Chemical Kinetics

Definition: The study of the rates of chemical reactions and the factors that affect these rates
Importance: Understanding reaction rates helps in designing and optimizing industrial processes
Goal: To determine the rate law and rate constant for a given chemical reaction

Factors Affecting Reaction Rates

Nature of reactants:
- Different substances have different reactivity
- Ex: Alkali metals react more vigorously than noble gases

Concentration of reactants:
- Higher concentration leads to more frequent collisions and increased reaction rate
- Ex: Increasing the concentration of hydrochloric acid increases the rate of reaction with magnesium

Temperature:
- Higher temperature increases the average kinetic energy of the reactant particles, leading to more frequent and energetic collisions
- Ex: The rate of decomposition of hydrogen peroxide increases with increasing temperature

Surface area:
- Increase in surface area provides more sites for collisions, increasing the reaction rate
- Ex: Finely powdered zinc reacts with hydrochloric acid much faster than a solid zinc piece

Catalysts:
- Substances that increase the rate of a chemical reaction without undergoing any permanent change themselves
- Lower activation energy and provide an alternative reaction pathway
- Ex: Platinum catalyst in the Haber process for ammonia synthesis

Rate Law

A mathematical expression that relates the rate of reaction with the concentrations of reactants
General form: rate = k[A]^m[B]^n where:
- k: rate constant (specific for each reaction)
- [A], [B]: concentrations of reactants
- m, n: reaction orders with respect to reactants A and B
Examples:
1. For the reaction: 2A + 3B -> C
  - Rate = k[A]^2[B]^3
2. For the reaction: A + B -> C
  - Rate = k[A][B] Note: The reaction order can be determined experimentally.

Integrated Rate Laws

Integrated rate laws give the relationship between the concentration of a reactant and time
For various order reactions, the integrated rate laws are different

Zero-order reaction:
- Rate = k[A]^0[B]^0 = k (constant)
- Integrated rate law: [A] = [A]₀ - kt where:
  - [A]: concentration of reactant A at time t
  - [A]₀: initial concentration of A
  - k: rate constant
  - t: time

First-order reaction:
- Rate = k[A]
- Integrated rate law: ln([A]/[A]₀) = -kt

Collision Theory

Explains the factors influencing the rate of reaction based on molecular collisions
For a reaction to occur, particles must:
- Collide with sufficient energy (activation energy)
- Properly orient during collision
Factors influencing collision rate:
1. Concentration of reactant particles
2. Temperature (affecting kinetic energy)
3. Surface area (affecting collision frequency)
4. Presence of catalysts
Not all collisions result in a reaction. Only collisions with sufficient energy and correct orientation lead to product formation.

Activation Energy (Ea)

Minimum energy required for a reaction to occur
Only a fraction of collisions has enough energy to overcome this energy barrier
Higher Ea leads to slower reactions, as fewer collisions have enough energy
Activation energy can be illustrated by the energy diagram: Potential energy | | ↓ | Initial reactants > Progress of reaction
The difference in energy between reactants and the highest energy point is the activation energy.

Arrhenius Equation

Developed by Swedish chemist Svante Arrhenius
Describes the temperature dependence of reaction rate constants
Equation: k = A * e^(-Ea/RT) where:
- k: rate constant
- A: pre-exponential factor (related to collision frequency)
- Ea: activation energy
- R: ideal gas constant (8.314 J/mol·K)
- T: temperature in Kelvin
As temperature increases, the rate constant (k) also increases due to a larger fraction of molecules having enough energy to react.

Reaction Mechanisms

Complex reactions often occur via a series of intermediate steps known as reaction mechanisms
Each step in the mechanism involves a simple reaction with its own rate law
Example mechanism:
1. A + B -> C (slow step)
2. C + D -> E (fast step)
- Overall reaction: A + B + D -> E
The rate of the overall reaction is determined by the rate of the slowest step (rate-determining step).

