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Are you dreaming or fabulating?Even with naked eyes anyone can see that both electrodes are consumed and no Fe deposition takes place. Why should Fe deposit again and not Zn? Have you replicated the experiment and saw the direction of the electric current?
"Both electrodes are consumed, hydrogen develops at both electrodes..."Which is exactly what you would expect if there was no wire connecting them.It is also what you would expect if there were a very high resistance in series with the wire.Do you agree so far?
H+ from the acid will react with either electrode with no wires needed:Fe + 2H+ --> Fe2+ + H2Zn + 2H+ --> Zn2+ + H2The fact that you measure current in the wire between the electrodes suggests that there is another reaction going on. This is not unusual in chemistry--in addition to the desired reaction, there are often dozens or hundreds of different chemical reactions ongoing in any flask, but most are either reversible and in equilibrium, or negligible.It is quite possible (in fact I would bet on it) that Fe2+ is getting reduced on the Fe electrode, using electrons coming from the oxidation of the Zn electrode. Using standard reduction potentials, it is apparent that this is a very favorable reaction, so if given the opportunity (Fe and Zn electrodes in same solution and connected by wire) this reaction will happen--even if there is another reaction (or 10,000) going on simultaneously in the same apparatus.