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Substance j in a mixture g j t

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Unformatted text preview: fined by n1, n2, ..., nJ,... Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 155 Examples of such partial molar quantities are: VJ The partial molar volume of substance J (volume occupied by one mole of J in the mixture with all other substances present) € The partial molar enthalpy of substance J SJ € HJ The partial molar entropy of substance J UJ The partial molar energy of substance J € We can apply all previously derived thermodynamic expressions to the € partial molar quantities. For example, we can write an expression for the change in the chemical potential of substance J in a mixture with temperature and pressure as: d GJ = dµ J = − SJdT + VJdP where: € $∂G ' $∂G ' SJ = −& J ) and VJ = & J ) % ∂T (P % ∂P ( T We can also derive the corresponding Maxwell equation for that substance: € $∂S ' $ ∂V ' −& J ) = & J ) % ∂P ( T % ∂T (P The other Maxwell equations are obtained in a similar fashion using € expressions for: Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 156 d UJ , d HJ , and dAJ € Similarly, we can derive the Gibbs- Helmholtz equation for substance J in a € € mixture: # # G && % ∂% J ( ( % $ T ' ( = − HJ % ∂T ( T2 % ( $ 'P In the same way as thermodynamic equations allowed us in Chapters 2 and € 3 to describe the evolution of a system and of its properties during a process, relationships between various partial molar properties allow us to understand evolution of the properties of a given substance within a mixture during any process. Let us now focus on how we can actually derive values for the partial molar properties of substances in a mixture. We are going to consider the “thermodynamic quantity” of interest to be the volume for a mixture consisting of two components A and B, so we will see how we can determine the partial molar volume of substances A and B in the mixture. Again, as was implied above,...
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