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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 · 2019 · Paper I

Q5(d). Linear fall of [A] with time: zero order

  • 10 marks
  • Answered
Question

For the reaction A→ B the plot of conc. of A against time (t) was found to be linear with a negative slope. Predict the order of reaction. Justify your answer.

Answer in brief

Zero order: -d[A]/dt=k, so [A]=[A]₀-kt, a straight line of slope -k.

Key points

  • for order zero the rate does not depend on [A]: -(d[A])/(dt)=k. Integrating from [A]₀ at t=0: [A]=[A]₀-kt.
  • this is y=c+mx with intercept [A]₀ and slope -k: a straight line with negative slope, exactly as observed. The rate constant is the magnitude of the slope.
  • first order gives [A]=[A]₀e^(-kt), a curve (only ln[A] against t is linear); second order makes 1/[A] linear. A linear [A]–t plot rules them out.
  • t_(1/2)=([A]₀)/(2k), proportional to the starting concentration; the reaction is complete at t=[A]₀/k (the line meets the axis) and the rate law then fails.

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. Integration: for order zero the rate does not depend on [A]: -(d[A])/(dt)=k. Integrating from [A]₀ at t=0: [A]=[A]₀-kt.
  2. Match with the graph: this is y=c+mx with intercept [A]₀ and slope -k: a straight line with negative slope, exactly as observed. The rate constant is the magnitude of the slope.
  3. Not first or second order: first order gives [A]=[A]₀e^(-kt), a curve (only ln[A] against t is linear); second order makes 1/[A] linear. A linear [A]–t plot rules them out.
  4. Consequences: t_(1/2)=([A]₀)/(2k), proportional to the starting concentration; the reaction is complete at t=[A]₀/k (the line meets the axis) and the rate law then fails.
  5. Why rate can be independent of [A]: the rate is limited by something else that is constant: a saturated catalyst surface (2NH₃ → N₂ + 3H₂ on hot W or Pt at high pressure), a fixed light intensity (photochemical H₂ + Cl₂), or an enzyme saturated with substrate.

Application. controlled-release drug tablets and transdermal patches are designed for zero-order release, so the dose delivered per hour stays constant.

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Model answer to Q5(d), 2019 Paper I: solution page 25
Solution page 25 of 40
Read the whole 2019 solution2019 question paper

All parts of Question 5