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I recently took a Gen. Chem. 2 exam that contained this question. I answered false, but my professor said the answer is true. My reasoning was that any electrons that leave the anode end up at the cathode, so the number of electrons should be conserved. This was consistent with the way we studied redox reactions and electric cells: reactions were always broken down into half-reactions in which the electrons exchanged appeared on opposite sides of the half-reaction equations and canceled out. We never discussed whether electrons are lost in electrical circuits - a strict conservation of electrons was always implied.

I asked a physics professor who teaches a class on electromagnetism for his thoughts, and he sent me the following reply:

The number of electrons is conserved if there are no losses or leakage. Probably what was meant is whether these are free electrons or not. Clearly, in a used battery you have less free electrons, since there is no more energy to strip them from whatever compound is used in the battery."

I sent this (as well as a list of other sources that I won't quote here) to my chemistry professor and received the following reply:

The question states electrons. Period. There are no "free" electrons in a battery (there can be delocalized electrons, but that's not the question). Batteries are made of atoms. Atoms are made of protons, neutrons and electrons. As a battery is used, through the flow of electrons, electrons are lost to the environment (fyi - there is energy/electron loss, albeit small to "run" the voltmeter and even in the flow of electrons through a conducting wire). Those electrons are no longer in the battery. Thus, the battery has the same number of protons and neutrons, but less electrons. This also means more unreactive metal cations exist in a used battery.

I appreciate all your research to make a point, but hopefully you now see the answer is true. Even your physics professor agrees because there is loss/leakage. Thus, less electrons in the battery.

Story: I have a family friend, who is a full professor of electrical engineering at Caltech. She is clearly on the cutting-edge of this field. In one of our discussions, she shared displeasure in online information. She told me her grad students often cited sources that were not true. There is more to this story, but I think the point has been made. Keep it simple. Electrons are energy. They flow. That energy goes elsewhere, leaving the initial system with less energy/electrons.

I was a bit baffled by the "electrons are energy" remark - this seems at best poetic. He seems to be conflating electrical potential energy with electrons, but these aren't the same thing. If electrons actually "were" the electrical potential energy in a battery, wouldn't that imply that the compound at the cathode would never actually be reduced, since all energy, and therefore all electrons that "flowed" through the circuit, would be lost after depletion of the battery's potential energy? My understanding is that electrons can have energy but are not themselves energy. Although I have a very low level of knowledge regarding this topic, I've done a few hours of research and found that the common notion of electricity as a flow of electrons akin to a river is wrong, and that although electrons do move very slowly through a circuit, the flow of energy is due to electromagnetic fields associated with charged particles.

Unfortunately, I could not find any sources that directly answered this question, so I would greatly appreciate direct answers to this question from experts on this topic.

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    $\begingroup$ Your reasoning is right, and "electrons are energy" is sheer nonsense. $\endgroup$ Nov 25 '21 at 23:01
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    $\begingroup$ True or false: “The OP is ready to say goodbye to GenChem and hello to physical chemistry”, $\endgroup$ Nov 26 '21 at 3:09
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    $\begingroup$ It seems really simple. Your instructor acknowledges that "the battery has the same number of protons and neutrons" before and after. So if the number of electrons were to decrease, the battery would acquire a net postiive charge as it's used. That's simply not the case. Indeed, if depleted batteries actually did have net positive charges, they could be used to create an electrical current! Perhaps you could ask your teacher to run this one by their family friend at Caltech. $\endgroup$
    – theorist
    Nov 26 '21 at 3:48
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    $\begingroup$ I guess technically a used battery does have less electrons than a new one, simply by wear and tear of the casing. Any object that's not new will lose molecules over time by usage, including their electrons. But of course that's not the intent of the question $\endgroup$ Nov 26 '21 at 7:52
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    $\begingroup$ Occasionally in academia, as in real life, you will meet someone who is drunk, stupid or fraulent. It is sad, but it is real. One of the important lessons to learn is to not answer with facts that match reality, but with the facts that your professor believes in. This is why one needs to attend classes, to learn what the teacher believes to be true, rather than the simpler truth of actual facts. This becomes more important as the academical rank of your teacher increases. A mere graduate can be corrected when wrong. A tenured multi-doctorate believes they are right, despite all evidence. $\endgroup$
    – PcMan
    Nov 26 '21 at 10:12
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Very bad explanation in the email response.

The explanation reads..

"Thus, the battery has the same number of protons and neutrons, but less electrons. This also means more unreactive metal cations exist in a used battery."

No, not at all. An electrochemical cell is not ionized. It is always neutral overall. However, the electrodes are indeed electrostatically charged (just like your charged comb). If you had a charge sniffer (e.g., a charge sensor from Vernier) and if you touch the positive end of the battery with such a sensor, it will indeed show that this end was electrostatically charged with a positive sign.

The negative pole of the battery is equally charged but with a negative sign. Overall an isolated battery as a system is electrically neutral.

Why don't you feel the charge like a charged balloon or a comb near a battery? The reason is the voltage is very low!

Second, point: No, electrons are not energy. Electrons in a wire/electrode behave very much like negative charge (see Hall effect if you are interested)

While you cannot say True or False for "A used AA battery contains fewer moles of electrons than a new AA battery."

The number of electrons before and after are the same for the reasons that a battery is electrically neutral overall, assuming no mass loss during the battery usage. For a closed ciruit, no electrons were wasted or lost. The electrons were just travelling from one pole to the other pole while traveling with a direction in the circuit.

