Equilibrium Constant

Dynamic equilibrium occurs when the rate at which a chemical substance reacts is equal to the rate at which it is formed. An equilibrium experssion can be formulated based on the chemical reaction rates for the forward and reverse reactions. The rate is the moles of A and B that are transformed to C and D per unit time.

The chemical formula and corresponding rate expression for a moles of substance A reacting with b of B to form c moles of C and d of D are given by

where kf is the rate constant for the forward reaction. The square brackets, [], are used to indicate concentration. Those for the reverse reaction are

where kr is that for the reverse reaction rate constant. At equilibrium, the forward and reverse rates are equal. We then write

The double arrow, , is used to indicate that chemical reaction procedes in both directions. Dynamic equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction. We then equate forward and reverse rate expressions to obtain

where the equilibrium constant, K, is equal to the ratio of chemical reaction rate constants.

The square brackets, [], indicate a concentration relative to the standard state for the particular phase. The standard states and their standard concentrations are

where P is the partial pressure of a substance, C is a concentration, and X is a mole fraction. Reference to the standard state is important when considering chemical activity. For most calculations required for this course, it is sufficient to remember that the molar concentrations are to be used in the equilibrium expressions.

Relationship to Thermodynamics

The equilibrium constant is related to the Gibb's free energy for the reaction through

where the DGA,B,C,D are free energy changes relative to the standard states. As usual, the DGRXN is defined by that of the products minus reactants. The reaction free energy is related to the enthalpy, DH, and entropy, DS, through

The equilibrium constant, in turn, is

where R is the constant, 8.314 J mol-1 K-1. Thus temperature, T (K), affects the equilibrium constant, and thus the ratio of products to reactants. The greater the heat evolved or used in the reaction, the greater the effect of temperature change on the equilibrium.

Types of Equilibria

There are 4 main types of chemical equilibria discussed in this course;


In solubility equilibrium, a moles of the analyte A reacts with r moles of the reagent, R, to form an insoluble species, AaRr. The standard state for a solid solution is X=1. The solid precipitate is assumed to be pure, thus has X=1. Because of this, the concentration of AaRr (s) does not appear in the solubility product expression.


In this case 1 mole of a poly-protic acid with n protons, HnA, protonates n moles of water leaving the conjugate base An-. Water acts as a Bronsted base, accepting the proton from the acid.

complex formation

Complexation reactions are typically Lewis acid-base reactions where the metal, M is a Lewis acid and the ligand, L is a Lewis base. Many metals form complexes with l=2, 4, or, even 6 Lewis base ligands.


Oxidation-reduction, also called "redox," reactions, require an oxidant and a reductant. The oxidant oxidizes a reduced species and a reductant reduces an oxidized species. Electrons are either effectively or actually transfered reductant to the oxidant. In the above reaction, o1 moles of Ox1 are reduced to r2 moles of Red2 while r1 moles of Red1 are oxidized to o2 moles of Ox2. Ox1 is an oxidant since it oxidizes Red1 to Ox2. Similarly, Red1 is a reductant since upon being oxidized to Ox2, Ox1 is reduced to Red2.

Step-Wise and Total Equilibrium Expressions

Often equilibrium involves a number of intermediate steps. For example, many metals react with up to four ligands to form complexes in a series of equilibrium steps

The equilibria can be expressed in the four formation constant equations

where the b are the products of equilibrium constants, e.g.,

More examples of complex chemical equilibria

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This page was created by Professor Stephen Bialkowski, Utah State University.

Tuesday, August 03, 2004