If the Van der Waal's equation for 1 mole of the gas is represented as , in place of , the correct r — States of Matter and Gaseous State Chemistry Question
Question
If the Van der Waal's equation for 1 mole of the gas is represented as $Z = \frac{PV}{RT} = 1 + B'P + C'P^2 + \dots$, in place of $Z = \frac{PV}{RT} = 1 + \frac{B}{V} + \frac{C}{V^2} + \dots$, the correct relation(s) is/are
💡 Solution & Explanation
Comparing the volume and pressure virial expansions: $Z = 1 + \frac{B}{V} + \frac{C}{V^2} = 1 + B'P + C'P^2$. At low pressures, substituting the ideal approximation $1/V \approx P/RT$ yields $Z \approx 1 + \frac{B}{RT}P + \frac{C}{(RT)^2}P^2$. Equating the linear coefficients gives $B' = \frac{B}{RT} \implies B = B'RT$. A more rigorous substitution using $P = \frac{RT}{V}(1 + \frac{B}{V} + \dots)$ into the pressure expansion yields $C' = \frac{C - B^2}{(RT)^2}$, which rearranges to $C = B^2 + C'(RT)^2$. Therefore, correct answer is A,C.