Lecture 17 Classical Thermodynamics of Solutions Gibbs free

Lecture 17 Classical Thermodynamics of Solutions Ø Gibbs free energy of formation of solution Ø Ideal gas mixtures Ø Ideal, dilute and concentrated solutions Ø Excess functions

Gibbs free energy of mixing, GM XA mol of A + XB mol of B Since Therefore But Thus finally or

Ideal gas activity and GM Activity for a gas is Where is arbitrary. We can choose For which And the Gibbs free energy of mixing

Ideal gas - HM, and SM Since X is independent from temperature. From this the entropy of mixing of an ideal solution

Multicomponent condensed phases Chemical potential of a vapor For the solid In equilibrium, distributive equilibrium From which since in equilibrium

Ideal solution For ideal solution From which And

Dilute solution Pressure above dilute solute is proportional to its concentration From which Where Is the activity coefficient can be greater or smaller than one. It is 1 for ideal solutions.

Dilute solution - II Gibbs Duhem At constant T and P In terms of molar properties Thus for dilute solution of B in A

Dilute solution - III Recalling that And with Since activity coefficient is constant

Dilute solution - IV After differentiating the second term After integration since

Concentrated solutions Activity coefficient is not a constant any more However, for so-called regular solutions we still assume entropy of mixing same as for the ideal solution But the enthalpy of mixing will be not zero.

Excess functions Chemical potential of mixing For an ideal solution Which defines excess chemical potential of mixing Or in terms of partial molar from which