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Chemistry · Chemical Kinetics

NEET (UG) 2024 — Question 89

The rate of a reaction quadruples when temperature changes from 27∘C27^{\circ} \mathrm{C} to 57∘C57^{\circ} \mathrm{C}. Calculate the energy of activation.

Given R=8.314 J K−1 mol−1,log⁡4=0.6021\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, \log 4=0.6021

  1. Option A:

    38.04 kJ mol−138.04\ \mathrm{kJ\ mol^{-1}}

    Correct
  2. Option B:

    380.4 kJ mol−1380.4\ \mathrm{kJ\ mol^{-1}}

  3. Option C:

    3.80 kJ mol−13.80\ \mathrm{kJ\ mol^{-1}}

  4. Option D:

    3804 kJ mol−13804\ \mathrm{kJ\ mol^{-1}}

Answer: A

Step-by-step solution

  1. Convert temperatures to Kelvin: T1=27∘C+273=300 KT_1 = 27^\circ\mathrm{C} + 273 = 300\ \mathrm{K}, T2=57∘C+273=330 KT_2 = 57^\circ\mathrm{C} + 273 = 330\ \mathrm{K}.
  2. Rate quadruples, so k2/k1=4k_2/k_1 = 4. Take logarithm: log⁡(k2k1)=log⁡4=0.6021\log\left(\frac{k_2}{k_1}\right) = \log 4 = 0.6021.
  3. Arrhenius equation in logarithmic form: log⁡(k2k1)=Ea2.303R(1T1−1T2)\log\left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right).
  4. Compute the temperature difference: 1T1−1T2=1300−1330=330−300300×330=3099000=13300\frac{1}{T_1} - \frac{1}{T_2} = \frac{1}{300} - \frac{1}{330} = \frac{330 - 300}{300 \times 330} = \frac{30}{99000} = \frac{1}{3300}.
  5. Substitute into equation: 0.6021=Ea2.303×8.314×133000.6021 = \frac{E_a}{2.303 \times 8.314} \times \frac{1}{3300}.
  6. Solve for EaE_a: Ea=0.6021×2.303×8.314×3300E_a = 0.6021 \times 2.303 \times 8.314 \times 3300.
  7. Calculate: 0.6021×2.303=1.38660.6021 \times 2.303 = 1.3866, 1.3866×8.314=11.5271.3866 \times 8.314 = 11.527, 11.527×3300=38039.1 J mol−111.527 \times 3300 = 38039.1\ \mathrm{J\ mol^{-1}}.
  8. Convert to kJ/mol: Ea=38039.11000=38.04 kJ mol−1E_a = \frac{38039.1}{1000} = 38.04\ \mathrm{kJ\ mol^{-1}}. Therefore, the activation energy is 38.04 kJ mol−138.04\ \mathrm{kJ\ mol^{-1}}, which corresponds to option A.

Answer key and solution verified before publishing.

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Exam
NEET (UG) 2024
Paper
2024 paper
Subject
Chemistry
Chapter
Chemical Kinetics
Topic
Arrhenius Equation

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