Equilibrium Constants

Reaction Quotient (Q)

A numerical quantity calculated from the current concentrations or partial pressures of reactants and products using the same mathematical form as the equilibrium-constant expression.

Purpose of the Reaction Quotient

The reaction quotient describes the current composition of a reaction mixture and can be compared with the equilibrium constant to determine how the system must change to reach equilibrium.

Concentration Reaction Quotient (Qc)

The reaction quotient expressed using the current molar concentrations of the species in a reaction.

Pressure Reaction Quotient (Qp)

The reaction quotient expressed using the current partial pressures of gaseous species in a reaction.

Qc Expression

For a general reaction aA + bB ⇌ cC + dD, Qc = ([C]^c[D]^d)/([A]^a[B]^b).

Qp Expression

For a gaseous reaction aA + bB ⇌ cC + dD, Qp = ((PC)^c(PD)^d)/((PA)^a(PB)^b).

Stoichiometric Coefficients in a Reaction Quotient

The stoichiometric coefficients in the balanced chemical equation become exponents in the reaction-quotient expression.

Reaction Quotient Before Equilibrium

Q can be calculated for a reaction mixture whether or not the system has reached equilibrium.

Equilibrium Constant (K)

A numerical quantity describing the ratio of product terms to reactant terms for a reaction at equilibrium at a specified temperature.

Equilibrium-Constant Expression

An expression relating the equilibrium amounts of products and reactants, with each included species raised to the power of its stoichiometric coefficient.

Concentration Equilibrium Constant (Kc)

The equilibrium constant expressed in terms of equilibrium molar concentrations.

Kc Expression

For a general reaction aA + bB ⇌ cC + dD, Kc = ([C]eq^c[D]eq^d)/([A]eq^a[B]eq^b).

Pressure Equilibrium Constant (Kp)

The equilibrium constant expressed in terms of equilibrium partial pressures of gaseous species.

Kp Expression

For a gaseous reaction aA + bB ⇌ cC + dD, Kp = ((PC)eq^c(PD)eq^d)/((PA)eq^a(PB)eq^b).

Law of Mass Action

The principle that the equilibrium-constant expression is formed from product activities or corresponding concentration/pressure terms divided by reactant terms, with each term raised to its stoichiometric coefficient.

Q vs. K

Q describes the reaction mixture at its current state, whereas K describes the mixture when it is at equilibrium at a specified temperature.

Qc vs. Kc

Qc uses current concentrations, whereas Kc uses equilibrium concentrations.

Qp vs. Kp

Qp uses current partial pressures, whereas Kp describes the corresponding ratio when the gaseous system is at equilibrium.

Relationship Between Q and K at Equilibrium

At equilibrium, the reaction quotient equals the equilibrium constant: Q = K.

Q < K

If Q is smaller than K, the mixture contains too little product relative to equilibrium and the reaction proceeds in the forward direction.

Direction of Shift When Q < K

Reactants are consumed and products are formed until Q increases to K.

Q > K

If Q is larger than K, the mixture contains too much product relative to equilibrium and the reaction proceeds in the reverse direction.

Direction of Shift When Q > K

Products are consumed and reactants are formed until Q decreases to K.

Q = K

If Q equals K, the reaction mixture is already at equilibrium.

Reaction Direction from Q and K

Q < K means forward; Q > K means reverse; Q = K means equilibrium.

Why Does Q Predict Reaction Direction?

Comparing the current composition represented by Q with the equilibrium composition represented by K reveals which direction must change the composition toward equilibrium.

Product-Favored Equilibrium

An equilibrium for which products predominate relative to reactants, corresponding to a relatively large equilibrium constant.

Reactant-Favored Equilibrium

An equilibrium for which reactants predominate relative to products, corresponding to a relatively small equilibrium constant.

Large Equilibrium Constant

A large K indicates that the equilibrium mixture contains predominantly products relative to reactants.

Small Equilibrium Constant

A small K indicates that the equilibrium mixture contains predominantly reactants relative to products.

K ≫ 1

The equilibrium lies strongly toward the product side.

K ≪ 1

The equilibrium lies strongly toward the reactant side.

K Near 1

Neither reactants nor products are overwhelmingly favored, so appreciable amounts of both may be present at equilibrium.

Does a Large K Mean a Fast Reaction?

No. K describes the equilibrium composition, not how quickly equilibrium is reached.

Equilibrium Position

The relative proportions of reactants and products present when a reaction has reached equilibrium.

Equilibrium Lying to the Right

A description of an equilibrium that favors products and therefore has a relatively large K.

Equilibrium Lying to the Left

A description of an equilibrium that favors reactants and therefore has a relatively small K.

Does K Specify the Exact Equilibrium Concentrations by Itself?

No. K specifies a relationship among equilibrium quantities; the actual equilibrium concentrations also depend on the system's composition and constraints.

Temperature Dependence of K

The equilibrium constant for a given reaction has a particular value at a specified temperature and can change when temperature changes.

Equilibrium Constant and Initial Concentrations

Changing the initial concentrations can change the equilibrium concentrations reached, but it does not by itself change K at a fixed temperature.

Equilibrium Constant and Reaction Composition

K characterizes the equilibrium ratio required by a particular reaction at a specified temperature rather than the initial composition of one particular mixture.

Reaction Quotient as an Equilibrium Test

Calculate Q from the current reaction mixture and compare it with K to determine whether the system is at equilibrium and, if not, which direction it will proceed.