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Chapter 5

# We say that such an expression melting temperature

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Unformatted text preview: A + nB) [xA ln(xA) + xB ln(xB)] If the solution is not ideal, then: aA = PA / PA* = gA xA and aB = PB / PB* = gB xB and ΔGmixreal = RT (nA + nB) [xA ln(aA) + xB ln(aB)] = RT (nA + nB) [xA ln(γA xA) + xB ln(γB xB)] ΔGmixreal = RT (nA + nB) [xA ln(xA) + xB ln(xB)] + RT (nA + nB) [xA ln(γA) + xB ln(γB)] ΔGmixreal = ΔGmixid + RT (nA + nB) [xA ln(γA) + xB ln(γB)] Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 174 We define the excess free energy of mixing of a solution, the difference between the free energy of mixing of that solution and that of the corresponding ideal solution: ΔGmixexcess = RT (nA + nB) [xA ln(γA) + xB ln(γB)] Note that this quantity provides a measure of the departure of the real solution from ideal behavior and can be easily calculated through the knowledge of partial pressures of components A and B at a given mole fraction xA if one knows the partial pressure of pure components A and B since γA = PA / xA PA* and γB = PB / xB PB*. Obviously, the activity coefficients are equal to one if the solution is ideal or if each component obeys Raoult’s law. Think about what you can say about the relationship between the value of γ (larger or smaller than unity), and whether the components A and B like each other or dislike each other in the mixed liquid state. Recall that the fugacity coefficient was concerned with similar issues for real gases. N.B. You should note that the activity and activity coefficients were defined assuming the refere...
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