The virial equation of state uses coefficients that account for molecular interactions. Which coefficients are used?

• A. Virial coefficients
• B. Ideal gas law
• C. Clausius-Clapeyron relation
• D. Van der Waals equation

Answer: (A)

The main idea is that the virial equation uses temperature-dependent virial coefficients to account for intermolecular forces and finite-molecule effects, adding corrections to the ideal gas behavior. In this approach the compressibility factor Z = PV/RT is written as a series: Z = 1 + B(T)/V_m + C(T)/V_m^2 + D(T)/V_m^3 + ..., or equivalently P = RT/V_m [1 + B(T)/V_m + C(T)/V_m^2 + ...]. Here B, C, D, and so on are virial coefficients that reflect two-body, three-body, and higher-order interactions among molecules; their values change with temperature and can be obtained from experiments or molecular theories.

This framework distinguishes itself from the ideal gas law, which would give Z = 1 with no corrections, and from the Van der Waals equation, which uses specific parameters a and b rather than a systematic series of coefficients. It also isn’t about phase equilibria like the Clausius-Clapeyron relation.