The free energy of a reaction changes as pressure, concentration and temperature change. Some of these changes in the entropy term are described above in the entropy section. For the chemist interested in the driving force of a reaction, the concentration changes are of particular concern because the concentration of reactants decreases as a reaction proceeds. Standard conditions are more precisely defined as an activity of 1 rather than a molarity of 1.

Since ions in solution interact with one another and sometimes even form ion pairs, concentrations are not always a true picture of the mass action in a concentrated solution. Entropy is also diminished by ions in solution being surrounded by water molecules oriented with the opposite charge next to the ion. To correct for these interaction, a factor γ called the activity coefficient is used in calculations.

a = γ M

The true thermodynamic laws depend on activities. However, concentrations may be used without correction for estimates and approximate calculations. Activities coefficients, γ, approach 1 in dilute solutions. For more details about activity coefficients, you may want to see the "Solutions" course.

The dependence of the free energy of a component on activity (adjusted concentration) can be derived for gas solutions and extended to ionic solutions. Basically, the free energy change between the standard state and new concentration is calculated to derive this dependence.

G₁ - G^o₁ = nRTln (a₁/1)

G₁ = G^o₁ + nRTln a₁

The free energy/mole of a component of a system is called the chemical potential, μ₁.

μ₁= G₁/n = μ^o₁ RTln a₁

These chemical potentials may be calculated at non-standard conditions and combined to determine the chemical potential of a reaction. Multiplying by the number of moles then gives the free energy of the reaction at non-standard conditions. Standard free energies in tables are usually listed as chemical potentials, that is the free energy/mole.

To calculate the free energy of a reaction at non standard activity conditions, the free energies of the reactants are subtracted from the free energy of the products. The reaction of lead with chloride is worked as an example.

Pb²⁺ + 2 Cl^- ---> PbCl_2(s)

R₁ = Pb²⁺ ; R₂ = Cl^- ; and P = PbCl₂

ΔG = G_P - (G_R1 + 2*G_R2) = 1*G^o_P + 1*RTln a_p - 1*G^o_R1 - 1*RTln a_R1 - 2*G^o_R2 - 2*RTln a_R2

ΔG = G^o_P - (G^o_R1 + G^o_R2) + RT [ln a_p - ln a_R1 - 2*ln a_R2 ]

ΔG = ΔG^o + RT ln [ a_p / ( a_R1 * a_R2 ²)]

The activities of solids are 1 so this equation reduces to:

ΔG = ΔG^o RT ln [ 1 / ( a_R1 * a_R2 ²)]

The logarithmic term is frequently denoted as Q which is the same expression that is derived from a mass action law. When equilibrium is established, the Q value is the same as the equilibrium constant for the reaction.

ΔG = ΔG^o + RT ln Q

If solutions are dilute, substituting concentrations for activities is usually sufficiently accurate for most purposes. Even with concentrated solutions, the concentration may be used to estimate free energy when activity coefficients are unavailable. An estimate is useful to predict whether a reaction is spontaneous at a particular set of concentrations. If ΔG is close to zero, activity coefficients are required for a prediction of spontaneity.