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Thermodynamics question

2025 · 23 Jan · Shift 2 · Q8
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  5. /2025 · 23 Jan · Shift 2 · Q8

Thermodynamics question

2025 · 23 Jan · Shift 2 · Q8

JEE MainChemistryThermodynamicsMCQ+4 / −1

The effect of temperature on spontaneity of reactions are represented as :

Δ\DeltaΔ H Δ\DeltaΔ S Temperature Spontaneity
(A) +++ −-− any T Non spontaneous
(B) +++ +++ low T spontaneous
(C) −-− −-− low T Non spontaneous
(D) −-− +++ any T spontaneous

The incorrect combinations are :

  1. A
    (A) and (C) only
  2. B
    (B) and (D) only
  3. C
    (A) and (D) only
  4. D
    (B) and (C) only
View written solutionFree

Correct answer: D

We use the spontaneity criterion:

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

A reaction is spontaneous when:

ΔG<0\Delta G < 0ΔG<0

Now check each combination.


1. Case (A): ΔH>0,  ΔS<0\Delta H > 0,\; \Delta S < 0ΔH>0,ΔS<0

Then

ΔG=(+)−T(−)=(+)+(+)\Delta G = (+) - T(-) = (+) + (+)ΔG=(+)−T(−)=(+)+(+)

So ΔG\Delta GΔG is always positive for any TTT. Hence the reaction is non-spontaneous at any temperature.

So (A) is correct.


2. Case (B): ΔH>0,  ΔS>0\Delta H > 0,\; \Delta S > 0ΔH>0,ΔS>0

Then

ΔG=(+)−T(+)\Delta G = (+) - T(+)ΔG=(+)−T(+)

At low TTT, the ΔH\Delta HΔH term dominates, so ΔG>0\Delta G > 0ΔG>0. At high TTT, the TΔST\Delta STΔS term can dominate, so ΔG<0\Delta G < 0ΔG<0.

Therefore this reaction is spontaneous at high temperature, not low temperature.

So (B) is incorrect.


3. Case (C): ΔH<0,  ΔS<0\Delta H < 0,\; \Delta S < 0ΔH<0,ΔS<0

Then

ΔG=(−)−T(−)=(−)+(+)\Delta G = (-) - T(-) = (-) + (+)ΔG=(−)−T(−)=(−)+(+)

At low TTT, the negative ΔH\Delta HΔH term dominates, so ΔG<0\Delta G < 0ΔG<0. At high TTT, the positive T∣ΔS∣T|\Delta S|T∣ΔS∣ term can dominate, so ΔG>0\Delta G > 0ΔG>0.

Therefore the reaction is spontaneous at low temperature. The table says low TTT, non-spontaneous, which is wrong.

So (C) is incorrect.


4. Case (D): ΔH<0,  ΔS>0\Delta H < 0,\; \Delta S > 0ΔH<0,ΔS>0

Then

ΔG=(−)−T(+)\Delta G = (-) - T(+)ΔG=(−)−T(+)

Both terms make ΔG\Delta GΔG negative for all temperatures. So the reaction is spontaneous at any temperature.

So (D) is correct.


5. Incorrect combinations

The incorrect rows are:

  • (B)
  • (C)

Hence the correct option is:

D: (B) and (C) only\boxed{\text{D: (B) and (C) only}}D: (B) and (C) only​
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