UPSC Civil Services (Mains), Chemistry optional · 2023 · Paper I
Q1(e)(i). E° of Cr³⁺/Cr from two couples
Question
Calculate the E° value for the half-reaction Cr³⁺(aq) + 3e⁻ → Cr. Given that at 25 °C: Cr³⁺(aq) + e⁻ → Cr²⁺(aq), E° = −0.424 V; Cr²⁺(aq) + 2e⁻ → Cr, E° = −0.90 V.
Answer in brief
E°(Cr³⁺/Cr) = [1(−0.424) + 2(−0.90)]/3 = −0.741 V.
Key points
- E° is an intensive quantity; the two steps carry different numbers of electrons, so the quantity that adds is ΔG° = −nFE°.
- ΔG°₁ = +0.424F for the one-electron step and ΔG°₂ = +1.80F for the two-electron step; the sum is ΔG°₃ = +2.224F.
- E°₃ = (n₁E°₁ + n₂E°₂)/(n₁ + n₂) = −2.224/3 = −0.741 V.
- The value lies between the two given potentials, nearer the two-electron step; chromium dissolves in acid with evolution of hydrogen.
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.
Coversstandard electrode potentialLatimer diagramGibbs energy additivityFrost diagramchromium
All parts of Question 1
- 1(a) Light emitted by a particle in a box; the uncertainty principle10 marks
- 1(b) Lewis structures of [Br₃]⁻ and thiourea; the most polar bond10 marks
- 1(c) Bragg equation and the layer spacing10 marks
- 1(d) Root-mean-square speed of water molecules10 marks
- 1(e)(i) E° of Cr³⁺/Cr from two couples5 marks
- 1(e)(ii) Surface tension, contact angle and loss of gravity5 marks