 15\right) K}{\frac{760}{760} \cdot 1.013 \cdot {10}^{5} P a \cdot 252 \cdot {10}^{- 6} {m}^{3}} =$
$= 43.3 g \cdot m o {l}^{- 1}$