How is the Gibbs energy of mixing of two perfect gases expressed?

The Gibbs energy of mixing for two perfect gases can be derived from thermodynamic principles that account for the entropy and the ideal mixing behavior of gases. For an ideal solution of two components A and B, the change in Gibbs energy upon mixing is related to the mole fractions of the components and their respective contributions to the system.

The correct expression for the Gibbs energy of mixing is derived from the formula for the maximum work obtainable from a reversible process, combined with the statistical considerations related to ideal gases. When two gases mix, the Gibbs energy change is influenced by the uncertainty (entropy) brought by the mixing process, which is mathematically represented by the natural logarithm of the mole fractions.

The formula expresses the Gibbs energy of mixing as:

Δ_mixG = nRT(x_A ln x_A + x_B ln x_B),

where n is the total number of moles of gas, R is the ideal gas constant, T is the temperature in Kelvin, and x_A and x_B are the mole fractions of gases A and B, respectively. This expression captures how the mixing of components affects the overall free energy of the system, reflecting both the entropic contribution due to mixing and the ratios of the components.

In thermodynamic terms, when gases mix,