Are the potentials of the electrolytes equal in Galvanic cell?

Question

My book defines Electrode Potential for a Galvanic Cell as follows:

A potential difference that develops between the electrode and the electrolyte is called Electrode Potential

$$E= V_{electrode} - V_{electrolyte}\tag1$$

It further defines cell potential as:

The potential difference between the two electrodes of a galvanic cell is called Cell Potential.

Mathematically, I interpret it as $$E_{Cell} = V_{electrode,anode} - V_{electrode,cathode}\tag2$$

However my book further mentions that

The cell potential is the difference between the electrode potential of the anode and cathode.

I interpret this as: $$E_{Cell} = E_{anode} - E_{cathode}$$ From (1) $$E_{cell}=(V_{electrode,anode} - V_{electrolyte,anode} )- (V_{electrode,cathode} - V_{electrolyte,cathode})\tag3$$ To keep the above consistent with (2), $$V_{electrolyte,anode} = V_{electrolyte,cathode}\tag4$$

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I find (4) illogical as there is no basis for the two electrolytes to be at same potential.

What is going on here?

Answer 1

There is a potential difference between an electrode and an electrolyte, but it is not directly measurable and the electrolyte potential is rather undefined.

We do not use electrolyte potentials as reference potentials, as reference must be well defined. By mechanical analogy, it would be like defining the relative height wrt a level that is not clearly given. By other words, the conventional electrode potential is NOT the potential difference between the electrode and electrolyte, even if this difference does exist.

By convention, the electrode potential is considered the potential difference between the electrode and the standard hydrogen electrode(SHE) $E - E^{\circ}_{\ce{H2/H+/Pt}}$.

The cell potential is called rather the cell voltage or the cell electrode potential difference. The cell voltage is difference of electrode potentials, which are difference of electrode potentials wrt SHE.

$$U_\mathrm{cell} = E_\mathrm{cathode} - E_\mathrm{anode} \\ = ( E_\mathrm{cathode,absolute} - E^{\circ}_{\ce{H2/H+/Pt}}) - (E_\mathrm{anode,absolute} - E^{\circ}_{\ce{H2/H+/Pt}})\\ = E_\mathrm{cathode,absolute} - E_\mathrm{anode,absolute}$$

Note that cathode is the more negative one for electrolytic cells, but more positive one for galvanic cells.

The cell voltage and the potential electrode difference wrt SHE ( = the cell voltage if the other electrode were replaced by SHE ) does not depend on the electrolyte potential.