Positive ∆G: If ∆G is positive, then there is a net gain of energy, and the reaction does not go spontaneously from B to A (Fig. 6.2B). 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 ∆G: If ∆G = 0, then the reaction is in equilibrium. [Note: When a reaction is proceeding spontaneously (that is, ∆G is negative), the reaction continues until ∆G reaches zero and equilibrium is established.]
B. ∆G 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 ∆G of the forward reaction is −5 kcal/mol, then that of the back reaction is +5 kcal/mol. [Note: ∆G can also be expressed in kilojoules per mole or kJ/mol (1 kcal = 4.2 kJ).]
C. ∆G and reactant and product concentrations
The ∆G 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 ∆G0 is the standard free energy change (see D. below) 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 ∆G0 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 ∆G negative. For example, consider the reaction:
D. Standard free energy change
The standard free energy change, ∆G0, is so called because it is equal to the free energy change, ∆G, under standard conditions (that is, when reactants and products are at 1 mol/l concentrations; Fig. 6.3B). 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.
∆G0 and reaction direction: Under standard conditions, ∆G0 can be used to predict the direction a reaction proceeds because, under these conditions, ∆G0 is equal to ∆G. However, ∆G0 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 ∆G0 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 Keq 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 ∆G is zero (Fig. 6.3C). 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 Keq. Thus,
This equation allows some simple predictions: 3.
∆G0s of two consecutive reactions: The ∆G0s are additive in any sequence of consecutive reactions, as are the ∆Gs. For example: 4.