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The compressibility factor for 1-mole of a Vander Waal’s gas at 0°C and 100 atm pressure is found to be 0.5. Assuming that volume of gas molecules is negligible, calculate the Vander Waal’s constant a. Give your answer by multiplying it 4 i.e. 4a?
Given R=0.0821 litre atm/mole.K

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answer is 5.

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Detailed Solution

For 1-mole of the gas
$\begin{array}{l} Z = \frac{{PV}_{m}}{RT}, 0.5 = \frac{100 . V_{m}}{22.4}, {PV}_{m} + \frac{a}{V_{m}} = RT, 11.2 + \frac{a}{0.112} = 22.4 \\ \frac{a}{0.112} = 11.2, a = 1.25, 4 a = 5 \end{array}$

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