Equilibrium Constants Relation to Energy and Entropy Changes

2 Equilibrium Constants Relation to Energy and Entropy Changes 

Both cyclopropane and propene are stable at room temperature for extended periods. At elevated temperatures, however, the forward and backward reaction rates ultimately produce an equilibrium between cyclopropane and propene. This equilibrium is characterized by an equilibrium constant 

As noted above, not every molecule with an energy equal to the activation energy reacts the energy has to be in the correct bonds to form the transition state. For this reason, the preexponential factors are proportional to the ratio of the number of states available  

So the equilibrium constant is a simple function of the difference in energy and the difference in number of available states between the reactants and the products. We can also understand Equation 4.47 by forgetting about the intermediate state, and just applying the Boltzmann distribution directly to the reactants and products. 

For an isomerization reaction such as this one, the change in volume A V 0. In a more general reaction done under constant-pressure conditions, we would have to add the work done on the surroundings (PAV discussed in Section 3.2) to the energy difference between the reactants and products, and we would replace AE with the enthalpy difference A H = AH+PAV. Now take the natural log ofboth sides of Equation 4.47, and convert Q into the entropy using Equation 4.29  

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