For of a real gas at a low pressure and moderate temperature, the van der Waals equation simplifies — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

At low pressure, the volume $V_m$ is relatively large, so the excluded volume '$b$' can be neglected ($V_m - b \approx V_m$). The van der Waals equation becomes $(P + \frac{a}{V_m^2})V_m = RT \implies PV_m + \frac{a}{V_m} = RT \implies PV_m = RT - \frac{a}{V_m}$. Dividing by $RT$ gives $Z = 1 - \frac{a}{V_mRT}$.