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The Equilibrium Constant

A chemical reaction will occur if the total free energy of the products is less than the total free energy of the reactants. (ie. The free energy change for the reaction is negative.) If the system containing the reactants and products is closed (if there is no input of reactants, for example), the concentration of reactants will decrease and the concentration of products will increase as the reaction proceeds. This will alter the state of the system and therefore alter the free energy change for the reaction (see equation 14, above).

The reaction will continue if the free energy change remains negative. Hence, the system proceeds down a free energy gradient with respect to composition and this gradient provides the driving force for the reaction to proceed. The system alters the quantities of reactants and products in response to the driving force until a minimum in free energy is reached and the gradient is zero. This is a point of equilibrium.

At equilibrium the free energy change for the reaction is equal to zero:

$$\displaylines{ \Delta G = \Delta G^\circ + RT\ln \left( {{{{p_C}} \over {{p_A}{p_B}}}} \right) \cr = 0 \cr} $$
Therefore

$$\displaylines{ \Delta G^\circ = - RT\ln {\left( {{{{p_C}} \over {{p_A}{p_B}}}} \right)_{equilibrium}} \cr = - RT\ln {K_P}. \cr}\;\;\;\;(15) $$     

For the composition at equilibrium, the quotient is equal to GP - the equilibrium constant for the reaction at constant pressure. We see that the equilibrium composition of the system is defined by the standard free energy change, ΔG°. Equation 15 provides a link between the thermodynamics of a reaction and its chemistry. ΔG° for a reaction is hence a very useful value to know.


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