Concept Version 7
Created by Boundless

Equilibrium Constant Expression

The equilibrium constant is an expression that gives the ratio of reactants and products at equilibrium.

Learning Objective

  • Recall that neat solids and liquids are given a value of 1 when input into an equilibrium constant

Key Points

    • When calculating the equilibrium constant, solids and liquids concentrations are given a value of 1, effectively meaning that their presence will not affect the equilibrium constant.
    • For the generic equation: $mA+nB\rightleftharpoons xC+yD$ the equilibrium constant can be denoted as the ratio of the products to reactants:${ K }_{ eq }=\frac { { [C] }^{ x }{ [D] }^{ y } }{ { [A] }^{ m }{ [B] }^{ n } }$.
    • By convention, products are always placed in the numerator of the equilibrium constant expression and reactants are placed in the denominator.
    • The equilibrium constant is used for reversible reactions; irreversible reactions do not have equilibrium constant expressions associated with them because there are no reactants left at equilibrium.

Terms

  • equilibrium constant

    referring to a numerical value derived from the ratio of concentrations of products to reactants of a reversible reaction

  • ratio

    The relative magnitudes of two quantities (usually expressed as a quotient).

Full Text

Equilibrium Constant Expression

The law of chemical equilibrium states that, at any given temperature a chemical system reaches a state in which a particular ratio of reactant and product activities has a constant value. This constant is known as the equilibrium constant. For the generic reaction

$mA+nB\rightleftharpoons xC+yD$

the equilibrium constant denoted by Keq is given by

${ K }_{ eq }=\frac { { [C] }^{ x }{ [D] }^{ y } }{ { [A] }^{ m }{ [B] }^{ n } }$

where [X] is the activity of X. The activity of X is equal to the concentration of X if it is a gas or liquid. The activity is equal to 1 if its a pure liquid or solid. In other words, pure solids and liquids do not affect the equilibrium constant as long as there is enough for the reaction to proceed. Their activity is 1, so they do not need to be written in the equilibrium constant. Since activity is a dimensionless quantity, the equilibrium constant, Keq, is also a dimensionless quantity.

By convention, the equilibrium concentrations of the substances appearing on the right hand side of the chemical equation (the products) are always placed in the numerator of the equilibrium constant expression; the concentrations of the substances appearing on the left hand side of the chemical equation (the reactants) are placed in the denominator. The larger the value of the equilibrium constant, the more the reaction proceeds to completion. Irreversible reactions can be thought to have an infinite equilibrium constant since there are no reactants left .

The Equilibrium Constant

The equilibrium constant,denoted by K, is the ratio of products to reactants at equilibrium.

Example:

Take the reaction:

${ H }_{ 2 }(g)+{ I }_{ 2 }(g)\rightleftharpoons 2HI(g)$

The forward reaction is:

${ H }_{ 2 }+{ I }_{ 2 }\rightarrow HI$

The reverse reaction is:

$2HI{ \rightarrow H }_{ 2 }+{ I }_{ 2 }$

The equilibrium constant expression for this reaction is:

${ K }_{ eq }=\frac { { [HI] }^{ 2 } }{ { [H }_{ 2 }]{ [I }_{ 2 }] }$

The progress of an equilibrium reaction can be visualized. At time = 0, the rate of the forward reaction is high and the rate of the reverse reaction is low. As the reaction proceeds, the rate of the forward reaction decreases and the rate of the reverse reaction increases, until both occur at the same rate, reaching equilibrium.

What is the Equilibrium Constant, Keq?

This lesson discusses Keq, including the derivation from the law of mass action, and writing-interpreting Equilibrium Expressions.
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