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)