Starting with the thermodynamic relationships, G=H-TS,derive the following relationship:

deltaG=-TdeltaS(total).

G = H - TS

on differentiating

∆G = ∆H - T∆S - S∆T

The reaction occurs at constant T, so ∆T = 0

∆G = ∆H - T∆S

We also know that entropy change of surrounding, ∆Ssurr = -∆H / T

∆H = - T.∆Ssurr

Substituting this value in ∆G = ∆H - T∆S

∆G = - T.∆Ssurr - T.∆S

∆G = - T.(∆Ssurr + ∆S)

but we know that ∆Ssurr + ∆S = ∆Stotal

∆G = - T.(∆Stotal)

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