Chapter 15: Chemical Equilibrium – Structured Study Notes

Chemical Equilibrium

Dynamic Equilibrium

Dynamic equilibrium occurs when two opposing processes happen at the same rate, resulting in no net change in the system. In chemistry, this refers to the state where the forward and reverse reactions proceed at equal rates.

• Dynamic equilibrium is not static; reactions continue but concentrations remain constant.

• Analogy: Like traffic moving in opposite directions at the same rate, the number of cars (or molecules) in each direction remains constant.

Equilibrium: Sameness and Constancy

Equilibrium is characterized by sameness (equal property with surroundings) and constancy (no further change). For example, a cup of hot water cools until its temperature matches the surroundings, reaching thermal equilibrium.

Life and Controlled Disequilibrium

Living organisms maintain controlled disequilibrium with their environment, such as body temperature regulation. Unlike inanimate objects, living things actively control their internal conditions.

The Rate of a Chemical Reaction

The rate of a chemical reaction measures how quickly reactants convert to products. Reaction rates are crucial for understanding equilibrium, as equilibrium is achieved when forward and reverse rates are equal.

• Reaction rate: Amount of reactant converted to product per unit time.

• Fast reactions: Rapid conversion; slow reactions: Gradual conversion.

• Factors affecting rate: Concentration and temperature.

Collision Theory of Chemical Reactions

According to collision theory, chemical reactions occur when molecules or atoms collide with sufficient energy to overcome the activation energy barrier.

• Activation energy: Minimum energy required for a reaction to occur.

• High-energy collisions lead to product formation; low-energy collisions do not.

• Factors influencing collision frequency and energy: Concentration and temperature.

Effect of Concentration on Reaction Rate

Increasing the concentration of reactants generally increases the reaction rate, as more molecules are available to collide.

• Higher concentration → more collisions → faster rate.

• The relationship varies for different reactions (studied in chemical kinetics).

Effect of Temperature on Reaction Rate

Raising the temperature increases molecular motion, resulting in more frequent and energetic collisions, thus increasing the reaction rate.

• Higher temperature → more collisions and higher energy → faster rate.

Summary of Collision Theory

• Reaction rates increase with reactant concentration and temperature.

• Reaction rates decrease as a reaction proceeds (reactant depletion).

Dynamic Chemical Equilibrium

Reversible Reactions and Dynamic Equilibrium

A reversible reaction can proceed in both forward and reverse directions. Dynamic equilibrium is reached when the rates of these directions are equal, resulting in constant concentrations of reactants and products.

• At equilibrium, concentrations no longer change.

• Reactants and products are formed and depleted at equal rates.

Population Analogy for Equilibrium

Dynamic equilibrium can be illustrated by populations moving between two kingdoms. When the rate of people moving in each direction is equal, populations remain constant.

The Equilibrium Constant (Keq)

Definition and Expression

The equilibrium constant (Keq) quantifies the relative concentrations of reactants and products at equilibrium. It is calculated using the balanced chemical equation:

• For a reaction: aA + bB ⇌ cC + dD

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

• Coefficients become exponents in the expression.

Significance of Keq

• Large Keq: High product concentration, low reactant concentration at equilibrium.

• Small Keq: High reactant concentration, low product concentration at equilibrium.

Summary Table: Keq Interpretation

Keq Value	Reaction Direction Favored	Equilibrium Composition
Keq << 1	Reverse	Mostly reactants
Keq ≈ 1	Neither	Significant reactants & products
Keq >> 1	Forward	Mostly products

Heterogeneous Equilibria

For reactions involving pure solids or liquids, their concentrations are omitted from equilibrium expressions because they are constant.

Calculating Equilibrium Constants

To calculate Keq, substitute equilibrium concentrations into the expression.

• Example: $K_{eq} = \frac{[HI]^2}{[H_2][I_2]}$

• Given: [H2] = 0.11 M, [I2] = 0.11 M, [HI] = 0.78 M

• $K_{eq} = \frac{(0.78)^2}{(0.11)(0.11)} = 5.0 \times 10^1$

Using Keq in Calculations

Keq can be used to solve for unknown concentrations at equilibrium.

