# How to deduct the concentration of chloride in a silver/silver chloride electrode, given the cell notation

I have this cell notation:

$$\ce{Zn|ZnCl_2(0.05M)||AgCl(s)|Ag} \tag{1}$$

What is the physical shape of this cell? I know $$\ce{AgCl}$$ has very low solubility, and the problem has no concentration on the right side. Is it an aqueous solution, and they just forgot to write the concentration of $$\ce{Ag+}$$ and $$\ce{Cl-}$$? Or is it really a solid with no aqueous solution? Can it have a porous disk or salt bridge if it is non aqueous?

The half reactions are:

oxidation: $$\ce{Zn -> Zn^{2+} + 2e^-}$$ reduction: $$\ce{2AgCl(s) + 2e^--> 2Ag(s) + 2Cl^-}$$ So, when calculating the reaction quotient: $$Q=[\ce{Zn^2+}][\ce{Cl-}]^2$$ What is the concentration that we use in the formula? Can we asume that the concentration/activity of the chloride in the left is the same as in the right?

The cell notation doesn't indicate, nor limit the shape of the electrochemical cell. In the form used by you, it only describes a zinc electrode in a (presumed aqueous) solution of $$\ce{ZnCl2}$$ ($$c = \pu{0.05 mol/L}$$) on one side, and a silver/silver chloride electrode (which isn't the same as a silver electrode proper, because the activity of the $$\ce{Ag+}$$ now is noticeably tied to the solubility product of $$\ce{AgCl}$$) on the other.

In addition: even if presumed water indeed is the solvent, it doesn't yet consider temperature as parameter.

Wikipedia's article on the silver electrode has the following:

$$\ce {{Ag(s)}\ |\ {AgCl(s)}\ |\ KCl(aq)\ (3M)}$$

That makes sense because the chloride has to come from somewhere (or go somewhere), and you need to know its concentration to plug into the Nernst equation.

For the zinc electrode, it might be better to write:

$$\ce{Zn(s) | Zn^2+(aq) (0.05M)}$$

because here, the chloride ions are spectator ions (switching to different anions would not affect the potential, ideally).

UPDATE:

The net equation could be written like this:

$$\ce{Zn(s) + 2AgCl(s) -> ZnCl2(aq) + 2 Ag(s)}$$

However, this ignores the aqueous chloride ions in the half cell with AgCl that you need to make the reaction go. For the equilibrium constant expression, this would be more useful:

$$\ce{Zn(s) + 2AgCl(s) -> Zn^2+(aq1) + 2 Ag(s) + 2Cl- (aq2)}$$

with (aq1) and (aq2) showing the two separated aqueous compartments (with independent concentrations).

If you attempt to "cancel out" the chloride, you get this incorrect net equation:

$$\ce{Zn(s) + 2Ag+(s) -> Zn^2+(aq) + 2 Ag(s)}$$

The presence of an ion in the solid state should alert you to the problem. I think this is sufficiently tricky to ask the instructor about it, referencing the question and answers in this thread.

• I added some information about the problem. We are asked to calculate the reaction quotient. Can we asume that the concentration of chloride in the cathode is fixed by the concentration of chloride in the anode? Commented Mar 7 at 17:04
• This could be one reasoning. The other would be the assumption that you always use saturated KCl. Why don't you ask your instructor instead of here?
– Karsten
Commented Mar 7 at 17:31
The cell description is somewhat vague and leaves much to the imagination; it indicates a liquid junction to a solid-state reaction. The Ag-AgCl electrode is reversible to the chloride ion. Its typical use is as a voltage standard used at minimal, hopefully zero, current draw (AKA a good pH meter). This requires a definite or at least constant concentration of chloride ions. The half reaction is: $$\ce{AgCl +e- <=> Ag + Cl-}$$. For the use as a voltage standard the electrode is immersed in a small container of chloride ion of definite concentration; the connection to the solution is usually a small restrictive flowing junction and the electrode system is immersed in a solution containing another electrode (for a pH meter a glass electrode) and the voltage measured.
Your cell suggests something else. Either a cell to oxidize zinc by reducing AgCl to Ag, or, at zero current flow, using the electrode as a chloride ion detector. If zinc metal were added to a solution of silver ions the silver ions would be reduced plating out silver metal. To make a cell there would have to be anode and cathode compartments connected by a salt bridge to keep the silver ions away from the zinc metal. The reaction is $$\ce{2Ag+ + Zn <=> Ag + Zn++}$$. The reaction quotient is $$\ce{[Zn++]/[Ag+]^2}$$. The pure silver and zinc both have activities defined as 1. (The reactions are in acid so there are plenty of negative spectator ions about.)
A second method to keep the silver ions away from the zinc is to enclose them in an almost insoluble salt such as AgCl (This makes the $$\ce{Ag+}$$ a poorer oxidant but it still works). A bare silver-silver chloride electrode is dipped into a solution containing $$\ce{Zn++}$$ and $$\ce{Cl-}$$ ion with a separated Zn metal electrode. [no need for the salt bridge] The reaction is: $$\ce{Zn + 2AgCl <=> Ag + Zn++ + 2 Cl-}$$. The reaction quotient is $$\ce{[Zn++][Cl-]^2}$$; the numerator is one because the activities of the pure Zn and AgCl are defined as 1. (This is an expensive way to make zinc ions.) When the bare electrode is paired with a standard enclosed Ag-AgCl (or calomel) electrode it becomes a chloride ion detector.