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Thermodynamics question

2021 · 31 Aug · Shift 2 · Q10
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Thermodynamics question

2021 · 31 Aug · Shift 2 · Q10

JEE MainChemistryThermodynamicsMCQ+4 / −1
The incorrect expression among the following is :
  1. A
    ΔGSystemΔSTotal=−T{{\Delta {G_{System}}} \over {\Delta {S_{Total}}}} = - TΔSTotal​ΔGSystem​​=−T (at constant P)
  2. B
    K=ΔH∘−TΔS∘RTK = {{\Delta H^\circ - T\Delta S^\circ } \over {RT}}K=RTΔH∘−TΔS∘​
  3. C
    K=e−ΔG∘/RTK = {e^{ - \Delta G^\circ /RT}}K=e−ΔG∘/RT
  4. D
    For isothermal process wreversible=−nRTln⁡VfVi{w_{reversible}} = - nRT\ln {{{V_f}} \over {{V_i}}}wreversible​=−nRTlnVi​Vf​​
View written solutionFree

Correct answer: B

  1. We check each option using standard thermodynamic relations.
  1. Option A

At constant temperature and pressure,

ΔGsystem=−T ΔStotal\Delta G_{\text{system}} = -T\,\Delta S_{\text{total}}ΔGsystem​=−TΔStotal​

Hence,

ΔGsystemΔStotal=−T\frac{\Delta G_{\text{system}}}{\Delta S_{\text{total}}} = -TΔStotal​ΔGsystem​​=−T

So Option A is correct.

  1. Option B

We know,

ΔG∘=ΔH∘−TΔS∘\Delta G^\circ = \Delta H^\circ - T\Delta S^\circΔG∘=ΔH∘−TΔS∘

and also,

ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln KΔG∘=−RTlnK

Therefore,

ln⁡K=−ΔG∘RT=−ΔH∘−TΔS∘RT\ln K = -\frac{\Delta G^\circ}{RT} = -\frac{\Delta H^\circ - T\Delta S^\circ}{RT}lnK=−RTΔG∘​=−RTΔH∘−TΔS∘​

So the correct relation is

K=e−ΔH∘−TΔS∘RTK = e^{-\frac{\Delta H^\circ - T\Delta S^\circ}{RT}}K=e−RTΔH∘−TΔS∘​

not

K=ΔH∘−TΔS∘RTK = \frac{\Delta H^\circ - T\Delta S^\circ}{RT}K=RTΔH∘−TΔS∘​

Thus Option B is incorrect.

  1. Option C

Using

ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln KΔG∘=−RTlnK

we get

K=e−ΔG∘/RTK = e^{-\Delta G^\circ/RT}K=e−ΔG∘/RT

So Option C is correct.

  1. Option D

For a reversible isothermal expansion/compression of an ideal gas,

wrev=−nRTln⁡(VfVi)w_{\text{rev}} = -nRT\ln\left(\frac{V_f}{V_i}\right)wrev​=−nRTln(Vi​Vf​​)

So Option D is correct.

  1. Therefore, the only incorrect expression is:
B\boxed{\text{B}}B​
  1. Comparison with stored correct answer

Stored correct answer = B

My derived answer = B

So they agree.

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