• Example: $K_{eq} = \frac{[CO_2][CF_4]}{[COF_2]^2}$

• Rearrange to solve for [CO2]: $[CO_2] = K_{eq} \frac{[COF_2]^2}{[CF_4]}$

• Given: [COF2] = 0.255 M, [CF4] = 0.118 M, Keq = 2.00

• $[CO_2] = 2.00 \frac{(0.255)^2}{0.118} = 1.10 \text{ M}$

Le Châtelier’s Principle

Principle Overview

Le Châtelier’s Principle states that when a system at equilibrium is disturbed, it shifts in a direction that minimizes the disturbance.

• Disturbances include changes in concentration, volume, or temperature.

Effect of Adding Products or Reactants

• Adding products shifts equilibrium toward reactants (left).

• Adding reactants shifts equilibrium toward products (right).

Effect of Volume Change on Equilibrium

Changing the volume of a gas mixture affects equilibrium by altering pressure.

• Decrease in volume (increase in pressure): Reaction shifts to side with fewer moles of gas.

• Increase in volume (decrease in pressure): Reaction shifts to side with more moles of gas.

• If moles of gas are equal on both sides, volume change has no effect.

Effect of Temperature Change on Equilibrium

Temperature changes affect equilibrium differently for exothermic and endothermic reactions.

• Exothermic: Heat is a product. Increasing temperature shifts equilibrium left (toward reactants).

• Endothermic: Heat is a reactant. Increasing temperature shifts equilibrium right (toward products).

Solubility-Product Constant (Ksp)

Definition and Expression

The solubility-product constant (Ksp) describes the equilibrium for the dissolution of an ionic compound. Solids are omitted from the expression.

• Large Ksp: Compound is very soluble.

• Small Ksp: Compound is not very soluble.

Calculating Molar Solubility from Ksp

To calculate molar solubility, write the dissolution equation and Ksp expression, then solve for solubility (S).

• Example: BaSO4(s) ⇌ Ba2+(aq) + SO42–(aq)

• $K_{sp} = [Ba^{2+}][SO_4^{2-}] = S^2$

• $S = \sqrt{K_{sp}}$

• Given: $K_{sp} = 1.07 \times 10^{-10}$

• $S = \sqrt{1.07 \times 10^{-10}} = 1.03 \times 10^{-5} \text{ M}$

Reaction Pathways and Catalysts

Activation Energy and Reaction Rate

Activation energy is the energy barrier that must be overcome for a reaction to proceed. Higher activation energy means slower reaction rate.

Ways to Increase Reaction Rate

• Increase reactant concentration.

• Increase temperature.

• Use a catalyst to lower activation energy.

Enzymes: Biological Catalysts

Enzymes are biological catalysts that speed up biochemical reactions by lowering activation energy. They are essential for life, as many reactions would be too slow otherwise.

Summary Table: Selected Solubility-Product Constants

Compound	Formula	Ksp
Barium sulfate	BaSO4	1.07 × 10–10
Calcium carbonate	CaCO3	4.96 × 10–9
Calcium fluoride	CaF2	1.46 × 10–10
Calcium hydroxide	Ca(OH)2	4.68 × 10–6
Calcium sulfate	CaSO4	4.68 × 10–5
Copper(II) sulfide	CuS	8.5 × 10–36
Iron(III) carbonate	FeCO3	3.7 × 10–11
Iron(III) hydroxide	Fe(OH)3	1.1 × 10–36
Lead(II) chloride	PbCl2	1.17 × 10–5
Lead(II) sulfate	PbSO4	9.04 × 10–7
Magnesium carbonate	MgCO3	6.8 × 10–6
Magnesium hydroxide	Mg(OH)2	2.06 × 10–13
Silver chloride	AgCl	1.77 × 10–10
Silver chromate	Ag2CrO4	1.12 × 10–12
Silver iodide	AgI	8.51 × 10–17