Example on Rate Law-1

Consider the following reaction: A + B ⟶ C
The initial concentrations are: [A]₀ = 0.2 M and [B]₀ = 0.1 M
The rate constant (k) for the reaction is 0.05 M⁻¹s⁻¹
Find the rate of reaction at t = 2 s using the rate law equation.

Example on Rate Law-1 (contd.)

Given: [A]₀ = 0.2 M, [B]₀ = 0.1 M, k = 0.05 M⁻¹s⁻¹
The rate law equation for this reaction is: rate = k[A][B]
Substitute the given values: rate = (0.05 M⁻¹s⁻¹)(0.2 M)(0.1 M) rate = 0.001 M/s

Reaction Rate vs. Concentration Graph

For a first-order reaction, the reaction rate depends on the concentration of a single reactant
The graph of rate vs. concentration will be linear
Example:
- Rate = k[A]
- If [A] = 0.1 M, rate = 0.05 M/s
- If [A] = 0.2 M, rate = 0.1 M/s
- The graph will show a linear increase in rate as concentration increases

Reaction Rate vs. Concentration Graph (contd.)

The slope of the graph in the rate vs. concentration plot corresponds to the rate constant (k) of the reaction
The intercept of the graph corresponds to zero concentration (t = 0 or initial concentration)
Example:
- Rate = k[A]
- If initial [A] = 0.5 M, and the rate is 0.1 M/s, then the slope of the graph will be 0.1 M/s / 0.5 M = 0.2 s⁻¹

Effect of Temperature on Reaction Rate

Temperature affects the rate of reaction due to its influence on the average kinetic energy of particles
As temperature increases, particle energy increases, leading to more successful and energetic collisions
Example:
- The rate constant (k) for a reaction at 298 K is 0.02 s⁻¹
- Calculate the rate constant at 350 K using the Arrhenius equation

Effect of Temperature on Reaction Rate (contd.)

Given: k₁ = 0.02 s⁻¹ (at 298 K), T₁ = 298 K, T₂ = 350 K, Ea = 50 kJ/mol, R = 8.314 J/mol·K
Using the Arrhenius equation: k₂ = k₁ * e^(-Ea/R * (1/T₂ - 1/T₁)) k₂ = 0.02 s⁻¹ * e^(-50,000 J/mol / (8.314 J/mol·K) * (1/350 K - 1/298 K))

Effect of Temperature on Reaction Rate (contd.)

Calculate k₂:
- Convert Ea to J/mol: 50 kJ/mol * 1000 = 50,000 J/mol
- Calculate the values inside the exponential term
- Substituting the values, k₂ is obtained
The rate constant (k₂) at 350 K can be compared to the rate constant (k₁) at 298 K to observe the effect of temperature on the reaction rate.

Collision Theory - Example

Let’s consider a reaction A + B ⟶ C
The activation energy (Ea) for this reaction is 100 kJ/mol
At 300 K, the rate constant (k) is 0.05 s⁻¹
Calculate the rate constant at 350 K using the Arrhenius equation

Collision Theory - Example (contd.)

Given: Ea = 100 kJ/mol, R = 8.314 J/mol·K, T₁ = 300 K, T₂ = 350 K, k₁ = 0.05 s⁻¹
Using the Arrhenius equation: k₂ = k₁ * e^(-Ea/R * (1/T₂ - 1/T₁)) k₂ = 0.05 s⁻¹ * e^(-100,000 J/mol / (8.314 J/mol·K) * (1/350 K - 1/300 K))

Collision Theory - Example (contd.)

Calculate k₂:
- Convert Ea to J/mol: 100 kJ/mol * 1000 = 100,000 J/mol
- Calculate the values inside the exponential term
- Substituting the values, k₂ is obtained
The rate constant (k₂) at 350 K can be compared to the rate constant (k₁) at 300 K to observe the effect of temperature on the reaction rate.

Reaction Rate Determination by Method of Initial Rates

The method of initial rates is used to determine the order of reaction with respect to each reactant.
It involves measuring the initial rates of reaction for different initial concentrations of reactants.
The order is determined based on how the rate changes with the concentration of each reactant.

