A chemical mixture at equilibrium is in a stable state of minimal free energy. For a system at equilibrium (ΔG = 0, Q = K_eq) under standard conditions, we can write

ΔG°′ = –2.3 RTlogK_eq = –1362 logK_eq (2-8)

(note the change to base 10 logarithms). Thus, if we determine the concentrations of reactants and products at equilibrium (i.e., the K_eq), we can calculate the value of ΔG°′. For example, the K_eq for the interconversion of glyceraldehyde 3-phosphate to dihydroxyacetone phosphate (G3P ⇌ DHAP) is 22.2 under standard conditions. Substituting this value into Equation 2-8, we can easily calculate the ΔG°′ for this reaction as –1840 cal/mol.

By rearranging Equation 2-8 and taking the antilogarithm, we obtain

K_eq = 10^{–(ΔG°′/2.3RT)} (2-9)

From this expression, it is clear that if ΔG°′ is negative, the exponent will be positive, and hence K_eq will be greater than 1. Therefore, at equilibrium there will be more products than reactants; in other words, the formation of products from reactants is favored. Conversely, if ΔG°′ is positive, the exponent will be negative, and K_eq will be less than 1. The relationship between K_eq and ΔG°′ further emphasizes the influence of the relative free energies of reactants and products on the extent to which a reaction will occur spontaneously.