Here is how A.F. Kip describes (explains ?) emf of a
chemical cell in "Fundamentals of Electricity and
Magnetism", 2nd edition, section 7.6).
"In order to understand the production of an emf by chemical
forces, let us examine the experimental facts. If a piece of metal,
say, copper, is placed in a dilute acid solution, there is a tendency
for doubly charged ions (Cu++) to leave the metal surface and to
go into solution. This tendency is called solution pressure, and
results from the attraction of water molecules for the metal ions
that overcomes the attraction of the metal surface for the ion. "
[The role of the acid (and its concentration) is not explained;
should one assume that the same will occur in pure water?]
"Each ions that goes into solution leaves its electronic charge
behind, so that the potential of the metal with respect to the
solution becomes increasingly negative. The metal continues
to dissolve until the equilibrium state is reached. This occurs
when the rate at which ions escape from the metal surface is
equal to the rate at which they come back to the surface from
the solution."
[In other words, the size of the container is essential. If the
volume of water were very large then the metal would dissolve
in it without reaching the equilibrium. Right?]
"The equilibrium is also affected by the potential difference that
has been reached as a result of the electronic charges left behind
by the escaping ions. For a given concentration of ions of the
metal in solution, each kind of metal comes to a characteristic
negative potential upon reaching equilibrium. If we place two
electrodes, say, Cu and Zn, in a solution, both some Cu++ and
some Zn++ ions go into solution, leaving a net negative charge
on both electrodes. But because of the greater solution pressure,
the Zn becomes more negative than Cu."
[Why does the "solution pressure" of Zn differ from that
of Cu? This question is not answered. Presumably it a
well known fact, to be learned in chemistry. The solution
pressure is not calculated from the state equation or from
the analysis of molecular forces. Such analysis can not
possibly be made without QM, I suppose. That is why, in
my opinion, an explanation of emf is not possible in an
introductory course. We describe what happens, we
measure what happens but we do not calculate emf as
we calculate forces or currents.]
Ludwik Kowalski