What is the volume occupied by 20.7 g of argon gas at a pressure of 1.04 atm and a temperature of 409 K?

Feb 28, 2016

$V$ $=$ $\frac{n R T}{P}$ $=$ ???

Explanation:

Pressure is moderate, temperature is elevated, and the gas is inert, so we would guess the ideal gas equation will give a good approximation:

$V$ $=$ $\frac{\left[\frac{20.7 \cdot \cancel{g}}{39.9 \cdot \cancel{g} \cdot \cancel{m o {l}^{-} 1}}\right] \cdot 0.0821 \cdot L \cdot \cancel{a t m} \cdot \cancel{{K}^{-} 1} \cdot \cancel{m o {l}^{-} 1} \times 409 \cancel{K}}{1.04 \cdot \cancel{a t m}}$

$=$ ?? $L$

The difficult part of this question is choosing the appropriate gas constant $R$. Here, the use of
$R$ $=$ $0.0821 \cdot L \cdot a t m \cdot {K}^{-} 1 \cdot m o {l}^{-} 1$ gives appropriate units.

You should (I think) always be quoted these constants in an examination, but you have to be able to use them dimensionally. If you cancel out the units in tne above exprression you get an answer in $\text{litres}$ AS REQUIRED for volume. Of course, in an examination you will not be required to reproduce this dimensional treatment. I include it as a method of self-checking my answer. I wanted an answer in $\text{litres}$, I got an answer in $\text{litres}$.