Lecture 8: Theory of Chemical Equilibria Dr. Ronald M. Levy Statistical Thermodynamics.

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Lecture 8: Theory of Chemical Equilibria Dr. Ronald M. Levy Statistical Thermodynamics

Chemical reaction in solution (or gas phase): reactants products Want to find a statistical mechanics expression for the concentrations of species A, B, C, D at equilibrium. Consider the Helmoltz free energy of the solution: Change of free energy upon infinitesimal change of conditions: For chemical reactions occurring at fixed T, V only composition changes. McQuarrie, chapter 9.

Introduce progress variable,, for the reaction. (If A moles of A react, with B moles of B, C moles of C and D moles of D are generated.) Define: Where j is positive for products and negative for reactants. Then: At equilibrium: So:

We have shown that: Substituting... constant (depends only on C° and T ) Standard free energy of the reaction (change in free energy of the system upon unitary progress of the reaction at standard concentrations at a given temperature) Therefore:

Remember that: Effective potential energy of solute i in solution. Given a model for the effective potential energy we can compute the molecular partition functions and predict the binding constant for the reaction. Then: