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I have a background in solid state physics but am new to electrochemistry. I have been following the example of a physical chemistry (Mortimer) book that looks an electrochemical cell with a hydrogen electrode and a silver-silver choloride electrode. Electrochemical cell example from Physical Chemistry page 294, by Mortimer, 2000

The two half reactions are: \begin{align} \ce{H2(g) &-> 2 H+(aq) + 2 e-(aq)}\\ \ce{AgCl(s) + e^- &-> Ag(s) + Cl^-(aq)} \end{align}

The silver-silver chloride electrode consists of a silver wire coated with a silver-chloride solid. If we connect the two electrodes and allow current to flow then there will be a flow of electrons from left to right. The half-reaction on the silver-silver chloride reaction says that the chloride will come off of the solid and go into solution in the electrolyte. The hydrogen electrode has hydrogen gas being constantly flowed into the system. However, the silver-silver chloride electrode, for me, will eventually run out of silver-chloride if the cell is run continuously. I can't seem to find any texts that treat this.

I found this question here, but it doesn't quite address the same issue.

This seems to be a key point in the cell-type reactions that the reactants are supplied such that the activities/concentrations do not change. Thus there is a stable current. It also seems to bring up a few ideas on chemical equilibrium. In my intuition as long as there is an electrical current the reaction is ongoing, thus the reactants and products are not in thermodynamic equilibrium...

Excuse the rambling question, it is not all quite straight in my head yet.

Thanks

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    $\begingroup$ Note that reference electrodes as SHE or AgCl ones are NOT assumed to be used under any significant current load. Rather measured in stationary state with very high input impedance of digital voltmeters. When there is ongoing significant current activity in electrolytic or in galvanic mode, there are used "working electrodes" and the reference electrode is used as the 3rd, reference point in "currentless" mode. Note that AgCl electrode will be kinetically very limited due very low Ag+ ion concentration. $\endgroup$
    – Poutnik
    Commented Aug 25, 2023 at 13:49
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    $\begingroup$ Note you can write $$\ce{H2(g) -> 2 H+(aq) + 2 e-(aq)}$$ to get $$\ce{H2(g) -> 2 H+(aq) + 2 e-(aq)}$$ as Chemistry SE site uses by default the optional mhchem MathJax package (usable on other SE sites too via \require{mhchem} ) $\endgroup$
    – Poutnik
    Commented Aug 25, 2023 at 13:57
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    $\begingroup$ Chem+Math Expression formatting reference: MathJax Basics / Chem+Math expressions/formulas/equations / Upright vs italic / Math SE Mathjax tutorial // MathJax is preferred not to be used in CH SE Q titles. $\endgroup$
    – Poutnik
    Commented Aug 25, 2023 at 14:00

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Yes, it will absolutely run out. To put it simply, this is a battery, and it will run out of juice like any other battery.

You're also correct about which reactant would run out first. The hydrogen can presumably be pumped in indefinitely, but there is only so much $Ag^+$ available. So in this cell, the oxidizer would run out first.

As Poutnik noted in the comments, these are reference electrodes. They are not intended to supply a singificant amount of power. In other words, as a battery, this setup is very poor, and would never actually be used. But if you were trying to design a silver-hydrogen battery, you would want to cram in as much silver chloride as possible, perhaps by having it on the surface of something like a mesh or sponge. That way you could get the reaction to continue for the longest possible time.

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