E3.4 Write expressions for common equilibrium constants | Ontario Grade 12 Chemistry (SCH4U)

Ontario Grade 12 Chemistry

Chemical Systems and Equilibrium

SCH4U study topic E3.4

A sealed container can reach a state where the amounts of reactants and products stop changing overall. At the particle level, the forward and reverse reactions continue, but the concentrations remain steady. This is dynamic equilibrium. The substances do not need to have equal concentrations. An equilibrium constant expression is a recipe for representing the equilibrium amounts using the balanced chemical equation. In this lesson, you will practise writing the expression, not calculating an equilibrium constant from measured data.

What you will learn

Identify the substances included in an equilibrium constant expression.
Use balanced-equation coefficients as exponents.
Write expressions for common equilibrium constants, including Kc, Kp, Ka, Kb, and Ksp.
Leave pure solids and pure liquids out of the expression.

1. From a balanced equation to Kc

Before writing an equilibrium expression, review two ideas. A balanced chemical equation conserves the number of each kind of atom and the total charge. Its coefficients show the reacting ratio of particles or formula units. In an equilibrium expression, those same coefficients become exponents.

For a general reaction, write each aqueous or gaseous product concentration in the numerator and each aqueous or gaseous reactant concentration in the denominator. Enclose each concentration in square brackets. Raise it to the power of its coefficient in the balanced equation. The symbol Kc means the equilibrium constant written using concentrations.

The expression describes the composition at equilibrium. Brackets in this context mean concentration, commonly measured in moles per litre, not a count of particles. A substance with coefficient 1 has an implied exponent of 1, which is usually not written.

K_c=\frac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}}

Balance the reaction before writing its expression.
Products go in the numerator; reactants go in the denominator.
Use each balanced coefficient as the exponent.

2. Which substances belong in the expression?

Include substances that are aqueous, written (aq), or gaseous, written (g). Do not include pure solids, written (s), or pure liquids, written (l). A pure substance is one present as its own solid or liquid phase, rather than dissolved in a mixture. Its amount does not appear as a changing concentration in the expression used at this course level.

This rule matters for heterogeneous equilibria, which are equilibria involving substances in more than one physical state. For example, a solid can react with a gas while another gas forms. The solid is left out; the gaseous substances remain in the expression. Do not omit a dissolved aqueous substance merely because it is a solid compound before dissolving.

The expression follows the equation as written. If the equation is reversed or its coefficients are changed, the corresponding expression changes too. Therefore, do not simplify an expression by changing coefficients or cancelling a species unless the chemical equation has also been rewritten consistently.

Include aqueous and gaseous species.
Omit pure solids and pure liquids.
Use the equation exactly as balanced and written.

3. Common forms of equilibrium constants

Kc is the general concentration-based form. For a reaction involving gases, Kp is a form written with equilibrium partial pressures instead of concentrations. A partial pressure is the pressure contributed by one gas in a mixture. The products and reactants still follow the same numerator, denominator, and exponent rules.

Some reactions have familiar names for their equilibrium constants. For an acid ionizing in water, Ka is the acid ionization constant. For a base reacting with water, Kb is the base ionization constant. For a sparingly soluble ionic solid dissolving into ions, Ksp is the solubility product constant. In each expression, use the balanced equation and omit pure liquid water and the pure solid when they appear.

Water may be shown as a reactant or product in the balanced equation, but it is a pure liquid in these aqueous reactions. It is therefore omitted from the expression. Aqueous ions and molecules remain. The labels Ka, Kb, and Ksp identify the kind of equilibrium; they do not change the rules for coefficients and phases.

K_p=\frac{(P_{\text{products}})^{\text{coefficients}}}{(P_{\text{reactants}})^{\text{coefficients}}}

Kp uses gas partial pressures in place of concentrations.
Ka, Kb, and Ksp are named forms for particular equilibria.
The balanced equation and physical states determine what appears.

