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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I

Q6(a)(i). Effect of temperature on the rate constant

  • 5 marks
  • Answered
Question

Explain the effect of temperature on rate constant.

Answer in brief

The rate constant rises exponentially with temperature, k=Ae^(-Eₐ/RT) (Arrhenius). Near room temperature many reactions double their rate for a 10 K rise.

Key points

  • k=Ae^(-Eₐ/RT), with A the pre-exponential (frequency) factor and Eₐ the activation energy. A plot of ln k against 1/T is a straight line of slope -Eₐ/R.
  • only collisions with energy at least Eₐ react. The fraction of such molecules is e^(-Eₐ/RT) (Maxwell–Boltzmann tail). A small rise in T enlarges this tail many times, while the collision frequency rises only as √T.
  • ln(k₂)/(k₁)=(Eₐ)/(R)((1)/(T₁)-(1)/(T₂)). A reaction with Eₐ=53 kJ mol⁻¹ doubles its rate between 298 and 308 K (temperature coefficient k_(T+10)/k_T≈2).
  • The larger Eₐ, the steeper the line and the more sensitive the rate to temperature. Reactions with Eₐ≈0 (radical recombination) hardly change.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

  1. Arrhenius equation: k=Ae^(-Eₐ/RT), with A the pre-exponential (frequency) factor and Eₐ the activation energy. A plot of ln k against 1/T is a straight line of slope -Eₐ/R.
  2. Why: only collisions with energy at least Eₐ react. The fraction of such molecules is e^(-Eₐ/RT) (Maxwell–Boltzmann tail). A small rise in T enlarges this tail many times, while the collision frequency rises only as √T.
  3. Two temperatures: ln(k₂)/(k₁)=(Eₐ)/(R)((1)/(T₁)-(1)/(T₂)). A reaction with Eₐ=53 kJ mol⁻¹ doubles its rate between 298 and 308 K (temperature coefficient k_(T+10)/k_T≈2).
  4. The larger Eₐ, the steeper the line and the more sensitive the rate to temperature. Reactions with Eₐ≈0 (radical recombination) hardly change.
  5. Exceptions: enzyme reactions fall above an optimum temperature (denaturation); some termolecular reactions (2NO + O₂) slow down on heating.

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Model answer to Q6(a)(i), 2018 Paper I: solution page 35
Solution page 35 of 55
Read the whole 2018 solution2018 question paper

All parts of Question 6