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A reaction that has reached chemical equilibrium no longer shows changes in reactant and product concentrations, but forward and reverse reactions are still going on. I'm confused whether a completely discharged battery is in a state of equilibrium.

Argument that an equilibrium has been reached

If I measure the cell potential, it will be zero. That means that the Gibbs free energy of reaction is zero, which is a property of a chemical equilibrium. When I discharge a battery by shorting it, there are concentration changes in the battery that cease when the battery is discharged, which looks like a reaction going toward and then attaining equilibrium.

Argument that this is not an equilibrium state

One property of a chemical equilibrium is that it is dynamic, i.e. the forward and reverse reactions are ongoing but occur at the same rate. For the battery, the reaction does not happen unless I close the circuit by electrically connecting the electrodes (e.g. shorting the battery with a wire). Even if I connect the electrodes with a wire, no current will flow because the battery is dead. So I don't see forward and reverse reactions going on. This would be like placing two beakers with 1 M aqueous salt solutions next to each other and saying they are at equilibrium. However, if the solutions were both contacting a dialysis membrane, ions would flow in either direction (at the same rate) so it would be fair to call this a state of dynamic equilibrium.

Which argument wins?

Is the discharged battery at a state of equilibrium or not? Does it matter whether the electrodes are connected electrically to decide on the answer? Does it make sense to discuss a state of equilibrium in the context of electrochemistry in the first place?

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  • $\begingroup$ Yes a discharged battery, with the two terminals of the battery connected, is at a state of equilibrium. $\endgroup$ – MaxW Mar 28 at 15:50
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You can ask yourself: if the universe is expanding (that is, if it is in a dynamic state), is thermodynamics truly ever applicable? The answer is that in science we need to take approximations, during measurement or when extracting information from data. So it is in thermodynamics, which works well enough even though on long enough scales the approximations fail (on timescales of the "in the long run we are all dead" sort).

This is of course a tricky point. We often need to distinguish between "real equilibrium states" and "kinetically trapped or metastable states". However it is useful to invoke a "duck-typing" rule applicable to thermodynamics problems: if the measured properties of the system remain constant and homogeneous during the interval of the experiment, then the system can be considered to be at equilibrium during that interval. This definition is particularly valuable since thermodynamics is an empirical science. Caveat: that doesn't mean you can be sure that the system is in the state you meant it to be in (!), since if you wait long enough you might end up in another state (which might be the one you actually wanted the system to be in!). Perhaps more important is reproducibility: can you put the system into the desired state, reproducibly?

To summarize: the concept of equilibrium, like that of reversibility, is subject to the practical condition that no variations be observed across the system or over time during the course of the experiment, when the system is in the proposed state.

As regards a battery, if you don't see a change in the potential, you can regard the system as being "at equilibrium", at least temporarily! Again, the definition of equilibrium is not as strict as we'd like to think. The materials in the battery, left exposed to the environment long enough, will rust and fall apart, leading eventually to other "equilibrium" states.

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