A used battery is reaching equilibrium which means that the battery is no longer able to do useful work (on the electrons in the external conductor). The voltage starts slowly to drop as you keep drawing current. The current also decreases.

For example, keep a flashlight running on battery overnight and you will initially see a bright bulb going dimmer, dimmer and finally no light at all.

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    $\begingroup$ (+1) Wow, even if batteries were just charged supercapacitors, and they are not, that “electrons are energy” nonsense is wacky! What are they teaching these students now? I hope that teacher/professor reads up on free energy before “teaching” it! $\endgroup$
    – Ed V
    Nov 26 '21 at 2:37
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    $\begingroup$ The OP should share this answer with his instructor. I am glad there are still a few students who can challenge their teachers for their wrong answers. $\endgroup$
    – M. Farooq
    Nov 26 '21 at 2:52
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    $\begingroup$ This question and accepted answer illustrate how a question about batteries actually had nothing much to do with how batteries work: it was about electricity, etc. Replace battery with DC power supply and it would have been the same. And the answer, that was accepted, was about the Poynting vector! ;-( $\endgroup$
    – Ed V
    Nov 26 '21 at 14:31
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    $\begingroup$ M. Farooq - thank you for taking the time to write that answer. I just sent an email to my professor summarizing all of the arguments presented here. I quoted your answer (with the exception of the first line!). I'll let you know what he says. Ed V - would you mind elaborating on what you meant re the answer about the Poynting vector? $\endgroup$
    – Logicus
    Nov 27 '21 at 4:12
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    $\begingroup$ As I said in a linked comment, “This comes up fairly often over at the chemistry stack exchange. You can benefit greatly by getting this and working through it: K. Schmidt-Rohr, "How Batteries Store and Release Energy: Explaining Basic Electrochemistry", J. Chem. Ed., 95 (10) (2018) 1801-1810. The Zn and Cu Daniell cell is addressed in great detail. TL; DR Cohesive energy differences are the major factor in explaining the behavior of this famous galvanic cell. Look up the famous Daniell cell.” Understanding how cells and batteries convert chemical potential energy into electrical energy (cont) $\endgroup$
    – Ed V
    Nov 27 '21 at 13:06
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Your professor is wrong, and you can prove it.

According to your "professor":

As a battery is used, through the flow of electrons, electrons are lost to the environment ... Those electrons are no longer in the battery. Thus, the battery has the same number of protons and neutrons, but less electrons.

which implies the charge of the battery would become more positive during use, which it doesn't, but let's see if it would be large enough to measure.

An AA battery has about 10,000 J of stored energy, and a voltage of 1.5 V.

We know Joules = Volts * Coulombs, so if he's correct, the static charge of the battery would be 10000/1.5 = 6666 Coulombs!

Why the exclamation mark? For comparison, rubbing a balloon on certain fabrics typically creates a static charge of only about 1 millionth of a coulomb (no single credible source; consensus of lots of searching), yet such a charge produces macro effects like making a person's hair raise when held near and can allow the balloon to "stick" to the ceiling etc.

Another comparison: Lightning bolts have about 100 coulombs (albeit at colossal voltage).

The battery would have a charge billions of times that of a ballon and many times that of a lightning bolt. We wouldn't need sensitive instruments to detect such a static charge; it would be leathal.

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  • $\begingroup$ Thank you for providing this argument, Bohemian. I just quoted it (except the very beginning!) in an email to my professor. I suspected that there would be an absurd result like the one you describe if he were right. However, I expect he'll respond that not all of the electrons are lost, but only a small number. How would you respond to that? I'm thinking of just shifting the burden to him and asking for sources to support his theory. Our textbook certainly never discussed this issue one way or the other! $\endgroup$
    – Logicus
    Nov 27 '21 at 4:21
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    $\begingroup$ @logicus even a small number of "lost" electrons would create a very notable charge on the battery. The (very obvious) static charge on a fabric rubbed balloon is caused by the transfer of a very small number of electrons. Get your prof to do some calculations and see what he says. $\endgroup$
    – matt_black
    Nov 27 '21 at 10:26
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    $\begingroup$ @Logicus come on, is teaching chemistry after all. Ask him if the same story would happen in a reaction flask. He cannot stay so blind forever, even assuming he has no idea about electricity and free energy of reaction, at least it should be familiar with the notion of balancing reactions. Obviously, I am not encouraging you to be disrespectful. The important point is that is clear to you. $\endgroup$
    – Alchimista
    Nov 27 '21 at 11:07
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The disagreement may have come from mutual misunderstanding.

Unless a cell has lost some matter, it contains the stable count of electrons, safe random fluctuations and eventual net charge caused by external electrostatic potential.

Aside of that, some of these electrons relate/belong to electro-active substances taking part in electrode half-reactions, releasing/absorbing electrons to/from ekectrodes. These electrons are able to leave the cell via anode and the equal count to come to the cell via cathode.

The total count of these migrating electrons decreases as the cell capacity decreases by static or cycling ageing.

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    $\begingroup$ Misunderstanding is always possible. However the answer to the questions as formulated in the title is Not. Except for some part of it flying off. But the same could be said for everything, it is certainly not the meaning of the story. $\endgroup$
    – Alchimista
    Nov 27 '21 at 11:10

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