# Galvanic cell - when do we get electric potential?

In the galvanic cell in this image (2nd one with salt bridge): Link

Before putting the copper wire into the solution, do the Zn metal electrons have potential energy with respect to Cu2+'s electric field? The reason I'm asking is that there must be an electric potential difference between the anode and the cathode, hence the electrons moving from the anode to the cathode must have decreasing potential energy, which means they had to have potential energy to begin with. But then, when and where did the Zn valence electrons get this potential energy from?

• In the electrolyte and in the metal, the current flows from the higher potential to the lower potential. On the other hand, at the boundary between the anode electrode and the electrolyte and between the cathode electrode and the electrolyte, the current flows in the opposite direction of the potential gradient. This is probably due to the EMFs in the opposite direction. Since electric potential is a single valued function, electric potential alone cannot explain the direction of current. I believe the origin of EMFs in batteries is unknown. Commented May 10, 2023 at 22:07
• When do Zn metal valence electrons get this potential energy - before or after connecting the wire ? Commented May 10, 2023 at 22:13
• Comparing the case of a bean bulb in a battery with the circuit closed and switched on with the circuit open and switched off, we estimate that the EMF values are almost the same in both cases, but the potential distribution is immediately different and the total electric field is zero, although the EMF is non-zero even in the open circuit. Commented May 10, 2023 at 22:32
• Electrons don't move in a galvanic cell. The current is carried by ions. Commented May 10, 2023 at 23:47
• The galvanic cell IS the battery. Potential energy is there even before the potential difference is created. If you have the wire but no solution, then there is no potential difference, even though there is potential energy. If you have the solution but no wire, then there is potential energy and potential difference. If you have both solution and wire, then electrons flow, using the potential energy and potential difference to do something. Commented May 11, 2023 at 1:07

The potential comes from the chemical energy of the reaction. In fact if the Gibbs free energy for the reaction is $$\Delta G$$ then the EMF is simply:

$$ΔG = -zFE \tag{1}$$

where $$z$$ is the number of electrons involved in the reaction ($$z = 2$$ in this case) and $$F$$ is the charge of a mole of electrons. This is the Nernst equation.

Suppose we move a charge $$q$$ through a potential $$E$$ then work needed to do this is simply:

$$W = qE$$

For the reaction:

$$\mathrm{Zn} + \mathrm{Cu}^{2+} \to \mathrm{Zn}^{2+} + \mathrm{Cu}$$

we are moving two moles of electrons, i.e. a charge $$2F$$, for every mole of zinc that reacts so if the cell EMF is $$E$$ the work done per mole of zinc reacting is $$2FE$$. The energy required for this work comes from the energy of the reaction and hence we get equation (1).

• I think the Gibbs free energy argument is probably correct, but it is thermodynamics, so it is a law for many-particle systems. For minority particle systems, I would like to know what happens to the electric field applied to individual charged particles. Commented May 11, 2023 at 6:29