Chapter 10 – Reaction Rates and Chemical Equilibrium: Study Notes

Chapter 10 – Reaction Rates and Chemical Equilibrium

Section 10.1: Rates of Reactions

Chemical reactions occur at different rates, which can be measured by the change in concentration of reactants or products over time. Understanding reaction rates is essential for controlling chemical processes in laboratory and industrial settings.

• Rate of Reaction: Defined as the change in concentration of a reactant or product divided by the change in time. $\text{Rate of reaction} = \frac{\text{change in concentration of reactant or product}}{\text{change in time}}$

• Example: For the reaction $\mathrm{N_2(g) + O_2(g) \rightarrow 2NO(g)}$:

  • Rate of reaction = amount of NO formed / change in time

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

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

Collision Theory

Collision Theory explains how chemical reactions occur through collisions between molecules or atoms. Not all collisions result in a reaction; certain conditions must be met.

• Three Conditions for a Reaction:

  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.

• Proper Orientation: Only collisions with the correct orientation lead to product formation.

• Sufficient Energy: Collisions must have enough energy to break bonds in reactants.

Activation Energy ($E_a$)

The activation energy is the minimum energy required to break the bonds between atoms of the reactants. It represents the energy barrier that must be overcome for a reaction to proceed.

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

• Equation: $E_a$ is the difference between the energy of the activated complex and the reactants.

Exothermic and Endothermic Reactions

Reactions can either release or absorb energy, classified as exothermic or endothermic.

• Exothermic Reaction: Releases energy; products have lower energy than reactants. $\Delta H = H_{\text{products}} - H_{\text{reactants}}$ Example: $\mathrm{H_2(g) + Cl_2(g) \rightarrow 2HCl(g)}$ $\Delta H = -185\ \mathrm{kJ}$

• Endothermic Reaction: Absorbs energy; products have higher energy than reactants. $\Delta H = H_{\text{products}} - H_{\text{reactants}}$ Example: $\mathrm{N_2(g) + O_2(g) \rightarrow 2NO(g)}$ $\Delta H = +180\ \mathrm{kJ}$

Factors That Affect the Rate of a Reaction

The rate of a chemical reaction is influenced by several factors:

• Temperature: Increasing temperature increases kinetic energy, leading to more frequent and energetic collisions.

• Reactant Concentration: Higher initial concentrations lead to more collisions between reactant molecules.

• Catalyst: A catalyst provides an alternative pathway with lower activation energy, increasing the rate without being consumed.

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

Section 10.2: Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time.

• Forward Reaction: Reactants form products.

• Reverse Reaction: Products can revert to reactants.

• Reversible Reactions: Most reactions are reversible, occurring in both directions simultaneously.

• At Equilibrium:

  • Rate of forward reaction = rate of reverse reaction

  • Concentrations of reactants and products no longer change with time

Section 10.3: Equilibrium Constants ($K_c$)

The equilibrium constant ($K_c$) quantifies the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.

• General Expression: For $aA + bB \rightleftharpoons cC + dD$: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Conventions:

  • $K_c$ is usually given without units.

  • Concentrations are in molarity (M).

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

• Example: For $2CO(g) + O_2(g) \rightleftharpoons 2CO_2(g)$: $K_c = \frac{[CO_2]^2}{[CO]^2[O_2]}$

Calculating Equilibrium Constants

To calculate $K_c$, use the equilibrium concentrations of reactants and products.

• Example: For $N_2O_4(g) \rightleftharpoons 2NO_2(g)$, if $[N_2O_4] = 0.45$ M and $[NO_2] = 0.31$ M: $K_c = \frac{[NO_2]^2}{[N_2O_4]} = \frac{(0.31)^2}{0.45} = 0.21$

Section 10.4: Meaning of the Numerical Value of $K_c$

The magnitude of $K_c$ indicates the relative amounts of products and reactants at equilibrium.

• Large $K_c$ ($K_c > 1$): More products than reactants; reaction favors products.

• Small $K_c$ ($K_c < 1$): More reactants than products; reaction favors reactants.

• $K_c \approx 1$: Comparable amounts of reactants and products.

• Note: The size of $K_c$ does not affect how fast equilibrium is reached.

Practice and Application

• Energy Diagrams: Used to visualize activation energy and distinguish between exothermic and endothermic reactions.

• Equilibrium Expressions: Practice writing $K_c$ for various reactions, ensuring correct use of stoichiometric coefficients and exclusion of solids/liquids.

• Calculating $K_c$: Substitute equilibrium concentrations into the $K_c$ expression to solve for the constant.

Summary Table: Factors Affecting Reaction Rate

Factor	Effect on Rate
Increase Temperature	Increases rate (more collisions, higher energy)
Increase Concentration	Increases rate (more frequent collisions)
Add Catalyst	Increases rate (lowers activation energy)

Summary Table: Interpreting $K_c$ Values

$K_c$ Value	Mixture at Equilibrium
Large ($K_c > 1$)	Mostly products
Small ($K_c < 1$)	Mostly reactants
Near 1	Comparable amounts

Additional info: These notes are based on lecture slides and cover all major concepts from Chapter 10, including reaction rates, collision theory, activation energy, factors affecting rates, chemical equilibrium, equilibrium constants, and their interpretation. Practice problems and tables are included to reinforce understanding.