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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.

Logicus
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    Your reasoning is right, and "electrons are energy" is sheer nonsense. – Ivan Neretin Nov 25 '21 at 23:01
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    True or false: “The OP is ready to say goodbye to GenChem and hello to physical chemistry”, – Karsten Nov 26 '21 at 03:09
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    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. – theorist Nov 26 '21 at 03:48
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    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 – Ivo Nov 26 '21 at 07:52
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    Shocking truth: you have been in touch with a teacher of chemistry, a teacher of physics and a full professor of electrical engineering at Caltech and all of them said something wrong (even totally wrong, in one case). I am not surprised as for at the core of the question there is just a chemical fact, a reaction has occurred. (corrosion and physical losses as mentioned by @Ivo Beckers were of course not intended to be considered). You should really show this thread to them - once you are done with them! – Alchimista Nov 26 '21 at 08:56
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    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. – PcMan Nov 26 '21 at 10:12
  • @Ivan Neretin it's not nonsense. Any form of matter is equivalent to energy. – infinitezero Nov 26 '21 at 15:13
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    @infinitezero it is nonsense context given. I also wanted to comment that the discharged battery has lost an incredibly tiny amount of mass. But the way that teacher drop it in the discussion is nonsense. – Alchimista Nov 26 '21 at 16:42
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    @infinitezero technically true but irrelevant to the point of nonsense unless your battery is generating its power with nuclear reactions rather than chemical ones. That's the line that made it clear to me as a physicist that this prof does not understand the basics of electricity. – llama Nov 26 '21 at 19:17
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    He is wrong. Don't let him win here. This is really a physics question, not a chemistry one, so garner support from the physics department professors. Let us know if your professor eats humble pie and adjusts your test mark. Hopefully he can find a field of work in which he is competant and take that up instead of wasting people's time and money teaching falsehoods. – Bohemian Nov 26 '21 at 21:16
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    @Alchimista The prof. of EE at CalTech wasn't wrong; it's just the Gen Chem prof's phrasing might make it look that way. I.e., I thought the Gen Chem prof was recounting a prior discussion with the EE prof, in which the EE prof was merely discussing misinformation on the internet generally. When the Gen Chem prof then continued with the following quote, he was speaking in his own voice: "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." – theorist Nov 27 '21 at 01:34
  • @Alchimista - what was wrong in the physics professor's response? – Logicus Nov 27 '21 at 04:29
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    @Logicus he refers to some free electrons which are in a new battery and gone in a depleted one. There is no sense at all to invent description like this. There are no free electrons in the charged battery. He just wrongly reword that a new battery delivers current to an external circuits. But I agree is the less wrong of the three (assuming I got the clear picture from your description). – Alchimista Nov 27 '21 at 10:26
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    @theorist I see. Better it is so. This bullshit I expect from teachers but I was really surprised to hear that from a caltech professor. Indeed he shouldn't have been mentioned, even. – Alchimista Nov 27 '21 at 10:29
  • UPDATE: I'm pretty shocked. I wrote two emails to my professor, one for this one, and one for the other thread I posted. Combined, I wrote about 3,000 words. I wanted to be thorough so we could conclude this quickly. I just received the following reply: "Why can't you admit that my response to both questions made sense and are most accurate? Is it really worth this much of your time to attempt to prove a point?" That's it. Pretty unbecoming of a professor, I'd say. Any suggestions as to what to do next? Go straight to the dean? I'd rather not alienate him, but this is ridiculous... – Logicus Nov 28 '21 at 01:40
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    @Logicus, well, I'm two days late, and I suspect this follow-up question would be much better asked in Academia.SE, but I would personally do nothing at this point. Your instructor is apparently quite unreceptive to correction, so you have to decide what exactly you hope to gain by pushing matters further, and whether it's worth the opportunity cost for doing so. The time and hassle, as well as potential retaliation, would not be worth it to me. What makes it worth it to you? – a-cyclohexane-molecule Nov 30 '21 at 19:03
  • @a-cyclohexane-molecule I decided to not respond to his email and let it go for the time being. After our final exam (which is, fortunately, drafted by the ACS!) next week, I might bring it to the attention of the dean of natural sciences. As for my motive, I think I just care a lot about truth, and I can't stand to see people who should know better refusing not only to correct their errors, but also to even engage in reasonable discussion. I'm definitely not doing it for any personal gain, though I must say that the responses I've gotten on SE have been very encouraging. – Logicus Nov 30 '21 at 21:28

3 Answers3

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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.

AChem
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    (+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! – Ed V Nov 26 '21 at 02:37
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    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. – AChem Nov 26 '21 at 02:52
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    assuming no mass loss during the battery usage -- it doesn'e look like the fellow agrees with this assumption – Džuris Nov 26 '21 at 10:05
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    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! ;-( – Ed V Nov 26 '21 at 14:31
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    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?

     – Logicus Nov 27 '21 at 04:12
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    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) – Ed V Nov 27 '21 at 13:06
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    does not require any consideration of Poynting vectors. In fact, Poynting vectors and classical electromagnetism are to batteries as DC power sources as the details of solar nuclear fusion are to home solar cells as DC power sources. One last thing: a used up battery simply has run out of chemical reactant, so there is no more free energy to be had. The electrons just drifted around the external circuit, as always, but dead batteries can no longer “push them” as it were. – Ed V Nov 27 '21 at 13:09
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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.

Bohemian
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    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! – Logicus Nov 27 '21 at 04:21
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    @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. – matt_black Nov 27 '21 at 10:26
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    @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. – 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.

Poutnik
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    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. – Alchimista Nov 27 '21 at 11:10