Question

The compressiblity factor for nitrogen at $330\text{K}$ and $800\text{atm}$ is $1.90$ and at $570\text{K}$ and $200\text{atm}$ is $1.10$. A certain mass of $N_2$ occupies a volume of $1{\text{dm}}^3$ at $330\text{K}$ and $800\text{atm}$. Calculate volume occupied by same quantity of $N_2$ gas at $570\text{K}$ and $200\text{atm}$:

• A. $1\text{L}$
• B. $2\text{L}$
• C. $3\text{L}$
• D. $4\text{L}$

Answer 1

The correct option is D $4\text{L}$

$Z=\frac{PV}{nRT};\Rightarrow 1.90=\frac{1\times 800}{n\times R\times 330}\Rightarrow n=\frac{1\times 800}{1.90\times R\times 330}Z=1.10=\frac{V\times 200}{n\times R\times 570}\Rightarrow 1.10=\frac{V\times 200\times 1.90\times R\times 330}{800\times R\times 570}$
$\Rightarrow V=4\text{L}$