Question

The compressibility factor of nitrogen at 330 K and 800 atm is 1.90 and at 570 K and 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 occupied by the same quantity of $N_2$ gas at $570\text{K}$ and $200\text{atm}$.

• A. 1 L
• B. 2 L
• C. 3 L
• D. 4 L

Answer 1

The correct option is D 4 L

$PV=ZnRT.\therefore$ 'n' is const;
$\frac{PV}{ZT}=const\therefore \frac{P_1{V}_1}{Z_1{T}_1}=\frac{P_2{V}_2}{Z_2{T}_2}$
$\Rightarrow V_2=\frac{P_1}{P_2}\times \frac{Z_2}{Z_2}\times \frac{T_2}{T_1}\times V_1$
$=\frac{800}{200}\times \frac{1.1}{1.9}\times \frac{570}{330}=4L$