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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 · 2020 · Paper I

Q7(a)(i). A reaction complete in twice its half-life: zero order

  • 7 marks
  • Answered
Question

A reaction completes in twice the time of its half-life period. What is the order of the reaction? Give reason(s).

Answer in brief

Zero order. For a zero-order reaction [A] falls linearly: completion takes [A]₀/k and the half-life is [A]₀/2k, so t_(100%)=2t_(1/2). Reactions of any other order never reach completion in a finite time.

Key points

  • rate =-d[A]/dt=k, independent of concentration. Integrating: [A]=[A]₀-kt, a straight line that reaches zero.
  • [A]=0 at t_(100%)=([A]₀)/(k). Half-life: [A]=[A]₀/2 at t_(1/2)=([A]₀)/(2k)
  • Ratio: t_(100%)t_(1/2)=([A]₀/k)/([A]₀/2k)=2 ⇒ zero order
  • for first order [A]=[A]₀e^(-kt) only approaches zero (after 2t_(1/2), 25 % remains); for second order 1/[A]=1/[A]₀+kt also never reaches zero. Only for n<1 does a reaction finish in finite time, and only n=0 gives exactly…

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. Zero order: rate =-d[A]/dt=k, independent of concentration. Integrating: [A]=[A]₀-kt, a straight line that reaches zero.
  2. Completion: [A]=0 at t_(100%)=([A]₀)/(k). Half-life: [A]=[A]₀/2 at t_(1/2)=([A]₀)/(2k)
  3. Ratio: t_(100%)t_(1/2)=([A]₀/k)/([A]₀/2k)=2 ⇒ zero order
  4. No other order fits: for first order [A]=[A]₀e^(-kt) only approaches zero (after 2t_(1/2), 25 % remains); for second order 1/[A]=1/[A]₀+kt also never reaches zero. Only for n<1 does a reaction finish in finite time, and only n=0 gives exactly 2t_(1/2).

Application. zero order is shown by surface reactions at high pressure (PH₃ on hot tungsten) and by enzyme reactions with excess substrate: the drug release of a constant-rate (zero-order) formulation also follows this straight line.

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Model answer to Q7(a)(i), 2020 Paper I: solution page 34
Solution page 34 of 45
Read the whole 2020 solution2020 question paper

All parts of Question 7