Chapter 10 – Reaction Rates and Chemical Equilibrium: Study Notes

Chapter 10 – Reaction Rates and Chemical Equilibrium

Introduction

This chapter explores the factors that influence the rates of chemical reactions and the concept of chemical equilibrium. Understanding these principles is essential for predicting how chemical systems respond to changes in conditions and for controlling reactions in laboratory and industrial settings.

Review: Energy of Chemical Reactions

Exothermic and Endothermic Reactions

• Exothermic Reaction: Energy is released to the surroundings. The enthalpy change ($\Delta H$) is negative.

• Endothermic Reaction: Energy is absorbed from the surroundings. The enthalpy change ($\Delta H$) is positive.

Equations:

• Exothermic: $\Delta H = H_{\text{products}} - H_{\text{reactants}} < 0$

• Endothermic: $\Delta H = H_{\text{products}} - H_{\text{reactants}} > 0$

Example:

• $\ce{H2(g) + Cl2(g) \rightarrow 2HCl(g)}$ ($\Delta H = -185$ kJ, exothermic)

• $\ce{N2(g) + O2(g) \rightarrow 2NO(g)}$ ($\Delta H = +180$ kJ, endothermic)

Section 10.1: Rates of Reactions

Definition of Reaction Rate

The rate of reaction is the change in concentration of a reactant or product per unit time.

Formula:

$\text{Rate of reaction} = \frac{\text{change in concentration of reactant or product}}{\text{change in time}}$

Example: For $\ce{N2(g) + O2(g) \rightarrow 2NO(g)}$:

• Rate = amount of NO formed / change in time

• Rate = amount of N2 used up / change in time

• Rate = amount of O2 used up / change in time

Collision Theory

Collision Theory states that chemical reactions occur through collisions between molecules or atoms. For a reaction to occur, three conditions must be met:

1. Collision: Reactants must collide.

2. Orientation: Reactants must align properly to break and form bonds.

3. Energy: Collisions must provide sufficient energy of activation.

Collisions with Proper Orientation

• Even if a collision occurs, it must have the correct orientation for bonds to break and new bonds to form, leading to products.

Collisions with Sufficient Energy

• Colliding particles must have enough kinetic energy to overcome the activation energy barrier and break bonds in the reactants.

Activation Energy ($E_a$)

• Activation energy ($E_a$): The minimum amount of energy required to break the bonds between atoms of the reactants.

• Reactants must overcome this energy barrier to be converted into products.

Energy Diagram: Shows the energy profile of a reaction, with $E_a$ as the peak between reactants and products.

Practice: Energy Diagrams

• Endothermic reactions: Products have higher energy than reactants ($\Delta H > 0$).

• Exothermic reactions: Products have lower energy than reactants ($\Delta H < 0$).

Factors That Affect the Rate of a Reaction

The rate of a chemical reaction is influenced by:

Factor	Reason
Increase temperature	More collisions, more collisions with energy of activation
Increase reactant concentration	More collisions
Add a catalyst	Lowers energy of activation

1. Effect of Temperature

• Increasing temperature increases the kinetic energy of molecules.

• Molecules move faster, collide more often, and with more energy.

2. Effect of Concentration

• Higher initial reactant concentrations lead to more frequent collisions.

• As the reaction proceeds, reactant concentration decreases, so the rate generally decreases over time.

3. Effect of a Catalyst

• A catalyst provides an alternative pathway with lower activation energy ($E_a$).

• More collisions have sufficient energy to react, increasing the reaction rate.

• The catalyst is not consumed in the reaction.

Section 10.2: Chemical Equilibrium

Reversible Reactions

• Many reactions are reversible, meaning they can proceed in both the forward and reverse directions.

• Example: $\ce{H2(g) + I2(g) \rightleftharpoons 2HI(g)}$

• Forward reaction: Reactants form products.

• Reverse reaction: Products reform reactants.

Chemical Equilibrium

• As a reversible reaction proceeds, the rate of the forward reaction decreases and the rate of the reverse reaction increases.

• At equilibrium: Rate of forward reaction = rate of reverse reaction.

• The concentrations of reactants and products remain constant (but are not necessarily equal).

Example: Equilibrium Mixtures

• Whether starting with reactants or products, the same equilibrium mixture is produced.

Section 10.3: Equilibrium Constants

Definition of the Equilibrium Constant ($K_c$)

For a general reaction: $aA + bB \rightleftharpoons cC + dD$

The equilibrium constant is:

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

• Square brackets [ ] denote concentration in molarity (mol/L).

• Coefficients become exponents in the expression.

• Pure solids and liquids are not included in the $K_c$ expression.

• $K_c$ is usually given without units.

Guide to Writing $K_c$ Expressions

1. Obtain a balanced chemical equation.

2. Identify reactants and products, including their phases (s, l, g, aq).

3. Write the $K_c$ expression using only gases and aqueous species.

4. Use coefficients as exponents.

Example: $\ce{2CO(g) + O2(g) \rightleftharpoons 2CO2(g)}$

$K_c = \frac{[CO_2]^2}{[CO]^2[O_2]}$

Practice: Writing $K_c$ Expressions

• $\ce{H2(g) + I2(g) \rightleftharpoons 2HI(g)}$ → $K_c = \frac{[HI]^2}{[H_2][I_2]}$

• $\ce{C(s) + H2O(g) \rightleftharpoons H2(g) + CO(g)}$ → $K_c = \frac{[H_2][CO]}{[H_2O]}$

• $\ce{Al(OH)_3(s) \rightleftharpoons Al^{3+}(aq) + 3OH^-(aq)}$ → $K_c = [Al^{3+}][OH^-]^3$

Calculating Equilibrium Constants

• Use equilibrium concentrations of reactants and products in the $K_c$ expression.

• $K_c$ is temperature dependent; for a given reaction at a specific temperature, all equilibrium mixtures yield the same $K_c$ value.

Example: For $\ce{N_2O_4(g) \rightleftharpoons 2NO_2(g)}$ at 100°C, if $[N_2O_4] = 0.45$ M and $[NO_2] = 0.31$ M:

$K_c = \frac{[NO_2]^2}{[N_2O_4]} = \frac{(0.31)^2}{0.45} = 0.21$

Summary Table: Factors Affecting Reaction Rate

Factor	Effect on Rate
Increase temperature	Increases rate (more collisions with sufficient energy)
Increase concentration	Increases rate (more frequent collisions)
Add catalyst	Increases rate (lowers activation energy)

Key Terms and Concepts

• Reaction Rate: Speed at which reactants are converted to products.

• Collision Theory: Model explaining how chemical reactions occur and why reaction rates differ for different reactions.

• Activation Energy ($E_a$): Minimum energy required for a reaction to occur.

• Catalyst: Substance that increases reaction rate without being consumed.

• Chemical Equilibrium: State where the rates of the forward and reverse reactions are equal.

• Equilibrium Constant ($K_c$): Ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their coefficients.

Additional info: These notes are based on lecture slides and include expanded explanations, definitions, and examples for clarity and completeness.