Chemistry - Real Gas Question with Solution | TestHub

The density of a real gas can be expressed as a virial expansion in terms of pressure. The ideal gas law is a limiting case for real gases at very low pressures. To find the molar mass, we need to consider the ideal gas behavior, which occurs as pressure approaches zero.

The given density equation is:

$d=5P+0.2P^2+0.01P^3+\dots$

Divide by P:

$$\frac{d}{P}=5+0.2P+0.01P^2+\dots$$

Take the limit as $P\to 0$:

$$\underset{P\to 0}{\lim }\frac{d}{P}=5g/(L\cdot atm)$$

From the ideal gas law, $PV=nRT$. Since $n=\frac{m}{M}$ (where $m$ is mass and $M$ is molar mass) and $d=\frac{m}{V}$, we can derive:

$PV=\frac{m}{M}RT⟹\frac{m}{V}=\frac{PM}{RT}⟹d=\frac{PM}{RT}$

Rearranging for molar mass:

$M=\frac{d}{P}RT$

Substitute the limit value of $\frac{d}{P}$ and the given values for $R$ and $T$:

$M=(5g/(L\cdot atm))\times (0.08L\cdot atm/(K\cdot mol))\times (360K)$

$M=144g/mol$