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At the critical point of a van der Waals gas, the compressibility factor Z = P_c * V_c / (R * T_c) equals:

1. 3/8
2. 8/3
3. 3/4
4. 2/3

Correct answer: 3/8

Solution

Substituting P_c = a/(27b²), V_c = 3b, T_c = 8a/(27Rb) gives Z = [a/(27b²) * 3b] / [R * 8a/(27Rb)] = 3/8.

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