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 $570 K$ and $200 atm$ .

1 L

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2 L

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3 L

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4 L

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Solution

The correct option is D 4 L
$P V = Z n R T . ∴$ 'n' is const;
$\frac{P V}{Z T} = c o n s t ∴ \frac{P_{1} V_{1}}{Z_{1} T_{1}} = \frac{P_{2} V_{2}}{Z_{2} T_{2}}$
$\Rightarrow V_{2} = \frac{P_{1}}{P_{2}} \times \frac{Z_{2}}{Z_{2}} \times \frac{T_{2}}{T_{1}} \times V_{1}$
$= \frac{800}{200} \times \frac{1.1}{1.9} \times \frac{570}{330} = 4 L$

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