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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

Q1(e). E°(Ag⁺/Ag) from the equilibrium constant

  • 10 marks
  • Answered
Question

The equilibrium constant for the reaction:
Fe³+(aq) + Ag(s) ⇌ Fe²+(aq) + Ag+(aq); is 0.531 at 298 K. Calculate E°_(Ag+(aq)/Ag(s)) when E°_(Fe³+(aq)/Fe²+(aq))=0.770 V at 298 K.

Answer in brief

E°_(cell)=RT/Fln K=-0.0163 V =E°(Fe³+/Fe²+)-E°(Ag⁺/Ag), so E°(Ag⁺/Ag)=0.786 V.

Key points

  • cathode (reduction) Fe³+ + e⁻ → Fe²+; anode (oxidation) Ag → Ag⁺ + e⁻. One electron is transferred: n=1.
  • E°_(cell)=E°_(cathode)-E°_(anode)=E°(Fe³+/Fe²+)-E°(Ag⁺/Ag)
  • -nFE°_(cell)=-RTln K, so E°_(cell)=(RT)/(nF)ln K=(8.314×298)/(1×96485)ln(0.531)=(0.025678)(-0.6330), E°_(cell)=-0.0163 V
  • E°(Ag⁺/Ag)=0.770-(-0.0163), E°_(Ag⁺/Ag)=0.786 V

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

Given: K=0.531, T=298 K, E°(Fe³+/Fe²+)=0.770 V, n=1, F=96485 C mol⁻¹, R=8.314 J K⁻¹ mol⁻¹.

  1. Half-reactions: cathode (reduction) Fe³+ + e⁻ → Fe²+; anode (oxidation) Ag → Ag⁺ + e⁻. One electron is transferred: n=1.
  2. Standard cell potential: E°_(cell)=E°_(cathode)-E°_(anode)=E°(Fe³+/Fe²+)-E°(Ag⁺/Ag)
  3. From K: -nFE°_(cell)=-RTln K, so E°_(cell)=(RT)/(nF)ln K=(8.314×298)/(1×96485)ln(0.531)=(0.025678)(-0.6330), E°_(cell)=-0.0163 V
  4. Solve for silver: E°(Ag⁺/Ag)=0.770-(-0.0163), E°_(Ag⁺/Ag)=0.786 V
  5. Sign check: K<1 means Δ G°=-RTln K=+1.57 kJ mol⁻¹>0 and E°_(cell)<0: under standard conditions Fe³+ does not quite oxidise silver, so E°(Ag⁺/Ag) must lie a little above 0.770 V. The tabulated value is 0.80 V; the printed K gives 0.786 V.

Application. the two potentials are so close that the direction of the reaction is set by concentrations: a high [Fe³+], or removal of Ag⁺ (for example as AgCl), drives it forward. This is why iron(III) nitrate solution is used as a mild etchant for silver.

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Model answer to Q1(e), 2020 Paper I: solution page 6
Solution page 6 of 45
Read the whole 2020 solution2020 question paper

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