Question

The compressibility factor for $N_2$ at $-{50}^{\circ }C$ and 800 atm pressure is 1.95 and at ${100}^{\circ }C$ and 200 atm, it is 1.10. A certain mass of nitrogen occupied one litre at $-{50}^{\circ }C$ and 800 atm. Calculate the volume occupied by the same quantity of $N_2$ at ${100}^{\circ }C$ and 200 atm.

[as the nearest integer in L]

Answer 1

We know that

$z=\frac{PV}{nRT}$

Given,

$1.95=\frac{800\times 1}{nR\times 223}.........\left(i\right)$

$1.10=\frac{200\times V}{nR\times 373}.........\left(ii\right)$

From equation (i) and (ii),

$\Rightarrow \frac{1.95}{1.10}=\frac{800}{200}\times \frac{1}{V}\times 373223$ $V=3.77L$

The nearest integer is 4 L.