Free Energy Change

The change in free energy is represented in two ways, ΔG and ΔG⁰. The first, ΔG (without the superscript “0”), represents the change in free energy and, thus, the direction of a reaction at any specified concentration of products and reactants. ΔG, then, is a variable. This contrasts with the standard free energy change, ΔG⁰ (with the superscript “0”), which is the energy change when reactants and products are at a concentration of 1 mol/l. [Note: The concentration of protons (H+) is assumed to be 10⁻⁷ mol/l (that is, pH = 7). This may be shown by a prime sign (ʹ ), for example, ΔG⁰ʹ.] Although ΔG⁰, a constant, represents energy changes at these nonphysiologic concentrations of reactants and products, it is nonetheless useful in comparing the energy changes of different reactions. Furthermore, ΔG⁰ can readily be determined from measurement of the equilibrium constant . [Note: This section outlines the uses of ΔG, and ΔG⁰ is described in D. below.]
A. ΔG and reaction direction
The sign of ΔG can be used to predict the direction of a reaction at constant
temperature and pressure. Consider the reaction:

1. Negative ΔG: If ΔG is negative, then there is a net loss of energy, and the reaction goes spontaneously as written (that is, A is converted into B) as shown in Figure 1 A. The reaction is said to be exergonic.

Figure 1:  Change in free energy (ΔG) during a reaction. A. The product has a lower free energy (G) than the reactant. B. The product has a higher free energy than the reactant.
2. Positive ΔG: If ΔG is positive, then there is a net gain of energy, and the reaction does not go spontaneously from B to A (Fig. 1B). Energy must be added to the system to make the reaction go from B to A. The reaction is said to be endergonic.
3. Zero ΔG: If ΔG = 0, then the reaction is in equilibrium. [Note: When a reaction is proceeding spontaneously (that is, ΔG is negative), the reaction continues until ΔG reaches zero and equilibrium is established.]
B. ΔG of the forward and back reactions
The free energy of the forward reaction (A → B) is equal in magnitude but opposite in sign to that of the back reaction (B → A). For example, if ΔG of the forward reaction is −5 kcal/mol, then that of the back reaction is +5 kcal/mol. [Note: ΔG can also be expressed in kilojoules per mole or kJ/mol (1 kcal = 4.2 kJ).]
C. ΔG and reactant and product concentrations
The ΔG of the reaction A → B depends on the concentration of the reactant and product. At constant temperature and pressure, the following relationship can be derived:

where ΔG⁰ is the standard free energy change (
R is the gas constant (1.987 cal/mol K)
T is the absolute temperature (K)
[A] and [B] are the actual concentrations of the reactant and product ln represents the natural logarithm. A reaction with a positive ΔG0 can proceed in the forward direction if the ratio of products to reactants ([B]/[A]) is sufficiently small (that is, the ratio of reactants to products is large) to make ΔG negative. For example, consider the reaction:

Figure 2: A shows reaction conditions in which the concentration of reactant, glucose 6-phosphate, is high compared with the concentration of product, fructose 6-phosphate. This means that the ratio of the product to reactant is small, and RT ln([fructose 6-phosphate]/[glucose 6-phosphate]) is large and negative, causing ΔG to be negative despite ΔG⁰ being positive. Thus, the reaction can proceed in the forward direction.

Figure 2:  Free energy change (ΔG) of a reaction depends on the concentration of reactant and product . For the conversion of glucose 6-phosphate to fructose 6-phosphate, ΔG is negative when the ratio of reactant to product is large (top, panel A), is positive under standard conditions (middle, panel B), and is zero at equilibrium (bottom, panel C). ΔG⁰ = standard free energy change.
D. Standard free energy change
The standard free energy change, ΔG⁰, is so called because it is equal to the free energy change, ΔG, under standard conditions (that is, when reactants and products are at 1 mol/l concentrations; Fig. 2 B). Under these conditions, the natural logarithm of the ratio of products to reactants is zero (ln1 = 0), and, therefore, the equation shown at the bottom of the previous page becomes:

1. ΔG0 and reaction direction: Under standard conditions, ΔG0 can be used to predict the direction a reaction proceeds because, under these conditions, ΔG⁰ is equal to ΔG. However, ΔG⁰ cannot predict the direction of a reaction under physiologic conditions because it is composed solely of constants (R, T, and Keq [see 2. below]) and is not, therefore, altered by changes in product or substrate concentrations.
2. Relationship between ΔG⁰ and Keq: In a reaction A ⇔ B, a point of equilibrium is reached at which no further net chemical change takes place (that is, when A is being converted to B as fast as B is being converted to A). In this state, the ratio of [B] to [A] is constant, regardless of the actual concentrations of the two compounds:

where K_eq is the equilibrium constant, and [A]eq and [B]eq are the concentrations of A and B at equilibrium. If the reaction A ⇔ B is allowed to go to equilibrium at constant temperature and pressure, then, at equilibrium, the overall ΔG is zero (Fig. 2C). Therefore,

where the actual concentrations of A and B are equal to the equilibrium concentrations of reactant and product ([A]_eq and [B]_eq), and their ratio is equal to the K_eq. Thus,

This equation allows some simple predictions:

3. ΔG0s of two consecutive reactions: The ΔG⁰s are additive in any sequence of consecutive reactions, as are the ΔGs. For example:

4. ΔGs of a pathway: The additive property of ΔG is very important in biochemical pathways through which substrates (reactants) must pass in a particular direction (for example, A → B → C → D → …). As long as the sum of the ΔGs of the individual reactions is negative, the pathway can proceed as written, even if some of the individual reactions of the pathway have a positive ΔG. However, the actual rates of the reactions depend on the lowering of activation energies (E_a) by the enzymes that catalyze the reactions .