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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

Q3(a)(ii). Units of a, b, c and Δ S, Δ H from Δ G=a+bT+cT²

  • 15 marks
  • Answered
Question

Δ G (J mol⁻¹) for an electrochemical reaction, as a function of temperature, T (K) is given by Δ G=a+bT+cT²; where a, b and c are constants and independent of T.
(I) What are the units of a, b and c? and
(II) Find the expressions of Δ S and Δ H as a function of T.

Answer in brief

a: J mol⁻¹; b: J K⁻¹ mol⁻¹; c: J K⁻² mol⁻¹. Δ S=-b-2cT and Δ H=a-cT² (also Δ Cₚ=-2cT).

Key points

  • Every term of a sum has the unit of the sum, J mol⁻¹.
  • a: J mol⁻¹ (the value of Δ G extrapolated to T=0)
  • b: J K⁻¹ mol⁻¹ (the unit of entropy)
  • cT² in J mol⁻¹: c: J K⁻² mol⁻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.

RULE(∂Δ G/∂ T)ₚ=-Δ STHENΔ H=Δ G+TΔ SCELLΔ G=-nFE

(I) Units

  1. Every term of a sum has the unit of the sum, J mol⁻¹.
  2. a: J mol⁻¹ (the value of Δ G extrapolated to T=0)
  3. bT in J mol⁻¹ with T in K: b: J K⁻¹ mol⁻¹ (the unit of entropy)
  4. cT² in J mol⁻¹: c: J K⁻² mol⁻¹

(II) Δ S and Δ H

  1. Entropy. From dG=V dp-S dT, at constant pressure (∂Δ G/∂ T)ₚ=-Δ S: Δ S=-((∂Δ G)/(∂ T))ₚ=-d/dT(a+bT+cT²)Δ S=-b-2cT
  2. Enthalpy. Δ G=Δ H-TΔ S, so Δ H=Δ G+TΔ S=a+bT+cT²+T(-b-2cT): Δ H=a-cT²
  3. Check with Gibbs–Helmholtz: [(∂(Δ G/T))/(∂ T)]ₚ=d/dT(a/T+b+cT)=-aT²+c=-Δ HT², which gives Δ H=a-cT² again.
  4. Heat capacity of reaction: Δ Cₚ=(∂Δ H/∂ T)ₚ=-2cT; also T(∂Δ S/∂ T)ₚ=-2cT. If c=0, Δ H and Δ S are independent of T.
  5. Electrochemical form. Δ G=-nFE, so Δ S=nF((∂ E)/(∂ T))ₚ and Δ H=-nF[E-T((∂ E)/(∂ T))ₚ]. Measuring the cell EMF at several temperatures gives a, b and c.

Application. the temperature coefficient of cell EMF is the standard route to reaction entropies and enthalpies of ionic reactions (for example the Daniell cell), without any calorimetry.

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Model answer to Q3(a)(ii), 2017 Paper I: solution page 12
Solution page 12 of 38
Read the whole 2017 solution2017 question paper

All parts of Question 3