A certain quantity of real gas occupies a volume of 0.15 ${dm}^{3}$ at 100 atm and 500 K when its compressibility factor is 1.07. Its volume at 300 atm and 300K When its compressibility factor is 1.4 is 392 x 10^-x dm³. Then x is _______

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answer is 4.

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Detailed Solution

$Z = \frac{P V}{n R T}; n = \frac{P V}{Z R T}$

$Z_{1} = 1.07, P_{1} = 100 a t m, V_{1} = 0.15 L, T_{1} = 500 K$

$Z_{2} = 1.4, P_{2} = 300 a t m, T_{2} = 300 K, V_{2} = ?$

$\frac{P_{1} V_{1}}{Z_{1} R T_{1}} = \frac{P_{2} V_{2}}{Z_{2} R T_{2}} = n \Leftrightarrow V_{2} = \frac{1.4}{1.07} \times .03 = 392 \times 10^{- 4} d m^{3}$

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