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.
