UPSC Combined Geo-Scientist, Mains · 2019 · Mains Paper II
Q1(j). Zero-order half-life
Question
Define a zero-order reaction and show that its half-life is proportional to initial reactant concentration.
Answer in brief
For -d[A]/dt=k, t_(1/2)=[A]₀/(2k).
Key points
- A zero-order reaction has a rate independent of reactant concentration within the applicable regime.
- Integrating d[A]=-kdt gives [A]ₜ=[A]₀-kt. Setting [A]ₜ=[A]₀/2 gives the stated half-life.
- Thus doubling the initial concentration doubles the half-life at fixed k.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversZero-order half-lifeChemical kinetics
All parts of Question 1
- 1(a) Atomicity from heat capacities5 marks
- 1(b) Units of attraction parameter5 marks
- 1(c) Surface energy of cube and sphere5 marks
- 1(d) Atoms in a BCC sample5 marks
- 1(e) Volume independence of ideal-gas heat capacity5 marks
- 1(f) Entropy on doubling volume5 marks
- 1(g) Single-ion activity coefficients5 marks
- 1(h) Ammonia buffer5 marks
- 1(i) Pure-component vapour pressures5 marks
- 1(j) Zero-order half-life5 marks
- 1(k) Physical and chemical adsorption5 marks
- 1(l) Iron redox-electrode potential5 marks
- 1(m) Energy of one einstein5 marks
- 1(n) Bohr quantisation from matter waves5 marks
- 1(o) Spectral wavelength shifts5 marks
- 1(p) Bromobutane with one NMR signal5 marks