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The compressibility factor Z of a Van der Waals gas is 0.5 at 27 degrees C and 24 atm. Given b = 0.10 L/mol and R = 0.08 L-atm/(K-mol), find the Van der Waals constant a in atm-L²/mol².

1. 2.4
2. 4.0
3. 3.6
4. 9.0

Correct answer: 9.0

Solution

Molar volume V = ZRT/P = 0.5 L/mol. Substituting into the Van der Waals equation: (24 + a/0.25)(0.4) = 24, which gives 24 + 4a = 60, so a = 9.0 atm-L²/mol².

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