>> Key Terms (indicated in blue within the text below):

It is normal in a chemical reaction that not all the reactants become products. The energy profile (Chapter 14) shows that reactions are reversible. As the concentration of products increases, the rate of the reverse reaction increases. At the point where the rate of the forward reaction is the same as the reverse reaction, the concentrations of products and reactants are constant. This point is chemical equilibrium. At equilibrium, the concentrations of reactant and product are constant, but not equal. The constant concentration values also do not imply that the reaction stops. Individual molecules of reactants and products react, but the overall amount does not change.

                              >> Explore: Equilibrium Tutorial

The law of mass action states that any reaction mixture eventually reaches a state (equilibrium) in which the ratio of the concentration terms of the products to the reactants, each raised to a power corresponding to the stoichiometric coefficient for that substance in the balanced chemical equation, is a characteristic value for a given temperature. This is sometimes better seen as an equation. For the reaction

aA + bB cC + dD

the lowercase letters represent stoichiometric coefficients, A and B represent reactants, and C and D represent products. The ratio described by law of mass action is a constant, called the equilibrium constant (K). The mass action expression or equilibrium constant expression is then

KC

=

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

(Equation 15.7)

                              >> Explore: Solving Equilibrium Problems Tutorial

The C in K_C represents concentration. For gaseous reactions, partial pressures can be used instead of concentration values. If partial pressures are used, the mass action expression is

KP

=

PCcPDd PAaPBb

The relationship between K_C and K_P can be derived from the ideal gas law.

K_P = K_C(RT)ⁿ         (Equation 15.17)

where n is the difference in the number of moles of products (sum of their stoichiometric coefficients) and moles of reactants. Values for equilibrium constants can be determined from equilibrium concentrations of products and reactants. Similarly, reactant and product concentrations at equilibrium can be determined from initial concentration values and the equilibrium constant.

                              >> Explore: Equilibrium in the Gas Phase Tutorial

Unlike a gas, the volume of a solid or of a pure liquid depends on its mass. Therefore the concentration of a solid or pure liquid is a constant. This is normally combined with the equilibrium constant rather than being included as part of the equilibrium constant expression.

The way the reaction is written affects the value of the equilibrium constant. For example, reversing the reaction reverses the position of the products and reactants in the equilibrium constant expression. Therefore the equilibrium constant of the reverse reaction is the reciprocal of the equilibrium constant of the forward reaction. Similarly, multiplying the equation by some factor has the effect of raising the value of the equilibrium constant to that factor. In addition, the equilibrium constant for an equation that is the sum of two chemical equations is the product of the equilibrium constants of those two reactions. These relationships do not actually change the chemistry; they are instead artifacts of the math.

While the rate of the forward reaction is equal to the rate of the reverse reaction, equilibrium constant expressions are not a measurement of rate. The expression is determined from the overall reaction rather than from the rate-determining step. The concentrations are the values at equilibrium but give no information on how long it takes to reach that equilibrium. Catalysts will help the reaction reach equilibrium faster but will not affect the equilibrium concentration. Instead, equilibrium concentrations (and equilibrium constants) are related to thermodynamic parameters like G and H.

Reactions move toward equilibrium from either the products or the reactants. If nonequilibrium concentrations (or pressures) are used in the mass action expression, the value is called the reaction quotient (Q). If the value of Q is smaller than K, the reaction must go in a forward or spontaneous (–G) direction to reach the final value (K). If the value of Q is larger than K, products must react to reach the final value (K). The reaction goes in a reverse or nonspontaneous (+G) direction. The relationship between free energy and the equilibrim constant is

G = G° + RT ln(Q)         (Equation 15. 18)

At equilibrium, the rate is neither forward nor reverse, so G is zero. However, the equilibrium constant can be determined from the free energy at standard state.

G° = –RT ln(K)         (Equation 15.19)

                              >> Explore: Equilibrium and Thermodynamics Tutorial

A system at equilibrium can be perturbed by changing conditions. Le Chatelier's principle states that if a stress (perturbation) is applied to a system at equilibrium, the equilibrium will adjust to minimize that stress. Consequently, if reactant is added, the reaction must go in a forward reaction to use up that reactant and minimize the stress. Besides changes in concentration, other equilibrium stresses are changes in temperature and pressure.

                              >> Explore: Le Chatelier's Principle Tutorial