Why do lemon batteries work?

And chemistry, I guess

Making a lemon battery is the staple of middle school science activities. The experiment involves jamming two dissimilar metals into a lemon; copper and zinc are the usual picks. If you connect a voltmeter to the electrodes, it should read about 1 V. String two or three lemons in series and you can even light up a small LED.

A scientific diagram of the experiment. By author.

The chemistry of the lemon cell appears simple, up to a point. Lemon juice is essentially a 5% solution of citric acid in water. Water is a small and strongly polar molecule, so it can cleave the ionic bonds of many substances that were formed by the exchange of electrons and that are held together by the resulting electrostatic field.

This process — known as dissociation — produces electrically-charged halves that lead independent lives in the solution, but revert back to complete molecules once the solvent is removed. In the case of citric acid, we end up with some modest number of positively-charged hydronium cations and negatively-charged citrate anions floating around.

Dude, where’s my hydrogen?

Past this point, introductory texts get hand-wavy. Many metals react with acids in a redox reaction. Conceptually, the reaction involves hydronium ions snagging electrons from the metal and then turning into hydrogen gas; in parallel, electron-deficient atoms of metal turn into positive ions:

\(\ce{Zn (s) + 2 H^+ (aq) -> H2 ^ + Zn^2+ (aq)} \)

The high-school explanation is that the hydronium ions “want” the electrons more, and when they come across each other in a dark alley, the metal doesn’t put up a fight.

Phrased this way, it’s an electrically-neutral exchange, so it doesn’t quite explain the behavior of a battery. Just as important, the story doesn’t add up for zinc in dilute citric acid: the metal starts dissolving into Zn²⁺ cations at an appreciable rate only after an electrical connection is made. Even more confusingly, when the electrodes are connected together, the bulk of the hydrogen is evolving on the copper electrode, not on the zinc one.

In other words, it appears that zinc atoms are spontaneously falling off the electrode, leaving two electrons behind; there are no hydronium ions nearby holding a knife to their throats. After that, the electrons start moving through a wire toward the copper electrode, where the reduction of the hydronium ion occurs. Why?

The first half of the answer is that is the reduction of the hydronium ion doesn’t happen easily on the surface of zinc. The actual reaction is a multi-step process that involves atomic hydrogen absorbing into the metal; zinc is a poor substrate for that. In electrochemistry, we have the concept of overpotential — the excess voltage that would need to be applied to carry out the reaction, compared to what’s predicted by simple thermodynamics. The bottom line is that the reduction to atomic hydrogen can proceed at lower voltages on the copper side.

The crooked equilibrium

A more fundamental question is why do these reactions start happening in the first place. Electrostatic fields are quite powerful; why would an atom ever part with its electrons and then wander off if it’s not being persuaded to do? Doesn’t that add energy to the system? Why is zinc reacting and not copper? How can mirrors be real if our eyes aren't real?!

All good questions! If you’re familiar with electronics, a good analogy might be the p-n junction in semiconductors. If you’re not familiar with the concept, I recommend starting with this article, but in brief: we start by manufacturing an “n-type” material that has some energetic, mobile electrons in a high-energy conduction band. We bring it in contact with a “p-type” material, where electrons occupy a lower-energy valence band, and where there are some available vacancies (holes) in that band.

Both of the materials are electrically-neutral, but when we bring them together, something interesting happens: a number of the higher-energy electrons from the n-side falls into the lower-energy vacancies on the p-side. This is somewhat akin to a billiard ball falling into a pocket. The result is a region with an unbalanced distribution of charges and a built-in electrostatic field:

A basic illustration of a p-n junction.

The effect is self-limiting: eventually, the field grows strong enough that the net inflow of electrons must stop. But the bottom line is that despite the presence of a field, the situation at the junction is a lower-energy state. If you connect a voltmeter across, it will read zero volts: there are no electrons trying to go back where they used to be.

Semiconductor junctions are not special. Quantum-mechanical properties of molecules and crystal lattices often result in energetically-favorable spots that can be taken up by electrons “belonging” to some other substance. This usually doesn’t result in macroscopic voltages or currents because of the self-limiting nature of the process. That said, in the case of batteries, lower-energy products are continuously removed (as gas or ions), and higher-energy reagents are continuously exposed. If there is a pathway for current to keep the electric field in check, the process can go on until the entire electrode or the electrolyte is spent.

In fact, here’s a surprising tidbit: some migration of charges happens spontaneously if you simply bring two dissimilar metals together; no electrolyte is needed at all. The resulting field — known as the Volta potential — can be measured in a vacuum with sufficiently precise instruments. The importance of this field in guiding electrochemical reactions is apparently not a settled matter in battery science. Some think it’s the key factor; others arrive at similar results from more abstract principles.

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