The compressibility factor for nitrogen at 330 K and 800atm is 1.90 and at 570 K and 200 atm is 1.10. A certain mass of N2 occupies a volume of 1 dm3 at 330 K and 800 atm. calculate volume occupied by same quantity of N2 gas at 570 K and 200atm:

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The compressibility factor for nitrogen at 330 K and 800atm is 1.90 and at 570 K and 200 atm is 1.10. A certain mass of N₂ occupies a volume of 1 dm³ at 330 K and 800 atm. calculate volume occupied by same quantity of N₂ gas at 570 K and 200atm:

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1 L

2 L

3 L

4 L

answer is D.

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Detailed Solution

$\begin{matrix} Z = \frac{PV}{nRT}; 1 .90 = \frac{1 \times 800}{n \times R \times 330} \\ n = \frac{1 \times 800}{1 .90 \times R \times 330} \\ Z = 1 .10 = \frac{V \times 200}{n \times R \times 570} \\ 1 .10 = \frac{V \times 200 \times 1 .90 \times R \times 330}{800 \times R \times 570} \\ V = 4 L \end{matrix}$