Chemistry Physical How to Solve: Chemical Kinetics (IIT JEE Main + Advanced)

How to Solve: Chemical Kinetics (IIT JEE Main + Advanced)

Introduction

"Mastering chemical kinetics doesn’t just get you 10–15 marks in IIT JEE—it’s the key to designing life-saving drugs, controlling pollution, and even understanding how your body digests food. One wrong rate law, and your entire reaction mechanism collapses. Let’s make sure that never happens."

WHAT YOU NEED TO KNOW FIRST

1. Basic algebra – Solving linear equations, logarithms, and exponents.
2. Mole concept & stoichiometry – Balancing reactions and understanding reaction progress.
3. Graph interpretation – Plotting and analyzing straight-line graphs (slope, intercept).

KEY TERMS & FORMULAS

1. Rate of Reaction

• Definition: Change in concentration of reactant/product per unit time.
• Formula: [ \text{Rate} = -\frac{\Delta [A]}{\Delta t} \quad \text{(for reactant A)} ] [ \text{Rate} = \frac{\Delta [B]}{\Delta t} \quad \text{(for product B)} ]
• MEMORISE THIS: Negative sign for reactants (concentration decreases).

2. Rate Law (Differential Rate Law)

• Definition: Relationship between reaction rate and concentration of reactants.
• Formula: [ \text{Rate} = k [A]^m [B]^n ]
• (k) = rate constant (units depend on order)
• (m, n) = reaction orders (determined experimentally, not from stoichiometry)
• MEMORISE THIS: Order is not the same as stoichiometric coefficient.

3. Integrated Rate Laws (Concentration vs. Time)

• MEMORISE THIS: First-order half-life does not depend on initial concentration.

4. Arrhenius Equation

• Definition: Relates rate constant (k) to temperature (T).
• Formula: [ k = A e^{-E_a / RT} ]
• (A) = pre-exponential factor (frequency of collisions)
• (E_a) = activation energy (J/mol)
• (R) = gas constant (8.314 J/mol·K)
• (T) = temperature (K)
• Linear form (for graphing): [ \ln k = \ln A - \frac{E_a}{R} \left( \frac{1}{T} \right) ]
• MEMORISE THIS: Plot (\ln k) vs. (1/T) → slope = (-E_a/R).

5. Collision Theory

• Key Points:
• Molecules must collide to react.
• Collisions must have sufficient energy (≥ (E_a)).
• Collisions must have correct orientation.
• Effect of Temperature:
• Higher (T) → more molecules have (E ≥ E_a) → faster rate.

STEP-BY-STEP METHOD

Step 1: Determine the Rate Law (Order of Reaction)

Given: Initial rates at different concentrations. Steps:
1. Write the general rate law: (\text{Rate} = k [A]^m [B]^n).
2. Pick two experiments where only one concentration changes.
3. Divide the rates to eliminate (k) and solve for the order.
4. Repeat for other reactants.
5. Calculate (k) using any experiment’s data.

Step 2: Use Integrated Rate Law to Find (k) or Time

Given: Concentration vs. time data. Steps:
1. Check which plot gives a straight line: - ([A]_t) vs. (t) → 0th order - (\ln[A]_t) vs. (t) → 1st order - (1/[A]_t) vs. (t) → 2nd order
2. Find slope of the line: - 0th order: slope = (-k) - 1st order: slope = (-k) - 2nd order: slope = (+k)
3. Use the slope to find (k).

Step 3: Calculate Half-Life

Given: Order and (k). Steps:
1. Use the correct half-life formula based on order.
2. Plug in (k) and ([A]0) (if needed).
3. Solve for (t).

Step 4: Apply Arrhenius Equation

Given: (k) at two temperatures or (E_a). Steps:
1. If two (k) values at two (T) are given: [ \ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) ]
2. Solve for (E_a) or (k_2).
3. If graph is given, find slope = (-E_a/R).

Step 5: Collision Theory Questions

Given: Effect of temperature/concentration on rate. Steps:
1. Concentration: Higher ([A]) → more collisions → faster rate (if order > 0).
2. Temperature: Higher (T) → more molecules with (E ≥ E_a) → faster rate.
3. Catalyst: Lowers (E_a) → more molecules can react → faster rate.

