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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 · 2018 · Paper I

Q1(c)(ii). Temperature at which the spontaneity switches

  • 5 marks
  • Answered
Question

(ii) Is there a temperature at which formation of MgO switches from spontaneous to non-spontaneous or vice-versa? If no, explain why not? If yes, calculate the temperature at which the spontaniety of the reaction switches?

Answer in brief

Yes. Δ H and Δ S are both negative, so the reaction is spontaneous below T=Δ H/Δ S=5574 K and non-spontaneous above it.

Key points

  • Δ H<0 favours the reaction and Δ S<0 opposes it (one mole of gas, 12O₂, disappears). The entropy term -TΔ S is positive and grows with T. Such a reaction is enthalpy-driven: spontaneous at low T only.
  • T=(Δ H°)/(Δ S°)=-602 000 J mol⁻¹-108 J K⁻¹ mol⁻¹ T=5574 K (≈5300°C)
  • Below 5574 K, Δ G°<0 (spontaneous); above it, Δ G°>0 and MgO would decompose to Mg and O₂. The switch is from spontaneous to non-spontaneous on heating.
  • far below 5574 K, Mg and MgO melt and Mg boils, and Δ H and Δ S change. MgO is in practice stable at every temperature reached in a furnace. On an Ellingham diagram the MgO line rises with slope -Δ S but stays near the bottom,…

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. Both terms have the same sign: Δ H<0 favours the reaction and Δ S<0 opposes it (one mole of gas, 12O₂, disappears). The entropy term -TΔ S is positive and grows with T. Such a reaction is enthalpy-driven: spontaneous at low T only.
  2. The switch comes where Δ G°=0: T=(Δ H°)/(Δ S°)=-602 000 J mol⁻¹-108 J K⁻¹ mol⁻¹ T=5574 K (≈5300°C)
  3. Below 5574 K, Δ G°<0 (spontaneous); above it, Δ G°>0 and MgO would decompose to Mg and O₂. The switch is from spontaneous to non-spontaneous on heating.
  4. The figure is a limit of the model: far below 5574 K, Mg and MgO melt and Mg boils, and Δ H and Δ S change. MgO is in practice stable at every temperature reached in a furnace. On an Ellingham diagram the MgO line rises with slope -Δ S but stays near the bottom, which is why Mg reduces many other oxides.

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Model answer to Q1(c)(ii), 2018 Paper I: solution page 4
Solution page 4 of 55
Read the whole 2018 solution2018 question paper

All parts of Question 1