Equilibrium Expressions

Homogeneous Equilibrium

An equilibrium in which all reactants and products are present in the same phase.

Heterogeneous Equilibrium

An equilibrium in which reactants and products are present in two or more different phases.

Homogeneous Gas-Phase Equilibrium

A homogeneous equilibrium in which all participating reactants and products are gases.

Homogeneous Solution Equilibrium

A homogeneous equilibrium in which all participating reactants and products are dissolved in the same solution phase.

Equilibrium Expression for Gases and Solutes

Gaseous and dissolved species are included in equilibrium expressions using their appropriate pressure or concentration terms.

Pure Solid in an Equilibrium Expression

A pure solid is omitted from the equilibrium-constant expression.

Pure Liquid in an Equilibrium Expression

A pure liquid is omitted from the equilibrium-constant expression.

Why Are Pure Solids Omitted from Equilibrium Expressions?

The effective concentration of a pure solid remains constant, so its contribution is incorporated into the equilibrium constant rather than written explicitly.

Why Are Pure Liquids Omitted from Equilibrium Expressions?

The effective concentration of a pure liquid remains constant, so its contribution is incorporated into the equilibrium constant rather than written explicitly.

Pure Solid and Pure Liquid Rule

Pure solids and pure liquids do not appear explicitly in equilibrium-constant expressions.

Aqueous Species in an Equilibrium Expression

An aqueous species is included in a concentration-based equilibrium expression because its concentration can vary.

Gaseous Species in Kc

A gaseous species may appear in Kc using its molar concentration.

Gaseous Species in Kp

A gaseous species appears in Kp using its partial pressure.

Phase Labels and Equilibrium Expressions

The phase labels in a balanced equation help determine which species are included explicitly in an equilibrium expression.

Amount of a Pure Solid and K

Changing the amount of a pure solid does not change the value of the equilibrium constant as long as the solid phase remains present.

Amount of a Pure Liquid and K

Changing the amount of a pure liquid does not change the value of the equilibrium constant as long as the pure liquid phase remains present.

Equilibrium Expression for a Heterogeneous Reaction

A heterogeneous equilibrium expression includes the variable gaseous or dissolved species while omitting pure solids and pure liquids.

Kc–Kp Relationship

For a gaseous equilibrium, Kp and Kc are related by Kp = Kc(RT)^Δn.

R in the Kp–Kc Relationship

R is the ideal gas constant used in the relationship Kp = Kc(RT)^Δn.

T in the Kp–Kc Relationship

T is the absolute temperature in kelvins.

Δn in the Kp–Kc Relationship

Δn is the total stoichiometric moles of gaseous products minus the total stoichiometric moles of gaseous reactants.

Calculating Δn

Δn = Σ(coefficients of gaseous products) − Σ(coefficients of gaseous reactants).

Which Species Count Toward Δn?

Only gaseous species are counted when calculating Δn for Kp = Kc(RT)^Δn.

Do Solids Count Toward Δn?

No. Pure solids are not counted in Δn.

Do Liquids Count Toward Δn?

No. Liquids are not counted in Δn.

Do Aqueous Species Count Toward Δn?

No. Δn in the Kp–Kc relationship counts only gaseous species.

Kp and Kc When Δn = 0

If Δn = 0, then (RT)^0 = 1 and Kp = Kc.

Kp Relative to Kc When Δn > 0

If Δn is positive, Kp differs from Kc by the positive power (RT)^Δn.

Kp Relative to Kc When Δn < 0

If Δn is negative, Kp differs from Kc by the reciprocal power of RT.

Reverse Reaction Equilibrium Constant

When a chemical equation is reversed, the new equilibrium constant is the reciprocal of the original: Kreverse = 1/Kforward.

Why Does Reversing a Reaction Invert K?

Reversing the reaction exchanges reactants and products, so the numerator and denominator of the equilibrium expression are exchanged.

Forward and Reverse Equilibrium Constants

The equilibrium constants for a reaction and its reverse satisfy Kforward × Kreverse = 1.

Multiplying a Reaction by a Factor

If every coefficient in a balanced equilibrium reaction is multiplied by a factor n, the new equilibrium constant is K^n.

Dividing a Reaction by a Factor

If every coefficient in an equilibrium reaction is divided by n, the new equilibrium constant is K^(1/n).

Doubling a Reaction and K

If every stoichiometric coefficient is doubled, the new equilibrium constant is K².

Halving a Reaction and K

If every stoichiometric coefficient is halved, the new equilibrium constant is √K.

Why Does Scaling a Reaction Raise K to a Power?

Stoichiometric coefficients become exponents in the equilibrium expression, so multiplying all coefficients by n raises the entire original expression to the nth power.

Coupled Equilibria

Equilibrium reactions that can be algebraically combined to produce an overall reaction.

Adding Equilibrium Reactions

When equilibrium reactions are added together, their equilibrium constants are multiplied.

Overall Equilibrium Constant for Added Reactions

If reaction 1 has K₁ and reaction 2 has K₂, then the equilibrium constant for their sum is Koverall = K₁K₂.

Why Are Equilibrium Constants Multiplied When Reactions Are Added?

Intermediate species cancel when the reactions and their equilibrium expressions are combined, leaving the product of the individual equilibrium constants as the constant for the overall reaction.

Intermediate Species in Coupled Equilibria

A species produced in one reaction and consumed in another that cancels when the reactions are added to obtain the overall reaction.

Reaction Manipulation and K

The mathematical operation performed on an equilibrium reaction determines the corresponding operation performed on its equilibrium constant.

Reverse–Scale–Add Rule for K

Reverse reaction → take 1/K; multiply coefficients by n → use K^n; add reactions → multiply their equilibrium constants.

Order of Operations for Combined Equilibria

Manipulate each component reaction to match the desired overall equation, transform its K accordingly, and then multiply the resulting constants.

Equilibrium Constant for a Target Reaction

A desired equilibrium constant can be obtained from known reactions by algebraically manipulating those reactions and applying the corresponding reciprocal, power, and multiplication rules to their K values.