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Answer:
An anonymous professor, who is studying electrochemistry, kindly answered the question
above.
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Copper will be the "anode" (the negative electrode of the battery) and
copper metal will be oxidized to doubly positively charged copper
"cations", leaving back electrons in the metal which will travel to the silver "cathode" (positive electrode) through the outside
circuit and hydrogen ions will be reduced to hydrogen gas (positively charged hydrogen ions will accept electrons). |

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Lemon cell
From Hila Science
Camp, with permission
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The silver in this case
is just a source of electrons (inert electrode), it does not participate in any chemical reaction.
Yes, copper is above hydrogen in the "electromotive series", but that series gives the "standard potentials" correct at unit concentrations
of the ions. Now, the lemon has practically zero copper ions (luckily,
otherwise it would be a poison for us) but plenty of hydrogen ions (since it is sour or acidic). The concentrations will affect the
potential according to the "Nernst equation" and that will flip the potentials around. Admittedly, this is not a very good battery, the
copper ions will soon build up around the electrode to such a concentration that the battery will soon stop working. It would be much
better to use zinc in place of the copper, it will give higher potential and larger, and longer lasting current.
The terms used above can be found defined in the Electrochemistry
Dictionary.
It so happens that one of the first batteries ever built (Volta Pile, more than 200 years ago) used the zinc-silver pile system. You can find a
simply written article on it in the "Electrochemistry
Encyclopedia", and the Appendix of that article gives the chemical reactions occurring:
http://electrochem.cwru.edu/ed/encycl/art-v01-volta.htm
Acknowledgement
We would like to thank the anonymous professor for his kind answer.
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