The compressibility factor for nitrogen at 330 K and 800 atm is 1.90 and at 570

Question

The compressibility factor for 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 same quantity of

N_{2}

gas at 750 K and 200 atm.

Options:

A . 1 L

B . 2 L

C . 3 L

D . 4 L

Answer: Option D
:
D

Z = \frac{P V}{n R T} \Rightarrow 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 = 4L

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