Question

The compressibility factor of $N_2$ at 330 K and 800 atm is 1.90 and at 570K and 200 atm is 1.10. A certain mass of $N_2$ occupies a volume of 1 dm${}^3$ at 330 K and 800 atm. Calculate the volume of $N_2$ gas at 570 K and 200 atm.

• A. 1 L
• B. 2 L
• C. 3 L
• D. 4 L

Answer 1

The correct option is D 4 L

$Z=\frac{P{V}_m}{nRT}\Rightarrow 1.9=\frac{1\times 800}{n\times R\times 330}$
$n=\frac{1\times 800}{1.9R\times 330}$
$Z=1.1=\frac{V\times 200}{nR\times 570}$
$V=4L$