Example 1:
- For the reaction: A + B ⟶ C
- Initial concentrations:
  - [A]₀ = 0.1 M, [B]₀ = 0.2 M, rate = 0.05 M/s
  - [A]₀ = 0.2 M, [B]₀ = 0.2 M, rate = 0.1 M/s
- The order with respect to A can be determined by comparing the rate when [A] is changed while keeping [B] constant.

Example 2:
- For the reaction: A + B ⟶ C
- Initial concentrations:
  - [A]₀ = 0.1 M, [B]₀ = 0.2 M, rate = 0.05 M/s
  - [A]₀ = 0.1 M, [B]₀ = 0.4 M, rate = 0.1 M/s
- The order with respect to B can be determined by comparing the rate when [B] is changed while keeping [A] constant.

Combining the order of reaction with respect to each reactant gives the overall reaction order.
- For example, if the reaction is second-order with respect to A and first-order with respect to B, the overall reaction order is 3 (2 + 1).

Rate-Determining Step and Elementary Reactions

Complex reactions often occur through several elementary reactions.
The rate-determining step is the slowest step in the reaction mechanism and determines the overall rate of reaction.

Example:
- Reaction: 2NO + O₂ ⟶ 2NO₂
- Proposed mechanism:
  - Step 1: NO + NO ⟶ N₂O₂ (fast equilibrium)
  - Step 2: N₂O₂ + O₂ ⟶ 2NO₂ (slow)
- The rate-determining step is the slow Step 2. The rate equation is derived from this step.

The elementary reactions can be combined to obtain the overall balanced equation for the reaction.
- In the above example, the elementary reactions add up to give the balanced equation: 2NO + O₂ ⟶ 2NO₂

Half-Life of a Reaction

The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half.
It depends on the order of the reaction and can be used to compare the rates of different reactions.

Zero-order reaction:
- Half-life = [A]₀ / 2k
- The half-life remains constant throughout the reaction.

First-order reaction:
- Half-life = ln(2) / k
- The half-life of a first-order reaction is constant. It does not depend on the initial concentration.

Second-order reaction:
- Half-life = 1 / (k[A]₀)
- The half-life decreases as the initial concentration of the reactant increases.

Effect of Catalysts on Reaction Rates

Catalysts increase the rate of a reaction by providing an alternative reaction pathway with a lower activation energy.
They are not consumed in the reaction and can be used repeatedly.

Homogeneous catalysts:
- Catalysts present in the same phase as the reactants.
- They form intermediate complexes with reactants to lower the activation energy.

Heterogeneous catalysts:
- Catalysts present in a different phase than the reactants.
- They adsorb reactant molecules onto their surface, allowing for easier reactions.

Example:
- The Haber process for ammonia synthesis uses an iron catalyst to increase the rate of the reaction: N₂ + 3H₂ ⟶ 2NH₃

Factors Affecting Reaction Rate - Summary

Nature of reactants: Different substances have different reactivity.
Concentration of reactants: Higher concentration leads to an increased reaction rate.
Temperature: Higher temperature increases the rate due to increased kinetic energy of particles.
Surface area: Finely powdered substances react faster due to increased surface area.
Catalysts: Catalysts lower the activation energy and increase reaction rates.

Integrated Rate Laws - Summary

Zero-order reaction:
- [A] = [A]₀ - kt

First-order reaction:
- ln([A]/[A]₀) = -kt

Second-order reaction:
- 1/[A] = kt + 1/[A]₀

Collision Theory - Summary

Collision theory explains the factors influencing the rate of reaction based on molecular collisions.
Factors influencing collision rate: concentration, temperature, surface area, and presence of catalysts.
Only collisions with sufficient energy and proper orientation result in a reaction.
Activation energy (Ea) is the minimum energy required for a reaction to occur.
Arrhenius equation describes the temperature dependence of reaction rate constants.