Which equation represents the entropy of mixing for two liquids in an ideal solution?

The equation that represents the entropy of mixing for two liquids in an ideal solution is expressed as Δ_mixS = -nR(x_A ln x_A + x_B ln x_B). This equation is grounded in the principles of statistical thermodynamics, where the entropy change associated with mixing arises from the increase in disorder as the two components are combined.

In this equation, n represents the total number of moles, R is the universal gas constant, and x_A and x_B are the mole fractions of the two components in the mixture. The natural logarithm function reflects how the mixing process increases the number of possible arrangements for the mixed components, contributing to the overall entropy increase.

When two different substances are mixed, there are more ways to arrange the molecules than when they are kept separate. This increase in the number of microstates corresponds to greater disorder, which is what entropy measures. The negative sign in the equation indicates that the entropy of the pure components is lower than that of the ideal mixture due to this increase in disorder when two different liquids mix.

The other equations do not correctly represent the entropy of mixing in the context of ideal solutions and do not incorporate the logarithmic factor essential to capturing the nature