Lecture Notes: Chemical Kinetics and JEE Preparation

Introduction 🧪

• Session Focus: Understanding the '4 numbers in a fist' concept deeply, especially for Chemical Kinetics.
• Goal: Achieve confidence and proficiency so that even past JEE exam questions appear manageable.
• Structure: The lecture is divided into 5 key topics for a clear and concise understanding of Chemical Kinetics.

Topic 1: Rate of Reaction

Key Points:

• Balanced Chemical Equation Example: AA + BB → CC + DD.
• Rate Calculation:
  • Rate for reactant: -1/A (d[A]/dt).
  • Rate for product: 1/C (d[C]/dt).
• Terms:
  • Rate of Disappearance (Reactant): -d[A]/dt = change in concentration per unit time.
  • Rate of Appearance (Product): d[C]/dt = change in concentration of product per unit time.
• Types of Rate:
  • Average Rate: over a time interval.

$$\text{Average Rate} = - \frac{\Delta[A]}{\Delta t}$$

• Instantaneous Rate: at a specific point in time.

$$\text{Instantaneous Rate} = - \frac{d[A]}{dt}$$

Example JEE Questions:

• Calculation of rate from given concentration and time values.
• Conceptual questions relating rate of reaction and time, calculation of disappearance and appearance rates.

Topic 2: Rate Law Expression 📈

Key Points:

• Elementary vs Complex Reactions:
  • Elementary: Occurs in single step.
  • Complex: Involves multiple steps.
• Rate Law:
  • Rate = k[A]^x[B]^y
  • Order: Sum of powers in the rate law expression (Overall, w.r.t each reactant).
• Units of k: Depend on reaction order. Important orders include zero, first, second.
  • Zero Order: (mol/L)/sec
  • First Order: 1/sec
  • Second Order: (L/mol)/sec
• Determining Reaction Order: Experimentally (if not given as elementary, consider complex).
• Examples: Use changes in reactant concentrations and rates across experiments.

Topic 3: Degree of Completion 📊

Key Points:

• Definition: Fraction of reaction completed, also expressed as

$$\alpha = \frac{\text{Amount completed}}{\text{Initial amount}}$$

• Example:
  • 10% completion: (

$$\alpha = 0.1$$

• Equations for First and Zero Order Reactions:
  • Zero Order:

$$[A]_0 - [A]_t = kt$$

• First Order:

$$ln([A]_0 / [A]_t) = kt$$

• Half-Life (t1/2): Time it takes for half of the reactant to react.
  • Zero Order:

$$t_{1/2} = [A]_0 / 2k$$

• First Order:

$$t_{1/2} = 0.693 / k$$

Example JEE Questions:

• Calculate remaining concentration, rate constants, half-lives for given initial setups.

Topic 4: Transition State Theory 🛤️

Key Points:

• Activated Complex (Transition State): High-energy complex formed during the reaction.
  • Threshold Energy: Minimum energy required for molecules to collide and react.
  • Activation Energy (Ea): Energy difference between the reactants and the transition state.
  • Enthalpy of Reaction (ΔH): Difference between the energy of reactants and products.
• Graphs:
  • Endothermic: Product energy > reactant energy.
  • Exothermic: Product energy < reactant energy.
• Example JEE Questions: Graph interpretation, energy calculations.

Topic 5: Arrhenius Equation Equation 🔥

Key Points:

• Relationship: How K (rate constant) varies with temperature.

$$k = A e^{(-E_a / RT)}$$

• A: pre-exponential factor.
• Ea: activation energy.
• R: gas constant.
• T: temperature.
• Logarithmic Form:

$$ln k = ln A - (E_a / RT)$$

• Two temperatures:
  • Compare K values at T1 and T2:

$$ln (k_2 / k_1) =

$$\frac{E_a}{R}$$

$$ \left [ \frac{1}{T_1} - \frac{1}{T_2} \right ]$$

Example JEE Question:

• Calculate Ea with given K and temperatures.

Conclusion 🎯

• Final Note: Focus on understanding key points, practice PYQs, and stay consistent in revising these concepts.