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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 · 2017 · Paper I

Q5(a). Arrhenius equation for zero order; high-temperature limit of k

  • 10 marks
  • Answered
Question

For zero-order reaction, write down the Arrhenius equation, indicating name of the symbols and their units in SI system. What is high temperature limiting value of rate constant?

Answer in brief

k=A e^(-Eₐ/RT); for zero order k and A are in mol m⁻³ s⁻¹. As T→∞, e^(-Eₐ/RT)→1 and k→ A: the pre-exponential factor is the upper limit of the rate constant.

Key points

  • Arrhenius equation: k=A e^(-Eₐ/RT), or ln k=ln A-(Eₐ)/(RT)
  • Symbols and SI units (zero-order reaction, rate =-d[A]/dt=k): itemize
  • rate constant; same unit as the rate, mol m⁻³ s⁻¹ (in practice mol dm⁻³ s⁻¹).
  • pre-exponential (frequency) factor; the exponential is a pure number, so A has the unit of k, mol m⁻³ s⁻¹.

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=A e^(-Eₐ/RT), or ln k=ln A-(Eₐ)/(RT)
  2. Symbols and SI units (zero-order reaction, rate =-d[A]/dt=k): itemize
  3. k: rate constant; same unit as the rate, mol m⁻³ s⁻¹ (in practice mol dm⁻³ s⁻¹).
  4. A: pre-exponential (frequency) factor; the exponential is a pure number, so A has the unit of k, mol m⁻³ s⁻¹.
  5. Eₐ: activation energy, J mol⁻¹.
  6. R: gas constant, 8.314 J K⁻¹ mol⁻¹. T: thermodynamic temperature, K. itemize
  7. High-temperature limit. As T→∞, Eₐ/RT→0 and e^(-Eₐ/RT)→1: _(T→∞)k=A
  8. Meaning. e^(-Eₐ/RT) is the fraction of collisions with energy at least Eₐ. At very high T nearly every encounter has enough energy, so the rate is set by how often reactants meet in the right orientation, which is what A measures. k can never exceed A.
  9. From a plot: ln k against 1/T is a straight line of slope -Eₐ/R; its intercept at 1/T=0 is ln A.

Application. zero-order kinetics are met in surface-catalysed reactions at high pressure (decomposition of NH₃ on hot tungsten) and in enzyme reactions at saturating substrate; the Arrhenius plot of k gives Eₐ for such processes.

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Model answer to Q5(a), 2017 Paper I: solution page 19
Solution page 19 of 38
Read the whole 2017 solution2017 question paper

All parts of Question 5