Now that we have a symbol (⇌) to designate reversible reactions, we will need a way to express mathematically how the amounts of reactants and products affect the equilibrium of the system. A general equation for a reversible reaction may be written as follows:

This we can see that the equilibrium constant is equal to both a ratio of rate constants, as well as the ratio of concentrations within a given reaction. When evaluated using concentrations, it is called K_c, where the subscript “c” refers to concentration. We use brackets to indicate molar concentrations of reactants and products. The equilibrium constant, K_c, is equal to the molar concentrations of the products of the chemical equation (multiplied together) over the reactants (also multiplied together), with each concentration raised to the power of the coefficient of that substance in the balanced chemical equation. Solids and liquids are not included when writing K_eq. For the reaction above, we can write K_c as:

K_c = [latex]\frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}[/latex]

The magnitude of an equilibrium constant is a measure of the yield of a reaction when it reaches equilibrium. A large value for K_c (much greater than 1) indicates that equilibrium is attained only after the reactants have been largely converted into products. A small value of K_c (much less than 1) indicates that equilibrium is attained when only a small proportion of the reactants have been converted into products.

The correct units for each reactant/product in the equilibrium expression are Molar (for solutions) and partial pressure (for gases). It is important to remember that pure liquids and solids are always omitted from the equilibrium expression and the value of K is always unitless. Going more in depth into this is outside the scope of this course.

Homogeneous Equilibria

A homogeneous equilibrium is one in which all of the reactants and products are present in a single solution (by definition, a homogeneous mixture). In this chapter, we will concentrate on the most common type of homogeneous equilibria which occurs in liquid-phase solutions. Reactions between solutes in liquid solutions belong to one type of homogeneous equilibria. The chemical species involved can be molecules, ions, or a mixture of both. Several examples are provided here.

In each of these examples, the equilibrium system is an aqueous solution, as denoted by the aq annotations on the solute formulas. Since H₂O(l) is the solvent for these solutions, its concentration does not appear as a term in the K_c expression, as discussed earlier, even though it may also appear as a reactant or product in the chemical equation.

Whenever gases are involved in a reaction, the partial pressure of each gas can be used instead of its concentration in the equation for the equilibrium expression because the partial pressure of a gas is directly proportional to its concentration at constant temperature. Using the partial pressures of the gases, we can write the equilibrium expression, denoted as K_p because it is the result of pressures, and calculate for the system. For example:

2 NH₃(g)   ⇌   N₂(g)  +  3 H₂(g)    K_p = [latex]\frac{P_{N_{2}}(P_{H_{2}})^{3}}{(P_{NH_{3}})^{2}}[/latex]