For a van der Waals gas the critical compressibility factor $Z_{c} = \frac{P _{c} V _{c}}{R T _{c}}$ equals

Answer: B

Substituting

V_{c} = 3 b

P_{c} = a /27 b^{2}

and

T_{c} = 8 a /27 R b

gives

Z_{c} = \frac{( a /27 b ^{2} ) ( 3 b )}{R ( 8 a /27 R b )} = \frac{3}{8} = 0.375

, independent of the gas. Real gases show

Z_{c}

of about 0.27 to 0.30.