To effectively interpret the course of a reaction in the presence of a mixture of components, such as in the cell, one needs to account for the free energies of the contributing components. This is accomplished by calculating total free energy which is comprised of the individual free energies. In order to carry out these calculations one needs to have a reference state from which to calculate free energies. This reference state, termed the standard state, is chosen to be the condition where each component in a reaction is at 1M. Standard state free energies are given the symbol: G°.
The partial molar free energy of any component of the reaction is related to the standard free energy by the following:
G = G° + RTln[X]
From this equation one can see that when the component X, or any other component, is at 1M the ln[1] term will become zero and:
G = G°
The utility of free energy calculations can be demonstrated in a consideration of the diffusion of a substance across a membrane. The calculation needs to take into account the changes in the concentration of the substance on either side of the membrane. This means that there will be a ΔG term for both chambers and, therefore, the total free energy change is the sum of the ΔG values for each chamber:
Equation for total free energy change
This last equation indicates that if [A]2 is less than [A]1 the value of ΔG will be negative and transfer from region 1 to 2 is favored. Conversely if [A]2 is greater than [A]1 ΔG will be positive and transfer from region 1 to 2 is not favorable, the reverse direction will be.
One can expand upon this theme when dealing with chemical reactions. It is apparent from the derivation of ΔG values for a given reaction that one can utilize this value to determine the equilibrium constant, Keq. As for the example above dealing with transport across a membrane, calculation of the total free energy of a reaction includes the free energies of the reactants and products:
ΔG = G(products) - G(reactants)
Since this calculation involves partial molar free energies the ΔG° terms of all the reactants and products are included. The end result of the reduction of all the terms in the equation is:
Standard free energy relation to reactant and product concentrations
When the above equation is used for a reaction that is at equilibrium the concentration values of A, B, C and D will all be equilibrium concentrations and, therefore, will be equal to Keq. Also, when at equilibrium ΔG = 0 and therefore:
0 = ΔG° + RTlnKeq
Equation of equilibrium constant (Keq) relationship to free energy change
This demonstrates the relationship between the free energy values and the equilibrium constants for any reaction.