# If E° of a Half Cell is based on the chosen reference Electrode (Generally SHE) then how is the equation ΔG°= -nFE° be valid for a Half Cell

For example let us take the reaction:

Zn(s) ---> Zn^2+(aq) + 2e^-(aq) ;ΔG°, which we are considering as our half cell

And now suppose, by taking the value of E° of SHE(Standard Hydrogen Electrode) as zero and using it as reference, we have measured the E° of the zinc electrode. But clearly this value is relative to SHE and not the absolute value.

Now we have the equation ΔG°= -nFE° , relating the change in Gibbs energy of the half cell reaction and the value of E°. The change in standard Gibbs energy of a reaction is constant at a constant temperature and has nothing to do with the chosen reference electrode so how can we relate both the values?

My another doubt is why even bother defining a reference electrode if we can find the electrode potentials of a half cell with its change in gibbs energy. Or is it the other way around, that we calculate the value of ΔG based on the measured value of E.

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If we use the tabelated reduction potential $$E°$$ of a half-reaction in the equation $$ΔG° = -nFE°$$ the we implicitly assume the reaction $$\ce{Ox(aq) + \frac n2 H2(g) -> Red(aq) + n H+(aq)}$$.
If other than SHE half reaction had been chosen as the conventional potential reference, the respective implicit reaction would have been different, with different $$ΔG°$$ and different $$E°$$ for both the reaction and the zinc half reaction.
If we consider two general half-reactions then $$Δ_\text{r}G{^\circ} = -nF(E{^\circ}_\text{cathode} - E{^\circ}_\text{anode} )$$
You can’t calculate the Gibbs energy for a half cell, just like you can’t do a redox reaction with a half cell, only. In the formula $$ΔG°= -n F E°$$ the $$E°$$ refers to the cell potential, not the half cell reduction potential. The former is independent of a reference electrode, while the latter is not.