Chemical Equilibrium and the Equilibrium Constant (K)

Chemical Equilibrium

Introduction to Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical system are equal, resulting in constant concentrations of reactants and products over time. This concept is fundamental in understanding how chemical reactions behave under different conditions.

• Dynamic equilibrium: Both forward and reverse reactions continue to occur, but there is no net change in the concentrations of reactants and products.

• Equilibrium position: The relative concentrations of reactants and products at equilibrium.

The Equilibrium Constant (K)

Definition and Interpretation

The equilibrium constant, K, is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective coefficients in the balanced chemical equation.

• K > 1: Products are favored; the equilibrium lies to the right.

• K < 1: Reactants are favored; the equilibrium lies to the left.

• K = 1: Neither reactants nor products are favored; significant amounts of both are present at equilibrium.

The general form of the equilibrium constant expression for a reaction:

$aA + bB \rightleftharpoons cC + dD$

is:

$K = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

where [X] denotes the concentration of species X at equilibrium.

States of Matter in K Expressions

• Only gases and aqueous species are included in the equilibrium expression.

• Solids and liquids are omitted because their concentrations do not change.

Writing Equilibrium Expressions

Examples

• Example 1: $2 \text{NO}_2 (g) \rightleftharpoons 2 \text{NO} (g) + \text{O}_2 (g)$ $K = \frac{[\text{NO}]^2 [\text{O}_2]}{[\text{NO}_2]^2}$

• Example 2: $2 \text{PbO} (s) \rightleftharpoons 2 \text{PbO}_2 (s)$ $K = 1$ (since both are solids, the equilibrium constant is not dependent on their concentrations)

• Example 3: $3 \text{X}_2F_2 (g) \rightleftharpoons 2 \text{IF}_5 (g) + 3 \text{Xe} (g)$ $K = \frac{[\text{IF}_5]^2 [\text{Xe}]^3}{[\text{X}_2F_2]^3}$

Practice Problems

Comparing Reactant and Product Amounts Using K

Given the value of K, determine whether reactants or products are present in greater amounts at equilibrium:

Reaction	K Value	Greater Amount at Equilibrium
N2(g) + O2(g) ↔ 2 NO(g)	1.0 × 10-5	Reactants
2 CO(g) ↔ CO2(g) + C(s)	2.2 × 102	Products
2 BrCl(g) ↔ Br2(g) + Cl2(g)	1	Neither (similar amounts)

Writing Equilibrium Expressions for Reverse Reactions

• For the reverse reaction, the equilibrium constant is the reciprocal of the forward reaction's K value.

• Example: If $K_{forward} = 2.2 \times 10^2$, then $K_{reverse} = \frac{1}{2.2 \times 10^2}$

Application: Calculating Equilibrium Concentrations

• Given K and equilibrium concentrations of all but one species, solve for the unknown concentration using the equilibrium expression.

• Example: For $2 \text{NO} (g) + \text{O}_2 (g) \rightleftharpoons 2 \text{NO}_2 (g)$, $K = 6.9 \times 10^2$ at 500 K. If $[\text{NO}_2] = 4.3 \times 10^{-3}$ M, $[\text{O}_2] = 1.5 \times 10^{-2}$ M, solve for $[\text{NO}]$:

$K = \frac{[\text{NO}_2]^2}{[\text{NO}]^2 [\text{O}_2]}$

Rearrange to solve for $[\text{NO}]$:

$[\text{NO}] = \sqrt{\frac{[\text{NO}_2]^2}{K \times [\text{O}_2]}}$

Summary Table: Interpreting K Values

K Value	Interpretation
K > 1	Products favored at equilibrium
K < 1	Reactants favored at equilibrium
K = 1	Neither favored; significant amounts of both

Key Terms

• Equilibrium constant (K): A value that expresses the ratio of product to reactant concentrations at equilibrium.

• Dynamic equilibrium: The state in which the forward and reverse reactions occur at the same rate.

• Homogeneous equilibrium: All reactants and products are in the same phase.

• Heterogeneous equilibrium: Reactants and products are in different phases.