Question

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

Answer 1

The compressibility factor $Z=\frac{PVM}{nRT}$

$\Rightarrow 1.9=\frac{1\times 800}{n\times R\times 330}$

Rearrange above expression to obtain n.

$n=\frac{1\times 800}{1.9R\times 300}$

For the second set of conditions

$z=1.1=\frac{V\times 200}{nR\times 570}$

V = 4 L

Hence, the volume of $N_2$ gas at 570 K and 200 atm is 4 L.