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Thermodynamics question

2025 · 24 Jan · Shift 1 · Q14
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Thermodynamics question

2025 · 24 Jan · Shift 1 · Q14

JEE MainChemistryThermodynamicsMCQ+4 / −1
Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction is spontaneous at boiling point of water. Choose the correct option.
  1. A
    Both ΔH\Delta \mathrm{H}ΔH and ΔS\Delta \mathrm{S}ΔS are (-ve)
  2. B
    ΔH\Delta \mathrm{H}ΔH is (+ve)(+\mathrm{ve})(+ve) but ΔS\Delta \mathrm{S}ΔS is (-ve)
  3. C
    ΔH\Delta \mathrm{H}ΔH is (−ve)(-\mathrm{ve})(−ve) but ΔS\Delta \mathrm{S}ΔS is (+ve)
  4. D
    Both ΔH\Delta \mathrm{H}ΔH and ΔS\Delta \mathrm{S}ΔS are (+ve)
View written solutionFree

Correct answer: D

  1. For spontaneity, we use the Gibbs free energy relation:

ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta SΔG=ΔH−TΔS

A reaction is spontaneous when:

ΔG<0\Delta G < 0ΔG<0

and non-spontaneous when:

ΔG>0\Delta G > 0ΔG>0

  1. The question states that the reaction is endothermic.

So,

ΔH>0\Delta H > 0ΔH>0

This already rules out options A and C.

  1. The reaction is non-spontaneous at the freezing point of water (0∘C=273 K0^\circ C = 273\,K0∘C=273K), but spontaneous at the boiling point of water (100∘C=373 K100^\circ C = 373\,K100∘C=373K).

That means:

  • At lower temperature: ΔG>0\Delta G > 0ΔG>0
  • At higher temperature: ΔG<0\Delta G < 0ΔG<0
  1. Since

ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta SΔG=ΔH−TΔS

and increasing temperature makes the reaction become spontaneous, the term −TΔS-T\Delta S−TΔS must become more negative as TTT increases.

This is possible only if:

ΔS>0\Delta S > 0ΔS>0

Because if ΔS\Delta SΔS were negative, then −TΔS-T\Delta S−TΔS would be positive and increasing temperature would make ΔG\Delta GΔG even more positive, not negative.

  1. Therefore, we have:

ΔH>0,ΔS>0\Delta H > 0, \qquad \Delta S > 0ΔH>0,ΔS>0

  1. Now evaluate the options:
  • A: ΔH<0\Delta H<0ΔH<0, ΔS<0\Delta S<0ΔS<0 → incorrect
  • B: ΔH>0\Delta H>0ΔH>0, ΔS<0\Delta S<0ΔS<0 → incorrect
  • C: ΔH<0\Delta H<0ΔH<0, ΔS>0\Delta S>0ΔS>0 → incorrect
  • D: ΔH>0\Delta H>0ΔH>0, ΔS>0\Delta S>0ΔS>0 → correct

Therefore, the correct option is:

D\boxed{D}D​

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