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I have the following problem that I would like to get checked.

I’m told to calculate the cell potential of a simple lemon battery experiment.

After Finding out the oxidizing agents and the reducing agents I find that the cell reaction is as follows:

$$\ce{2H+(aq) + Zn(s) —> H2(g) + Zn^2+(aq)}$$

with a cell potential of $E_\mathrm{cell} = +\pu{0.76 V}$.

Are the reactions and the cell potential correct?

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    $\begingroup$ Check the charge balance on the reaction equation. Something's amiss. $\endgroup$ May 1 '20 at 15:24
  • $\begingroup$ Hello, thanks for answering. I have made changes to the reaction. Is it expressed properly? $\endgroup$
    – Nathan
    May 1 '20 at 15:42
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I am afraid that nobody can predict the true potential of Zn/ Cu lemon battery. It is not a standard system. The electrode potentials you see in the published tables are measured or calculated under unknown or controlled conditions and one of the basic requirement is that the metal must be in equilibrium with its own ions.

The lemon battery, although looks very simple, it is too complicated to deal with.

  1. When you insert the electrodes into the lemon, there are no metallic ions to begin with, i.e., the concentration of Zn$^{2+}$ and Cu$^{2+}$ is essentially zero. Just using plug & chug approach for the Nernst equation will give you infinite potential difference. This is not what is experimentally observed.

1b. Even if we assume that some metal dissolves around in a few seconds, still the metal concentration is not high enough to allow a reliable use of Nernst equation.

  1. Citric acid is not only an acid, but it has complexing/chelating property as well.

  2. Any voltage which comes close the calculated potential from redox tables is a mere coincidence.

I think the proper way to determine the potentials generated by contact potentials. This is the realm of physics. Two dissimilar metals, when brought in contact, will generate a potential difference. See my previous answer Electrochemical reactions in a salt water battery

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    $\begingroup$ See en.m.wikipedia.org/wiki/Lemon_battery for experimental data. $\endgroup$ May 1 '20 at 20:13
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    $\begingroup$ I upvoted the answer because it clearly points out significant issues with this user-friendly, though misunderstood, voltaic cell. Not only does the “theory” of the lemon cell take unsupportable liberties with the Nernst equation, but the inert cathode composition matters, even though hydrogen gas is evolved. So copper, silver, gold and platinum cathodes do not all give the same cell potential, other things equal. $\endgroup$
    – Ed V
    May 31 '20 at 20:45

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