How is the Gibbs energy of mixing expressed for two liquids forming an ideal solution?

The Gibbs energy of mixing for two liquids forming an ideal solution is expressed with the equation that incorporates the mole fractions and their natural logarithms, which reflects the change in free energy associated with the mixing process. In an ideal solution, the mixing of two different components (such as liquids A and B) is characterized by the contributions of each component's fraction to the overall entropy of mixing.

The expression includes 'n' as the total number of moles, 'R' as the universal gas constant, and 'T' as the temperature in Kelvin. The terms (x_A) and (x_B) represent the mole fractions of the respective components.

The logarithmic terms ((x_A \ln x_A + x_B \ln x_B)) are crucial since they quantitatively describe how the configuration of the molecules and their interactions lead to an increase in entropy when mixed. In essence, this term captures how the disorder (effectively, the entropy) of the mixture is greater than that of the pure components, which is a key concept in thermodynamics.

This relationship aligns with the principles of statistical mechanics, where the multiplicity of configurations increases when different species are mixed, thus contributing positively to the entropy of the system. As