JEE Main · 2025 · Shift-ImediumTHERMO-154

Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

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.

(a) Both ΔH\Delta H and ΔS\Delta S are (+ve)(+\text{ve}) (b) ΔH\Delta H is (ve)(-\text{ve}) but ΔS\Delta S is (+ve)(+\text{ve}) (c) ΔH\Delta H is (+ve)(+\text{ve}) but ΔS\Delta S is (ve)(-\text{ve}) (d) Both ΔH\Delta H and ΔS\Delta S are (ve)(-\text{ve})

Options
  1. a

    Both ΔH\Delta H and ΔS\Delta S are (+ve)(+\text{ve})

  2. b

    ΔH\Delta H is (ve)(-\text{ve}) but ΔS\Delta S is (+ve)(+\text{ve})

  3. c

    ΔH\Delta H is (+ve)(+\text{ve}) but ΔS\Delta S is (ve)(-\text{ve})

  4. d

    Both ΔH\Delta H and ΔS\Delta S are (ve)(-\text{ve})

Correct Answera

Both ΔH\Delta H and ΔS\Delta S are (+ve)(+\text{ve})

Detailed Solution

🧠 Endothermic + non-spontaneous at low T but spontaneous at high T → both ΔH>0\Delta H > 0 and ΔS>0\Delta S > 0 For ΔG=ΔHTΔS\Delta G = \Delta H - T\Delta S to flip from positive to negative as TT increases, the entropy term must grow large enough to overcome ΔH\Delta H. This requires ΔS>0\Delta S > 0.

Since "endothermic" is given: ΔH>0\Delta H > 0. Spontaneous at 373K373\,\text{K} but not at 273K273\,\text{K}: Te=ΔH/ΔST_e = \Delta H / \Delta S lies between 273 and 373 K. This requires ΔS>0\Delta S > 0 so that at high enough TT, TΔS>ΔHT\Delta S > \Delta H.

Answer: (a) Both ΔH and ΔS are positive\boxed{\text{Answer: (a) Both } \Delta H \text{ and } \Delta S \text{ are positive}}

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