4. A reliable writing routine

First, check that the reaction is balanced. Next, mark each substance as aqueous, gas, liquid, or solid. Then write the products above the fraction bar and the reactants below it. Keep only aqueous and gaseous substances for Kc, or use partial pressures for gaseous substances in Kp. Finally, add the equation's coefficients as exponents.

When writing Ka, Kb, or Ksp, identify the process named by the constant and use its balanced equation. This prevents common errors such as leaving pure water in an aqueous acid expression or including a solid salt in a solubility product expression.

The expression is a symbolic relationship, not a numerical answer. If a question gives equilibrium concentrations or pressures, substitute them only after the expression is written correctly. The numerical value and units, if requested, depend on the information and convention specified in the question.

Check balance, states, placement, and exponents in that order.
Write the expression before substituting any equilibrium values.
Do not assume that equilibrium means equal concentrations.

Worked example

Writing a solubility product expression

A sparingly soluble ionic solid dissolves according to the balanced equation shown. Write its Ksp expression.

Read the balanced equation
The solid produces two aqueous ions. The coefficient 2 belongs to the hydroxide ion, while the coefficient 1 for the metal ion is understood.
$\mathrm{M(OH)_2(s) \rightleftharpoons M^{2+}(aq) + 2OH^-(aq)}$
Apply the phase rule
The pure solid is omitted from the expression. Both ions are aqueous, so both are included.
Apply the coefficients
Place the aqueous products in the expression. The coefficient 2 becomes the exponent on the hydroxide concentration.
$K_{sp}=[\mathrm{M^{2+}}][\mathrm{OH^-}]^2$

Answer: The solubility product expression is

K_{sp}=[\mathrm{M^{2+}}][\mathrm{OH^-}]^2

.

Check: The solid is absent, both aqueous ions are present, and the hydroxide concentration is squared to match its coefficient.

Common mistakes and how to avoid them

Putting reactants in the numerator and products in the denominator.

Correction: For the conventional expression, place products in the numerator and reactants in the denominator.

Using a coefficient as a multiplier instead of an exponent.

Correction: A coefficient of 2 gives a concentration squared, not twice the concentration.

Including a pure solid or pure liquid.

Correction: Leave pure solids and pure liquids out. Include aqueous and gaseous species.

Assuming the products and reactants must have equal concentrations at equilibrium.

Correction: Equilibrium means concentrations are steady overall; their values do not have to be equal.

Lesson summary

Balance the equation before writing an equilibrium constant expression.
Use products over reactants, with each balanced coefficient as an exponent.
Include aqueous and gaseous species; omit pure solids and pure liquids.
Kc uses concentrations, Kp uses gas partial pressures, and Ka, Kb, and Ksp name common equilibrium expressions.

Check your understanding

Question 1

For the balanced reaction

\mathrm{A(g) + 2B(aq) \rightleftharpoons C(aq)}

, which is the correct Kc expression?

$K_c=\frac{[\mathrm{A}][\mathrm{B}]^2}{[\mathrm{C}]}$
$K_c=\frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2}$
$K_c=\frac{[\mathrm{C}]^2}{[\mathrm{A}][\mathrm{B}]}$
$K_c=\frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]}$

Show answer and explanation

K_c=\frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2}

The product C goes in the numerator. A and B are reactants in the denominator, and B has exponent 2 because its coefficient is 2.

Question 2

In a Ksp expression for a solid dissolving into aqueous ions, which substance is omitted?

An aqueous positive ion
An aqueous negative ion
The pure solid
A gaseous product

Show answer and explanation

The pure solid

A pure solid is omitted. Aqueous ions and gaseous species are included when they appear in the equilibrium expression.

Key terms

Dynamic equilibrium: A state in a reversible reaction where forward and reverse changes continue, while concentrations remain steady overall.
Equilibrium constant expression: A symbolic relationship that places product amounts over reactant amounts, using equation coefficients as exponents.
Partial pressure: The pressure contributed by one gas in a mixture.
Heterogeneous equilibrium: An equilibrium involving substances in more than one physical state.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation E3.4. It is a study resource, not an official curriculum publication.

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E3.4 · Write expressions for common equilibrium constants