Equilibrium Constant Kc and How to Calculate It

Equilibrium Constant Definition

The equilibrium constant is the value of the reaction quotient that is calculated from the expression for chemical equilibrium. It depends on the ionic strength and temperature and is independent of the concentrations of reactants and products in a solution.

Calculating the Equilibrium Constant

For the following chemical reaction:
aA(g) + bB(g) ↔ cC(g) + dD(g)

The equilibrium constant K_c is calculated using molarity and coefficients:

K_c = [C]^c[D]^d / [A]^a[B]^b

where:

[A], [B], [C], [D] etc. are the molar concentrations of A, B, C, D (molarity)

a, b, c, d, etc. are the coefficients in the balanced chemical equation (the numbers in front of the molecules)

The equilibrium constant is a dimensionless quantity (has no units). Although the calculation is usually written for two reactants and two products, it works for any numbers of participants in the reaction.

Kc in Homogeneous vs. Heterogeneous Equilibrium

The calculation and interpretation of the equilibrium constant depends on whether the chemical reaction involves homogeneous equilibrium or heterogeneous equilibrium.

• All of the products and reactants are in the same phase for a reaction at homogeneous equilibrium. For example, everything could be a liquid or all the species could be gases.
• More than one phase is present for reactions that reach heterogeneous equilibrium. Usually, only two phases are present, such as liquids and gases or solids and liquids. Solids are omitted from the equilibrium expression.

The Significance of the Equilibrium Constant

For any given temperature, there is only one value for the equilibrium constant. K_c only changes if the temperature at which the reaction occurs changes. You can make some predictions about the chemical reaction based on whether the equilibrium constant is large or small.

If the value for K_c is very large, then the equilibrium favors the reaction to the right, and there are more products than reactants. The reaction may be said to be "complete" or "quantitative."

If the value for the equilibrium constant is small, then the equilibrium favors the reaction to the left, and there are more reactants than products. If the value of K_c approaches zero, the reaction may be considered not to occur.

If the values for the equilibrium constant for the forward and reverse reaction are nearly the same, then the reaction is about as likely to proceed in one direction, and the other and the amounts of reactants and products will be nearly equal. This type of reaction is considered to be reversible.

Example Equilibrium Constant Calculation

For the equilibrium between copper and silver ions:

Cu(s) + 2Ag⁺ ⇆ Cu²⁺(aq) + 2Ag(s)

The equilibrium constant expression is written as:

Kc = [Cu²⁺] / [Ag⁺]²

Note the solid copper and silver were omitted from the expression. Also, note the coefficient for the silver ion becomes an exponent in the equilibrium constant calculation.