# What occurs at the atomic level when two batteries are connected in series, resulting in their voltages being added together?

I know that this is a trivial question for most of you, but I do not understand why the voltages get added together when two batteries/voltaic cells are connected in series. I know that is the rule and I've been told the water analogy, but I would like to understand it directly. I think the crux of my confusion is what happens at the connection between the negative terminal of the first battery when it is connected to the positive terminal of the second battery. When only dealing with one voltaic cell in a complete circuit, with a potential difference of 3V across the terminals/electrodes, electrons move from a region of higher potential energy (negative electrode) to one of lower potential energy (positive electrode) and lose potential energy while doing so. With that in mind, I thought that the same thing would happen when connecting the batteries in series. Electrons flow from the negative terminal of the first battery to the positive terminal of the second battery, and electrons flow from the negative terminal of the second battery to the positive terminal of the first battery. The electrons went from 0V at the negative terminals to 3V at the positive terminal so it seems to me that the voltage was 3V throughout. I know this is wrong and I think that I'm supposed to ignore the connection between the batteries and just take it as a new battery with a greater potential difference across its terminal but I would like to understand it fully.

My understanding for a single voltaic cell: In an example voltaic cell, a solid strip of zinc is placed in a $$\ce{Zn(NO3)2}$$ solution to form a half-cell. A solid strip of copper placed in a $$\ce{Cu(NO3)2}$$ solution forms a second half-cell. The strips act as electrodes, conductive surfaces through which electrons can enter or leave the half-cells. Each metal strip reaches equilibrium with its ions in solution according to these half-reactions:

$$\ce{Zn(s) <=> Zn^2+ (aq) + 2 e^-}$$

$$\ce{Cu(s) <=> Cu^2+(aq) + 2 e^-}$$

However, the position of these equilibria is not the same for both metals. Zinc has a greater tendency to ionize than copper, so the zinc half-reaction lies further to the right. As a result, the zinc electrode becomes negatively charged relative to the copper electrode.

If the two half-cells are connected by a wire running from the zinc——through a lightbulb or other electrical device——to the copper, electrons spontaneously flow from the zinc electrode (which is more negatively charged, and therefore, repels electrons) to the copper electrode. As the electrons flow away from the zinc electrode, the $$\ce{Zn/Zn^2+}$$ equilibrium shifts to the right (according to Le Châtelier’s principle) and oxidation occurs. As electrons flow to the copper electrode, the $$\ce{Cu/Cu^2+}$$ equilibrium shifts to the left, and reduction occurs. The flowing electrons constitute an electrical current that lights the bulb. The electrical current is driven by a difference in potential energy (caused by an electric field resulting from the charge difference on the two electrodes).

• The question is sort of backwards here. The concept of voltage is constructed such that voltages can be trivially added. I think you really want to start from there and ask what kind of quantity is required in order for that property to hold.
– Zhe
Commented Jun 11 at 17:31

1. The voltages are added only in the ideal case of open circuit (in the example given in OP, lightbulb having a very large resistance), so that the reactions can reach near equilibrium.
2. The half cell reaction equilibria are modified by the electric field provided by connecting another battery. Basically, the 'solubility' of charged species ( $$\ce{Zn^2+}$$ ) is no longer driven by only microscopic short-range interactions between solvent and zinc surface, but now also the electric field from the other battery. Le Châtelier’s principle is valid for charge as well.

Around a single zinc electrode, the concentration of $$\ce{Zn^2+}$$ excess is larger near the zinc surface: it is held against diffusion by $$\ce{e^-}$$ excess in the electrode. Connecting another battery removes the $$\ce{e^-}$$ excess by providing a path for conduction electrons, which cannot go to the solution because their de Broglie wavelength does not fit between any of the shielding localized orbitals of the solvent molecules. In contrast, $$\ce{Zn^2+}$$ ions are attracted to these localized orbitals, preferring to dissolve. The long-range attraction of opposite charges is the only thing preventing zinc from fully dissolving in an open circuit.

• Can you go into a bit more detail about point 2. I think this is along the lines of what I'm trying to understand. Commented May 26 at 8:08
• Is it nonobvious to you, how solvent doesn't have a partially filled conduction band, but metal electrodes and wires have? Commented May 26 at 10:26
• @funso Added a paragraph. See, whether this helps. Commented May 26 at 11:09

... I do not understand why the voltages get added together when two batteries/voltaic cells are connected in series.

TL; DR - Connecting of any two independent voltage sources (with floating external potentials, like galvanic cells, not grounded secondary transformer coils, charged capacitors) in a series leads to adding their voltages together (or subtracting if anti-aligned).

Electrochemistry of the galvanic cells (or the way how the external voltage is created) has nothing to do with it.

If you are familiar with behavior of a single galvanic cell in general circuits (I assume you have expressed that you are), you know the behavior of cells in series as well. The same processes occur there and there is no electrochemical process related specifically to cells being in a series.

Each of cells acts independently as if it were the only galvanic cell in the whole circuit. The cell has no means to distinguish if any of other power sources is a galvanic cell or not.

The phenomena of addition of potential differences in serial connection of power sources does not depend on the mechanism how the potential differences are achieved. It can be a galvanic cell, it can be a capacitor, it can be transformed and rectified socket AC power, or whatever else.

• I do not want to view them as black boxes, I want to understand what is happening at a atomic/molecular level the way I described a single battery. Even if the rules apply to non-galvanic power sources like the mechanical battery in "Matter & Interactions" by Sherwood, I'd still like to be able to understand what is going on exactly in the actual voltaic cells when connected in series. I know some of the rules, but I'd like to understand the underlying mechanisms behind them. Commented May 26 at 8:13
• See the answer update. Commented May 26 at 9:06
• So, the same process (like the one I described for a single battery) is happening without any effect from or on the electrochemical process due to the addition of another battery? Commented May 26 at 16:43
• Exactly. There is obviously the effect of the other battery. But it is fully circuitry wise, due voltage forced upon the circuit by the other power source, regardless of its nature. Commented May 26 at 17:28