Human Biochemistry, Volume 1 - Murray R. 1993

Structure and Functions of Proteins and Enzymes
Enzymes: Kinetics
Equilibrium Constant

Since all Chemical Reactions are reversible, for the reverse reaction (relative to the one where n molecules of A react with m molecules of B)

Class="center">A_nB_m→ nA + mB

the corresponding expression for the reaction rate is given by

Reaction rate ∝ [A_nA_m].

Reversibility is indicated by double arrows:

nA + mB ⇄ A_nB_m.

This expression should be read as: n molecules of A and m molecules of B are in equilibrium with A_nB_m. The proportionality sign ∝ can be replaced by an equal sign by introducing a proportionality constant k characteristic of the reaction in question. In the general case,

nA + mB ⇄ A_nB_m

the expressions for The rate of the forward reaction (Rate₁) and the reverse reaction (Rate_-1) take the form

When the rates of the forward and reverse reactions are equal, the system is said to be in equilibrium:

Hence

The ratio of k₁ to k_-1 is called the equilibrium constant, K_eq. The following properties of a system at equilibrium should be kept in mind:

¹ Strictly speaking, molar activities should be used instead of molar concentrations.

1. The equilibrium constant is equal to the ratio of the rate constants of the forward and reverse reactions, k₁/k_-1.

2. At equilibrium, the rates of the forward and reverse reactions (but not their rate constants) are equal.

3. Equilibrium is a dynamic state. Although there is no net change in the concentrations of reactants and products at equilibrium, A and B are constantly being converted into A_nB_m, and vice versa.

4. If the equilibrium concentrations of A, B, and A_nB_m are known, the numerical value of the equilibrium constant can be determined.

Relationship between the equilibrium constant and the Standard Free energy change (∆G°) of a reaction

The equilibrium constant is related to ∆G by the expression

∆G = -RTln K_eq.

Here, R is the gas constant and T is the absolute Temperature. Since their values are known, knowing the numerical value of K_eq allows one to find ∆G°. If the equilibrium constant is greater than one, the reaction proceeds spontaneously, i.e., in the direction it is written (from left to right). If the equilibrium constant is less than one, the reverse reaction proceeds spontaneously. Note, however, that while the equilibrium constant indicates the direction in which a reaction can proceed spontaneously, it does not indicate whether the reaction will occur rapidly. In other words, it says nothing about the height of the reaction's energy barrier (∆G_F; see above). This is because K_eq determines only ∆G°. Reaction rates depend on the height of the energy barrier, not on the magnitude of ∆G°.

Most factors that affect the rates of enzymatic reactions exert their effect by altering the local concentrations of the reactants.