WORKED EXAMPLES

Example 1 – Basic: Determine Rate Law & (k)

Problem: For the reaction (A + B → C), the following data was obtained:

Find: Rate law and rate constant (k).

Solution:
1. Assume rate law: (\text{Rate} = k [A]^m [B]^n).
2. Find (m) (order w.r.t. A): - Compare Exp. 1 & 2: ([B]) constant, ([A]) doubles. - Rate doubles → (m = 1) (since (2^m = 2)).
3. Find (n) (order w.r.t. B): - Compare Exp. 1 & 3: ([A]) constant, ([B]) doubles. - Rate quadruples → (n = 2) (since (2^n = 4)).
4. Rate law: (\text{Rate} = k [A]^1 [B]^2).
5. Find (k): - Use Exp. 1: (2 \times 10^{-3} = k (0.1)^1 (0.1)^2) - (k = \frac{2 \times 10^{-3}}{0.1 \times 0.01} = 2 \, \text{M}^{-2}\text{s}^{-1}).

What we did and why: - Compared experiments where only one concentration changed to isolate the effect of each reactant. - Used the rate ratio to find orders, then plugged in values to find (k).

Example 2 – Medium: Integrated Rate Law & Half-Life

Problem: The decomposition of (N_2O_5) follows first-order kinetics. If the initial concentration is 0.1 M and the rate constant is (6.93 \times 10^{-3} \, \text{s}^{-1}), find: (a) Concentration after 100 s. (b) Half-life.

Solution: (a) Concentration after 100 s:
1. First-order integrated rate law: [ \ln[A]_t = \ln[A]_0 - kt ]
2. Plug in values: [ \ln[A]_t = \ln(0.1) - (6.93 \times 10^{-3})(100) ] [ \ln[A]_t = -2.3026 - 0.693 = -3.0 ]
3. Take antilog: [ [A]_t = e^{-3.0} = 0.0498 \, \text{M} ]

(b) Half-life:
1. First-order half-life formula: [ t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{6.93 \times 10^{-3}} = 100 \, \text{s} ]

What we did and why: - Used the first-order integrated rate law to find concentration at a given time. - Half-life for first-order reactions is constant and independent of initial concentration.

Example 3 – Exam-Style: Arrhenius Equation & Temperature Effect

Problem: The rate constant for a reaction doubles when the temperature is increased from 298 K to 308 K. Calculate the activation energy ((E_a)).

Solution:
1. Given: - (k_2 = 2k_1) - (T_1 = 298 \, \text{K}), (T_2 = 308 \, \text{K})
2. Arrhenius equation (two-point form): [ \ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) ]
3. Plug in values: [ \ln(2) = \frac{E_a}{8.314} \left( \frac{1}{298} - \frac{1}{308} \right) ]
4. Calculate: [ 0.693 = \frac{E_a}{8.314} \left( 3.356 \times 10^{-3} - 3.247 \times 10^{-3} \right) ] [ 0.693 = \frac{E_a}{8.314} (1.09 \times 10^{-4}) ] [ E_a = \frac{0.693 \times 8.314}{1.09 \times 10^{-4}} = 52,890 \, \text{J/mol} = 52.9 \, \text{kJ/mol} ]

What we did and why: - Used the two-point Arrhenius equation to relate (k) and (T). - Solved for (E_a) by plugging in the given temperature change and rate ratio.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before Exam)

"Listen up—this is your 60-second kinetics survival guide. First, rate law: compare experiments where only one concentration changes, find orders, then calculate (k). Second, integrated rate laws: plot ([A]_t), (\ln[A]_t), or (1/[A]_t)—whichever is linear gives the order. Third, half-life: first-order is (\ln 2 / k), zero-order depends on ([A]_0), second-order is (1/k[A]_0). Fourth, Arrhenius equation: (\ln k) vs. (1/T) gives (-E_a/R) as slope. Fifth, collision theory: more collisions, higher (T), or lower (E_a) → faster rate. And remember—order is not the same as stoichiometry. Now go crush that exam!