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An electrochemical cell is shown here.

$$\ce{Ag(s)~|~AgCl(s)~|~KCl(1M)~|~Hg2Cl2(s)~|~Hg(l)~|~Pt}$$

I am used to seeing cell representations with a $||$ for a salt bridge between the two electrode solutions (generally with the anodic solution written first followed by the cathodic solution).

I am seeing the above type of representation for the first time. Can someone tell me what it means? (including which are the anodic and cathodic solutions). Also, how do we write the reactions at anode and cathode for the above cell?

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This is an example of an electrolytic concentration cell.

Both the cathode and the anode have the same electrolyte present and both are in same solution. Thus, there is no need to separate the electrolyte in two different solution and connect by a salt bridge.

The anode and cathode both are metal-sparingly soluble salt-salt anion electrode. The $\ce {KCl}$ solution here is the common electrolyte.

The anode reaction is:$$\ce {Ag(\text{metal})(s) + Cl^-(\text{salt anion})(aq) -> AgCl(\text{sparingly soluble salt})(s) + e^-}$$

The cathode reaction is also similar: $$\ce {Hg2Cl2(s) + 2e^- -> 2\ce{Hg}(l) + 2Cl^-(aq)}$$

Observe that the $\ce {Cl^-} $ is present in both the reactions as a common electrolyte's ion.

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