1. Lecture 8: Theory of Chemical Equilibria Dr. Ronald M. Levy ronlevy@temple.edu Statistical Thermodynamics

2. 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.

3. 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:

4. 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:

5. 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: