Chemistry - Real Gas Question with Solution | TestHub

The free volume for a real gas is given by $V_{free}=V-nb$, where $V$ is the container volume, $n$ is the number of moles, and $b$ is the van der Waals constant.

Given:

Volume of one gas molecule $=25\times 10^{-23}{\mathrm{cm}}^3$

Number of moles, $n=\frac{10}{6}$ mol

Container volume, $V=10\mathrm{L}$

Avogadro's number, $N_A=6\times 10^{23}$

The van der Waals constant $b$ represents the excluded volume per mole and is approximately $4\times N_A\times (volumeofonemolecule)$

First, calculate $b$:

$b=4\times N_A\times (volumeofonemolecule)$

$b=4\times (6\times 10^{23}molecules/mol)\times (25\times 10^{-23}{\mathrm{cm}}^3/molecule)$

$b=4\times 6\times 25{\mathrm{cm}}^3/mol$

$b=600{\mathrm{cm}}^3/mol$

Convert $b$ to liters per mole:

$1\mathrm{L}=1000{\mathrm{cm}}^3$

$b=\frac{600{\mathrm{cm}}^3/mol}{1000{\mathrm{cm}}^3/\mathrm{L}}=0.6L/mol$

Now, calculate the free volume:

$V_{free}=V-nb$

$V_{free}=10\mathrm{L}-\left(\frac{10}{6}mol\right)\times (0.6L/mol)$

$V_{free}=10\mathrm{L}-(10\times 0.1)\mathrm{L}$

$V_{free}=10\mathrm{L}-1\mathrm{L}$

$V_{free}=9\mathrm{L}$

The free volume is $9\mathrm{L}$.