JEE Main Β· 2021 Β· Shift-IImediumTHERMO-071

The incorrect expression among the following is: (1) For isothermal process wreversible = -nRTVfVi (2) K = H - T SRT…

Thermodynamics Β· Class 11 Β· JEE Main Previous Year Question

Question

The incorrect expression among the following is:

(1) For isothermal process wreversible=βˆ’nRTln⁑VfViw_{\text{reversible}} = -nRT\ln\frac{V_f}{V_i} (2) ln⁑K=Ξ”Hβˆ˜βˆ’TΞ”S∘RT\ln K = \frac{\Delta H^\circ - T\Delta S^\circ}{RT} (3) Ξ”GSystemΞ”STotal=βˆ’T\frac{\Delta G_{\text{System}}}{\Delta S_{\text{Total}}} = -T (at constant P) (4) K=eβˆ’Ξ”G∘/RTK = e^{-\Delta G^\circ/RT}

Options
  1. a

    For isothermal process: wrev=βˆ’nRTln⁑VfViw_{\text{rev}}=-nRT\ln\frac{V_f}{V_i}

  2. b

    ln⁑K=Ξ”Hβˆ˜βˆ’TΞ”S∘RT\ln K=\frac{\Delta H^\circ-T\Delta S^\circ}{RT}

    βœ“
  3. c

    Ξ”GSystemΞ”STotal=βˆ’T\frac{\Delta G_{\text{System}}}{\Delta S_{\text{Total}}}=-T (at constant P)

  4. d

    K=eβˆ’Ξ”G∘/RTK=e^{-\Delta G^\circ/RT}

Correct Answerb

ln⁑K=Ξ”Hβˆ˜βˆ’TΞ”S∘RT\ln K=\frac{\Delta H^\circ-T\Delta S^\circ}{RT}

Detailed Solution

🧠 ln⁑K=βˆ’Ξ”G∘/RT\ln K = -\Delta G^\circ / RT β€” the sign matters Starting from Ξ”G∘=Ξ”Hβˆ˜βˆ’TΞ”S∘=βˆ’RTln⁑K\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ = -RT\ln K: ln⁑K=βˆ’(Ξ”Hβˆ˜βˆ’TΞ”S∘)RT=TΞ”Sβˆ˜βˆ’Ξ”H∘RT\ln K = \frac{-(\Delta H^\circ - T\Delta S^\circ)}{RT} = \frac{T\Delta S^\circ - \Delta H^\circ}{RT}

Option (2) writes ln⁑K=Ξ”Hβˆ˜βˆ’TΞ”S∘RT\ln K = \frac{\Delta H^\circ - T\Delta S^\circ}{RT} β€” the sign in the numerator is flipped. That makes it incorrect.

πŸ—ΊοΈ Checking the rest (1) wrev=βˆ’nRTln⁑(Vf/Vi)w_{\text{rev}} = -nRT\ln(V_f/V_i) β€” correct isothermal reversible work. βœ“

(3) Ξ”Gsystem/Ξ”Stotal=βˆ’T\Delta G_{\text{system}}/\Delta S_{\text{total}} = -T: since Ξ”G=βˆ’TΞ”Stotal\Delta G = -T\Delta S_{\text{total}} at constant PP, dividing both sides by Ξ”Stotal\Delta S_{\text{total}} gives βˆ’T-T. βœ“

(4) K=eβˆ’Ξ”G∘/RTK = e^{-\Delta G^\circ/RT}: rearranging Ξ”G∘=βˆ’RTln⁑K\Delta G^\circ = -RT\ln K gives this directly. βœ“

Only expression (2) = option (b) is wrong.

⚠️ Trap: The minus sign in ln⁑K=βˆ’Ξ”G∘/RT\ln K = -\Delta G^\circ/RT trips many students. A negative Ξ”G∘\Delta G^\circ gives a positive ln⁑K>0\ln K > 0, i.e., K>1K > 1 β€” which makes sense for a spontaneous reaction.

Answer:Β (b)\boxed{\text{Answer: (b)}}

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