Chemical Equilibrium: Principles, Constants, and Applications

Chemical Equilibrium

Dynamic Equilibrium

Chemical equilibrium is a state in which the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. This condition can occur in both physical and chemical processes.

• Dynamic equilibrium: Opposing processes occur simultaneously at the same rate.

• Physical changes (e.g., melting and freezing of ice) and chemical changes can both reach equilibrium.

• At equilibrium, concentrations of all species remain constant over time, though the reactions continue at the molecular level.

• Double-sided arrows (⇌) are used to indicate equilibrium in chemical equations.

Example: The melting and freezing of ice in water at 0 °C and 1 atm is a classic example of physical equilibrium, where the rate of melting equals the rate of freezing.

Chemical Equilibrium

In chemical equilibrium, the concentrations of reactants and products become stable, and the forward and reverse reaction rates are equal.

• Equilibrium can be established in closed systems for reversible reactions.

• Different initial amounts of reactants and products can lead to the same equilibrium ratio.

The Equilibrium Constant

Definition and Expression

The equilibrium constant (Kc) quantifies the ratio of product and reactant concentrations at equilibrium. It is calculated using molar concentrations (M) and is typically unitless because concentrations are divided by a standard concentration.

• Kc is often written as "products over reactants" in the balanced chemical equation.

• If Kc > 1, products are favored at equilibrium; if Kc < 1, reactants are favored.

Examples of Equilibrium Expressions

• Example 1: $2\,\mathrm{O}_3(g) \rightleftharpoons 3\,\mathrm{O}_2(g)$ $K_c = \dfrac{[\mathrm{O}_2]^3}{[\mathrm{O}_3]^2}$

• Example 2: $3\,\mathrm{H}_2(g) + \mathrm{N}_2(g) \rightleftharpoons 2\,\mathrm{NH}_3(g)$ $K_c = \dfrac{[\mathrm{NH}_3]^2}{[\mathrm{H}_2]^3[\mathrm{N}_2]}$

• Example 3: $2\,\mathrm{N}_2\mathrm{O}_5(g) \rightleftharpoons 4\,\mathrm{NO}_2(g) + \mathrm{O}_2(g)$ $K_c = \dfrac{[\mathrm{NO}_2]^4[\mathrm{O}_2]}{[\mathrm{N}_2\mathrm{O}_5]^2}$

Calculating the Equilibrium Constant

To determine Kc, measure the equilibrium concentrations of all species and substitute them into the equilibrium expression.

• Multiple experiments with different starting concentrations will yield the same Kc value for a given reaction at a fixed temperature.

• The ratio of products to reactants at equilibrium is constant for a given reaction and temperature.

Sample Problem

Given: $2\,\mathrm{O}_3(g) \rightleftharpoons 3\,\mathrm{O}_2(g)$, $K_c = 4.38 \times 10^{28}$, $[\mathrm{O}_2] = 0.0089\,\mathrm{M}$ Find: $[\mathrm{O}_3]$ at equilibrium.

Equilibrium Constant for Gases: Kp

Definition

For reactions involving gases, the equilibrium constant can be expressed in terms of partial pressures (Kp), measured in atmospheres (atm).

• Kp is usually not equal to Kc unless the change in the number of moles of gas is zero.

• Relationship between Kp and Kc:

$K_p = K_c (RT)^{\Delta n}$ where $\Delta n$ is the change in moles of gas, $R$ is the gas constant, and $T$ is temperature in Kelvin.

Example Problem

For $2\,\mathrm{NO}(g) + \mathrm{Cl}_2(g) \rightleftharpoons 2\,\mathrm{NOCl}(g)$ at 700 K, $K_p = 0.26$, $R = 0.08206\,\mathrm{L\cdot atm/(mol\cdot K)}$. Find $K_c$.

Manipulating Equilibrium Constants

Effect of Reaction Direction

• If a reaction is reversed, the equilibrium constant is inverted (reciprocal).

• If reactions are added, their equilibrium constants are multiplied: $K_{c,\mathrm{tot}} = K_{c1} \cdot K_{c2}$

• If a reaction is multiplied by a factor $n$, the equilibrium constant is raised to the $n$th power: $K_c' = (K_c)^n$

Multiple Equilibria

When multiple equilibria occur simultaneously, the overall equilibrium constant is the product of the individual constants for each step.

Heterogeneous Equilibria

Definition and Application

Heterogeneous equilibrium involves reactants and products in different phases (solid, liquid, gas, aqueous). The concentrations of pure solids and pure liquids are constant and are omitted from the equilibrium expression.

• Example: $\mathrm{Ni}(s) + 4\,\mathrm{CO}(g) \rightleftharpoons \mathrm{Ni(CO)}_4(g)$

• The concentration of solid Ni is constant and not included in the equilibrium expression.

Summary Table: Manipulating Equilibrium Constants

Operation	Effect on Kc
Reverse reaction	Take reciprocal: $K_c' = 1/K_c$
Add reactions	Multiply constants: $K_{c,\mathrm{tot}} = K_{c1} \cdot K_{c2}$
Multiply reaction by n	Raise to power: $K_c' = (K_c)^n$