The Dependence of Free Energy on Pressure

In this section we will discuss how pressure effects free energy. For and ideal gas, enthalpy does not depend on pressure but entropy does depend on pressure because of its dependence of volume. Pressure will effect free energy because of G = H - TS. For example, there is a volume of 10L of an ideal gas. If we made the volume bigger then the entropy will be greater because it has more positions available for its molecules. At a given temperature of an ideal gas

                S_{large volume} > S_{small volume}

and since pressure and volume are related the

                S_{low pressure} > S_{high pressure}

        To show how entropy and the free energy of an ideal gas depend on its pressure, we will consider it through the equation:

                G = G° + RT ln(Q)

where Q is the reaction quotient (from the law of mass action), T is the temperature in Kelvin, R is the gas law constant 8.3145 J/K/mo, G° is the free energy change for the reaction with all reactants and products at a pressure of 1 atm and G is free energy for pressures of reactants and products.

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