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Chapter 5

# Different compositions imply different chemical

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Unformatted text preview: S and V are the entropy and the volume of the whole system and the µJ are the chemical potentials for each of the substances “J” in the mixture and nJ are the number of moles of molecules of type “J” substance. The chemical potential of substance “J” should be viewed as the molar free energy of that substance within the mixture. As it will change with the composition of the mixture, this quantity is obviously different from the molar free energy (or the chemical potential) of the pure substance. Different compositions imply different chemical environments, thus different intermolecular interactions, molar volumes, molar entropies. From the above expression for dG, we can see mathematically that the chemical potential of a substance in a mixture is defined by: Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 154 # ∂G & µJ = % ( ∂nJ ' T,P,n \$ I(I≠J) The fact that µJ is defined as the partial of G with respect to nJ keeping T, P € and nI constant (I ≠ J), implies that the chemical potential of substance J is also equal to the change in the free energy of the system, when one adds one mole of substance J to that system (without changing the number of moles of any of the other substances in the mixture). Because of this mathematical definition of the chemical potential of a substance in a mixture, we could have also called µ J, the partial molar free energy. We can apply similar concepts to all other extensive functions we have so far defined and thereby define a partial molar quantity X J of an extensive thermodynamic function or variable X by: # ∂X & XJ = % ( \$ ∂nJ 'P,T,nI I≠J () This quantity is therefore equal to the change in property X for the system € when one mole of substance J is added to the mixture. It is also equal to the property X per mole of substance J in the mixture of composition de...
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