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Chapter 5

# So we conclude asta p alta p rta ln xa or

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Unformatted text preview: Raoult’s law, you see that γA = 1. Similarly, when B does not obey Raoult’s law, we can define an activity coefficient for B, γB such that: PB = γB xB PB*. These activity coefficients are associated with quantities, which we call activities and which allow us to define the chemical potential of a component in a mixture, which is not ideal (again analogy with fugacity and fugacity coefficients in the case of real gases). To see how we define activity, recall that we can write the chemical potential of A as: µAL(T, PA) = µA V(T, P ) + RT ln(PA / P ) when A is in a mixture and ∅ ∅ ∅ µA*L(T, PA*) = µA V(T, P ) + RT ln(PA* / P ) when A is pure. ∅ ∅ ∅ Therefore, combining these two equations, we write: µAL(T, PA) = µA*L(T, PA*) + RT ln(PA / PA*) If Raoult’s law is obeyed for A, we know that PA / PA* = xA Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 173 If Raoult’s law is not obeyed for A, we have defined the activity coefficient γA such that PA / PA* = γA xA We now define the activity of component A in a mixture as aA = PA / PA*. We therefore conclude that the activity of a component in a mixture is equal to the mole fraction of that component in the mixed liquid if that component obeys Raoult’s law. If the component does not obey Raoult’s law, the activity is equal to the product of the mole fraction by the activity coefficient. Therefore, we write in general, aA = PA / PA* and aB = PB / PB* and ΔGmix = RT (nA + nB) [xA ln(aA) + xB ln(aB)] If the solution is ideal, then aA = PA / PA* = xA and aB = PB / PB* = xB and ΔGmixid = RT (n...
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