At exactly the critical temperature, critical pressure, and critical volume, the theoretical critica — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

The critical constants for a van der Waals gas are $P_c = a / 27b^2$, $V_c = 3b$, and $T_c = 8a / 27Rb$. Substituting these into the compressibility factor formula $Z_c = P_c V_c / R T_c$, we get $(a/27b^2) \times 3b / [R \times (8a/27Rb)] = (a/9b) \times (27b/8a) = 3/8 = 0.375$.