Partial molar Helmholtz free energy

Ak Partial molar Helmholtz free energy of species k J/mol... 

Fi partial molar Helmholtz free energy of mixing of a component /... 

Derivation of a partial molar Helmholtz free energy equation for an ideal solution will provide a tool by which ideal and real solution behavior can be differentiated. Specifically, we will make use of the fact that the partial molar enthalpy of a real solution will depend on the type and eoncentration of solutes in a solution while for an ideal solution, the partial molar enthalpy for a solute is independent of the solution composition [18]. As a brief proof of this ideal solution property, consider the defining Eq. (12) for the chemical potential of a solute, Y y, in an ideal solution ... 

A similar expression for the ideal partial molar Helmholtz free energy, Y, cannot be determined directly from the preceding equations because no method for determining the electrostatic potential of an ion in an ideal solution is known. Only if the ionic structure of an ideal solution was known, could the electrostatic potential of an ion in an ideal solution be determined from electrostatic theory. We will return to the thermodynamic method used earlier to determine the functional dependence... 

From earlier discussions, it was found that this free energy difference represents a difference in screened and unscreened partial molar Helmholtz free energies. Thus, the activity coefficient can be seen to result from the partial molar free energy, which is due to the screening of the counter ion atmosphere surrounding each ion in any real solution. This definition is consistent with the view that the activity coefficient predicts electrostatic screening in real solutions or the difference between real and ideal solution properties. 

Therefore, the chemical potential is the partial molar Gibbs energy as they share the same independent variables T and P. It is not the partial molar internal energy, Helmholtz free energy, and enthalpy. 

F, free energy, partial molar Helmholtz energy of component i. 

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