[Big-Daddy]

We know the equation ΔS°=nF*(dE°/dT). I read that the temperature dependence of E° is given by the Gibbs-Helmholtz equation which involves ΔG°, but can't we just use ΔS°=nF*(dE°/dT), separate the variables and integrate? We'll get

ΔS° * (T₂-T₁) = nF * (E°_T2 - E°_T1)

unless I made a stupid mistake.

[Radu]

   There are two approaches for this problem:
                 - you either write Δ°G=Δ°H-TΔ°S and hence E°_T=-Δ°H/nF + Δ°S*T/nF
                 - or differentiating the first equation you obtain d(Δ°G)/dT= -Δ°S , and whence, knowing that Δ°G=-nEF, that dE°/dT = Δ°S/nF. Integrating from T=298 to T ( solving the differential equation) gives the explicite T dependence. No difference between them.

[Big-Daddy]

   There are two approaches for this problem:
                 - you either write Δ°G=Δ°H-TΔ°S and hence E°_T=-Δ°H/nF + Δ°S*T/nF
                 - or differentiating the first equation you obtain d(Δ°G)/dT= -Δ°S , and whence, knowing that Δ°G=-nEF, that dE°/dT = Δ°S/nF. Integrating from T=298 to T ( solving the differential equation) gives the explicite T dependence. No difference between them.

The methods are equivalent of course. Thanks. The first one is just using E°_T1 and ΔS° to calculate ΔH°, and then with both ΔS° and ΔH° you can calculate ΔG° at the required temperature T₂ and thus find E°_T2.

So you agree with my end result in the first post?

[Radu]

Yes, your result seems correct.
   Anyway, if we had a wide range of temperatures, say , ΔT>100K, only the second method would be viable, because Δ°H, as well as Δ°S, would have an explicit dependence of temperature.