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For example if we consider a solution of a and b a

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Unformatted text preview: nd’s Notes: Chapter 5 - The Properties of Simple Mixtures 166 We can relate the chemical potential of A in the vapor phase at temperature T and pressure PA* to that of component A in its standard state (i.e. pure and at pressure P = 1 bar) by: ∅ µA*V(T,PA*) = µA V(T, P ) + RT ln(PA* / P ) ∅ ∅ ∅ The same can be done for the liquid- vapor equilibrium for B: µB*L(T, PB*) = µB*V(T, PB*) = µB V(T, P ) + RT ln(PB* / P ) ∅ ∅ ∅ If we now consider components A and B in the mixture, where mixing occurs between A and B both in the liquid and in the vapor phases, and where for each component, their chemical component in the liquid phase is equal to that in the vapor phase, we have: µAL(T, PA) = µAV(T, PA) = µA V(T, P ) + RT ln(PA / P ) and ∅ ∅ ∅ µBL(T, PB) = µBV(T, PB) = µB V(T, P ) + RT ln(PB / P ) ∅ ∅ ∅ Note that in the previous two equations, we are not using the * notation, since the components are no longer pure. Also, note that the terms PA and PB correspond to the partial pressures of components A and B in the mixed vapor phase above the mixed liquid at temperature T. The Gibbs free energy of mixing nA moles of A with nB moles of B is equal to: ΔGmix = [nA µAL(T, PA) + nB µBL(T, PB)] - [nA µA*L(T, PA*) + nB µB*L(T, PB*)] which we can rewrite as: Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 167 ΔGmix = nA [µAL(T, PA) - µA*L(T, PA*)] + nB [µBL(T, PB) - µB*L(T, PB*)] Using the expressions for these various terms, we get: ΔGmix = RT [nA ln(PA / PA*) + nB ln(PB / PB*)] The above...
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