Chapter 4: Chemical Kinetics Class 12 Chemistry NCERT Solutions

NCERT Solutions for Class 12 Chemistry Chapter 4 – Chemical Kinetics (Exercises)

Question 4.1: From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.

Answer: (i) Rate = k [A]² → Second-order reaction. Units of k = L mol⁻¹ s⁻¹.
(ii) Rate = k [B] → First-order reaction. Units of k = s⁻¹.

Question 4.2: For the reaction R → P, the concentration of a reactant changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of the reaction using the unit min⁻¹.

Answer: Average rate = (0.03 – 0.02) / 25 = 0.01 / 25 = 4 × 10⁻⁴ mol L⁻¹ min⁻¹.

Question 4.3: For a reaction, A + B → Product, the rate law is Rate = k [A]ⁿ [B]ᵐ. Can the reaction be an elementary reaction if n or m are not equal to the stoichiometric coefficients?

Answer: No, for an elementary reaction, n and m must match the stoichiometric coefficients. If not, the reaction is complex with multiple steps.

Question 4.4: The conversion of molecules X to Y follows a first-order reaction. Half of X is converted to Y in 20 minutes. Calculate the time taken for 3/4 of X to be converted to Y.

Answer: Time for 3/4 conversion = 40 minutes.

Question 4.5: A first-order reaction is 50% complete in 30 minutes. Calculate the time required for 90% completion of the reaction.

Answer: Time required = 99.7 minutes.

Question 4.6: A first-order reaction takes 40 minutes for 30% decomposition. What is the half-life of the reaction?

Answer: Half-life t₁/₂ ≈ 12.03 minutes.

Question 4.7: What will be the effect of temperature on the rate constant?

Answer: The rate constant increases exponentially with temperature as per the Arrhenius equation.

Question 4.8: The rate of a reaction doubles when the temperature changes from 298 K to 308 K. Calculate the activation energy (Ea).

Answer: Activation energy Ea ≈ 52.86 kJ/mol.

Question 4.9: The activation energy for the reaction 2A → Products is 179.9 kJ/mol at 298 K. Calculate the rate constant at 318 K if the pre-exponential factor (A) is 6.2 × 10¹² s⁻¹.

Answer: Rate constant k ≈ 1.63 × 10⁻¹⁷ s⁻¹.

Question 4.10: In a pseudo first-order reaction, the concentration of a reactant decreases from 0.5 mol/L to 0.25 mol/L in 40 minutes. Calculate the rate constant.

Answer: Rate constant k = 0.0576 min⁻¹.

Question 4.11: Show that in a first-order reaction, time required for 99% completion is twice the time required for 90% completion.

Answer: For 90% completion: t₉₀ = 2.303 / k
For 99% completion: t₉₉ = 4.606 / k
Thus, t₉₉ / t₉₀ = 2.

Question 4.12: A reaction is first order in A and second order in B. Write the rate law. How is the rate affected if the concentration of A is tripled and B is doubled?

Answer: Rate law: Rate = k [A][B]²
New rate = 12 × original rate.

Question 4.13: The rate of the chemical reaction doubles for every 10°C rise in temperature. If the rate increases 8 times, calculate the temperature rise.

Answer: Temperature rise = 30°C.

Question 4.14: In a first-order reaction, 10% of the initial concentration is reacted in 20 minutes. Calculate the rate constant.

Answer: Rate constant k ≈ 0.0053 min⁻¹.

Question 4.15: What is the half-life of a first-order reaction whose rate constant is 0.693 min⁻¹?

Answer: Half-life t₁/₂ = 1 minute.

Question 4.16: Time required to decompose 75% of a reactant in a first-order reaction is 60 minutes. What is the half-life of the reaction?

Answer: Half-life t₁/₂ ≈ 30 minutes.

Question 4.17: The rate constant for a first-order reaction is 60 s⁻¹. How much time will it take to reduce the initial concentration to 1/16th?

Answer: Time ≈ 0.0462 seconds.

Question 4.18: For a first-order reaction, show that time required to complete 99.9% is 10 times the half-life.

Answer: Time for 99.9% completion = 10 × half-life.

Question 4.19: The following data were obtained for the decomposition of NH₃ on platinum surface: [NH₃] (mol/L) and Rate (mol/L/s) 1.5 × 10⁻³ → 3.7 × 10⁻⁸ 2.5 × 10⁻³ → 6.2 × 10⁻⁸ 3.5 × 10⁻³ → 8.7 × 10⁻⁸ Determine the order of the reaction.

Answer: Since rate ∝ concentration, the reaction is first-order.

Question 4.20: The decomposition of dimethyl ether at 504°C follows first-order kinetics. Initially, the pressure is 0.4 atm and after 10 minutes it becomes 0.274 atm. Calculate the rate constant.

Answer: Rate constant k ≈ 0.0379 min⁻¹.

Question 4.21: The following data were obtained for a first-order reaction: Time (min) and [A] (mol/L) 0 → 0.6 30 → 0.3 60 → 0.15 Show that it follows first-order kinetics. Also, calculate rate constant.

Answer: Since ln([A]₀/[A]) is proportional to time, first-order confirmed.
Rate constant k = 0.0231 min⁻¹.

Question 4.22: The rate constant for a reaction at 500 K and 700 K are 5.73 × 10⁻⁴ s⁻¹ and 8.73 × 10⁻² s⁻¹ respectively. Calculate the activation energy.

Answer: Activation energy Ea ≈ 73.19 kJ/mol.