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The compressi...

Question

The compression factor (compressibility factor) for one mole of a Vander Waals gas at $0^{o} C$ and $100$ atmospheric pressure is found to be $0.5$ . Assuming that the volume of a gas molecule is negligible, calculate the Van der Waals constant $a$ .

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Solution

The compressibity factor is given by,
$Z = \frac{P V}{R T} 0.5 = \frac{100 \times V}{0.082 \times 273} V = 0.0117 L$
Vanderwaals equation,
$(P + \frac{a}{v^{2}}) (V - 0) = R T P V = R T - \frac{a}{V} o r a = R T V - {P V}^{2}$
$s u b s t i t u t i n g t h e a b o v e v a l u e s, A = (0.082 \times 0.1119 \times 273) - (100 \times 0.1119 \times 0.1119)$
$1.253 a t m L^{2} m o l^{- 2}$

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