What factors determine the potential difference in a battery cell?

[iScience]

i first formally learned about the cell in my chemistry class. their explanations for how it works was very unsatisfactory for me; so i wondered if this was rather a physics question.

i have two half cells connected by a conductor (between the plates) and a salt bridge. i ask people why is there a flow of electrons in one particular direction and they keep telling me that "it's lower in energy to do so" but this doesn't explain ANYTHING about the mechanisms, ie the processes behind WHY it makes it lower in energy... all that statement does is that it provides me with a picture of a potential gradient which i am already aware of, because.. obviously if the electrons have a net direction then there MUST be a potential gradient. so that is obvious, but I'm interested in the process behind all of this that is responsible for setting up the potential gradient.


Cu(s)|Ag(aq)||Ag+(aq)|Ag(s)


this is the cell we've worked with in class. i don't understand why there exists a potential between two half cells.
basically what I'm looking for is, what property/quality of each half cell when considering them separately, is relatively high or relatively low when compared to the other half cell? there MUST exist a relative difference in something when considering them separately s.t when connecting them, they don't magically just "become lower in energy" to go in one particular direction; which is what the chem people were telling me. they keep saying that it's pointless considering them separately and that i had to consider them only when the two half cells were hooked up together.

so, what is this property/quality i am looking for?

i say quality because I'm looking for a qualitative description. I'm not looking for specific quantitatives.

 

[hilbert2]

Thermodynamically, the Gibbs energy change in the net process ##Cu+2Ag^{+} \rightarrow Cu^{2+}+2Ag## is negative, which makes the process spontaneous and drives the flow of electrons. The Gibbs energy change can be related to the cell potential with the equation

##\Delta G^{0}=NFE^{0}_{cell}##

Explaining why it's favorable in terms of Gibbs energy to have a ##Cu^{2+}## ion in solution rather than an ##Ag^{+}## ion would be a really complicated quantum chemical and statistical mechanical problem, so you just have to accept the electrochemical series as it is given.