A. Definition of Chemical Equilibrium

Many chemical reactions are reversible; that is, the products of the reaction can combine to re-form the reactants. An example of a reversible reaction is that of hydrogen with iodine to form hydrogen iodide:

H₂(g) + I₂(g) 2 HI(g)

We can study this reversible reaction by placing hydrogen and iodine in a reaction vessel and then measuring the concentrations of H₂, I₂, and HI at various times after the reactants are mixed. Figure 13.8 is a plot of the concentrations of reactants and products of this reaction versus time. The concentration of hydrogen iodide increases very rapidly at first, then more slowly, and finally, after the time indicated by the vertical line marked "Equilibrium," remains constant. Similarly, the concentrations of hydrogen and iodine are large at the start of the reaction but decrease, rapidly at first, and then more slowly. Finally, they, too, become constant.

If this reaction were not reversible, the concentrations of hydrogen and iodine would have continued to decrease and the concentration of hydrogen iodide to increase. This process does not happen. Instead, as soon as any molecules of hydrogen iodide are formed, some decompose into hydrogen and iodine. Two reactions are taking place simultaneously: the formation of hydrogen iodide and its decomposition. When the concentrations of all these components become constant (at the equilibrium point in Figure 13.8), the rate of the forward reaction (H₂ + I₂ 2 HI) must be equal to the rate of the reverse reaction (2 HI H₂ + I₂). A state of dynamic chemical equilibrium has then been reached, one in which two opposing reactions are proceeding at equal rates, with no net changes in concentration.

FIGURE 13.8 Concentration changes during the reversible reaction H2(g) + I2(g) 2 HI as it proceeds toward equilibrium.

We have encountered this criterion for equilibrium before. In the equilibrium between a liquid and its vapor, the rate of vaporization is equal to the rate of condensation. In the equilibrium of a saturated solution with undissolved solute, the rate of dissolution is equal to the rate of precipitation. In the equilibrium of a weak acid with its ions, the rate of dissociation is equal to the rate of recombination. Note that none of these reactions is static: Two opposing changes are occurring at equal rates.

B. The Characteristics of Chemical Equilibrium

1. Equal rates
At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction.

2. Constant concentrations
At equilibrium, the concentrations of the substances participating in the equilibrium are constant. Although individual reactant molecules may be reacting to form product molecules and individual product molecules may be reacting to re-form the reactants, the concentrations of the reactants and the products remain constant.

3. No free energy change
At equilibrium, the free energy change is zero. Neither the forward nor the reverse reaction is spontaneous and neither is favored. Consider the ice-water change. Above 0°C, ice melts spontaneously to form liquid water; G for this change is negative. Below 0°C, the change from ice to water is not spontaneous; G is positive. At 0°C, the two states are in equilibrium. The rate of melting is equal to the rate of freezing: the amount of ice and water and the amount of liquid water present remain constant, and the free energy change is zero as long as no energy is added to or subtracted from the mixture.

C. The Equilibrium Constant
In Chapter 12, we introduced the mathematical relationship between the concentrations of the components of an equilibrium, known as the equilibrium constant, K_eq. We said that, for the general equation of a reversible reaction

aA + bB cC + dD

the equilibrium constant expression is

Keq =

[C]c[D]d [A]a[B]b

where the brackets mean concentration in mol/L. Therefore, for the reversible reaction

H₂ + I₂ 2 HI

the equilibrium constant expression is

Keq =

[HI]2 [H2][I2]

In each of these expressions, the concentrations of the products of the reaction, each raised to a power equal to the coefficient of that product in the balanced equation for the reaction, are multiplied in the numerator. The concentrations of the reactants in the equation, each raised to a power equal to the coefficient of that reactant in the balanced equation, are multiplied in the denominator.

When we write an equilibrium constant expression, we omit the concentration of a substance that is a pure solid or a pure liquid. The concentration of a pure liquid or solid is so great that it remains essentially constant during a reaction. We tacitly admitted this fact in Chapter 12 by omitting water from the equation for the ionization of a weak acid and from the water ion product expression, K_w. The equation for ionization of acetic acid was gives as

HC2H3O2 H++ C2H3O2-

Ka =

[H+][C2H3O2-] [HC2H3O2]

even though water is required for the ionization to occur. Similarly, for the ionization of water

H₂O H⁺ + OH^-       K_w = [H⁺][OH^-]

the concentration of water molecules was not included in the constant K_w. Applying this rule to an equilibrium involving solids:

CaCO₃(s) CaO(s) + CO₂(g)     K_eq = [CO₂]

Example: Write the equilibrium constant expression for the reaction N2(g) + 3 H2(g) 2NH3(g) Solution 1. The numerator of the constant contains the product NH3 enclosed in brackets to represent concentration and raised to the second power, because 2 is the coefficient in the equation [NH3]2 2. The denominator includes the reactants of the equation, N2 and H2, enclosed in brackets. The nitrogen term is to the first power; the hydrogen term is raised to the third power: [N2][H2]3 3. The complete expression is Keq =    [NH3]2 [N2][H2]3

The value of an equilibrium constant does not depend on how equilibrium was reached. Table 13.2 presents data on the H₂ + I₂ 2 HI equilibrium. It shows several different sets of initial concentrations and the accompanying concentrations at equilibrium. The value of the equilibrium constant is given for each experiment. Notice that the value of the equilibrium constant is the same, regardless of whether the initial materials were hydrogen and iodine or the hydrogen iodide molecule or a combination of all and whether the components were present in equal or different concentrations.

The value of the equilibrium constant does depend on how the equation for the equilibrium is written. For example, the equilibrium constants given in Table 13.2 were calculated from the expression

Keq =

[HI]2 [H2][I2]

= 45.9

which is the equilibrium constant for the equation

H₂(g) + I₂(g) 2 HI(g)

If this equation is rewritten as

2 HI(g) H₂(g) + I₂(g)

the equilibrium constant becomes

Keq =

[H2][I2] [HI]2

= 2.18 X 10-2

The value of an equilibrium constant does change with a change in temperature. The equilibrium constant for the H₂ + I₂ 2 HI reaction is 45.9 only at 490°C. At 445°C, it is 64. At other temperatures, the equilibrium constant for this equation has other values, increasing as the temperature decreases and decreasing as the temperature increases.

The equilibrium constant is a very useful concept, for it allows the prediction and calculation of the concentrations of the various species present in a reaction mixture at equilibrium. This calculation is important in determining the pH of a solution, the solubility of a sparingly soluble salt, how far a reaction goes toward completion, and other similar data.