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This question might be elementary, but it is genuine. I realise that some users might downvote the question for being so basic, but I urge them to be a little merciful, and help out a confused high school student,

If a gas is expanded at a constant temperature then,

according to Boyles' Law, $p\propto\frac1V$ (if $n$ an $T$ are constant).

According to Avogadro's Law, $V\propto n$ (if $p$ and $T$ are constant).

We know that $T$ is constant, but what about $p$ and $n$?

If $n$ is constant, then Boyles' Law is valid. $p\propto\frac1V$ i.e. the pressure decreases on expanding the gas.

If $p$ is constant, then Avogadro's Law is valid. $V\propto n$ i.e. the number of moles increases on increasing the volume. However, this is found to be false.

Furthermore, intuitively, we know that for an ideal gas, $n=\frac{V_\text{gas}}{V_\text{molar}}$, and here, $V_\text{gas}$ continuously increases, indicating that $n$ should also continuously increase.

This doubt stemmed from a question from a question bank which prepares Indian students for a popular competitive engineering exam called JEE. The question, which has multiple correct options, reads:

If a gas expands at constant temperature :

(A) the pressure decreases

(B) the kinetic energy of the molecules remains the same

(C) the K.E. of the molecules decrease

(D) the number of molecules of the gas increase

I know that B is certainly correct, as the average kinetic energy of each molecule $A.K.E. = \frac32RT$, and temperature is constant. My doubt was in options (A) and (D). For this question, (B) and (A) are the only correct answers and (D) is wrong, but I didn't understand the rationale of (A) being correct and (D) being wrong.

If someone could explain why the number of moles of a gas doesn't increase despite the volume increasing i.e. it is expanded, as well as the reasoning of answering the JEE question bank question, it would be very helpful.

Edit: My doubt has been clarified by user Maurice. Here, the number of moles remains constant as no chemical reaction is taking place for them to increase. So Boyle's Law is valid, and the pressure decreases due to the increase in volume.

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    $\begingroup$ :/ While gas might break down to smaller molecules, this is lame gas law question, not chemical reactor problem. $\endgroup$
    – Mithoron
    Oct 14, 2023 at 18:40
  • $\begingroup$ Could you please elaborate a little bit? I did not understand the context of this with respect to the question. $\endgroup$
    – Bongo Man
    Oct 14, 2023 at 18:43
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    $\begingroup$ Well, how you imagine getting more moles of gas? Another option is a reaction creating new gas, but being created doesn't exactly mean expand. $\endgroup$
    – Mithoron
    Oct 14, 2023 at 18:53
  • $\begingroup$ One of the sentences Bongo Man writes has a wrong conclusion. I repeat it here in bold : If 𝑃 is constant, then Avogadro's Law is valid. 𝑉 is proportional to 𝑛 i.e. the number of moles increases on increasing the volume. However, this is found to be false. NO ! This is not "found to be false". If, in a syringe, the number of gaseous molecules increases without changing the pressure, the volume of the gas does increase. $\endgroup$
    – Maurice
    Oct 14, 2023 at 18:54
  • $\begingroup$ @Maurice I was referring to the context of the question, and how Avogadro's Law seemingly doesn't apply here. $\endgroup$
    – Bongo Man
    Oct 14, 2023 at 19:01

2 Answers 2

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Your last question may have two different correct answers. It depends on the parameters to be constant in the transformation. These constant parameters are forgottten in the question. I will give here the two interpretations. All depends of the first sentence of the question : If a gas expands at constant temperature Well, in order of a gas sample to expand at constant temperature, information must be given on the number of moles $n$ of this gas. Is this $n$ constant or not ?

$1$) The number of gaseous moles stays constant during the transformation. So now, if the volume increases, the pressure must decrease, and (A) is correct, and (D) is wrong. One should add that this transformation is not spontaneous. Usually it goes in the other sense. The increase of volume of a gas sample is produced by a decrease of pressure

$2$) The number of moles increases during the transformation, at constant temperature and pressure. This is not easy to imagine how this increase of moles is carried out. As Mithoron states, It may be due to a chemical reaction producing a gas like $\ce{Zn + 2 HCl -> ZnCl2 + H2}$. But this produces practical difficulties about how to measure this changing volume. If we suppose these practical difficulties are solved, the number of moles of gas must increase, and the total gases volume increases. So (A) is wrong, and (D) is correct

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    $\begingroup$ Thank you! I understood the concept now. Essentially, the number of moles cannot increase, unless there is some sort of reaction (which is clearly not taking place here), so it has to be constant. $\endgroup$
    – Bongo Man
    Oct 15, 2023 at 7:02
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Answers A or D could be correct. If you keep $n$ constant, A is correct. If you keep $P$ constant, D is correct. You still would have to explain how $n$ changed. It could be by adding particles (pumping up a flat tire) or by a chemical reaction (e.g. $\ce{N2O4 <=> NO2}$).

From the comments:

While gas might break down to smaller molecules, this is lame gas law question, not chemical reactor problem.

From the question prompt "If a gas expands", it does not sound like you are adding molecules or that a reaction is going on. For most multiple choice question, the best answer depends on what we know about the topic, and what we know about the author of the question (i.e. the answer key).

All the laws mentioned by the OP are ideal gas laws. The question does not state that the gas is ideal. You can still make qualitative statements ("increases", "decreases"), however, like in the answer choices.

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  • $\begingroup$ Your answers makes sense. But why isn't Avogadro's law valid here? If the volume increases, so should the number of moles. I appreciate the effort, but I still feel dissatisfied, as my original question is unanswered, and I still haven't understood the logic of (A) being right and (D) being wrong. $\endgroup$
    – Bongo Man
    Oct 14, 2023 at 19:05
  • $\begingroup$ @BongoMan (D) is not wrong, and Avogadro's law is valid, answer key notwithstanding. $\endgroup$
    – Karsten
    Oct 14, 2023 at 19:35
  • $\begingroup$ The answer is most certainly right, as it was supervised by a very experienced and senior Chemistry faculty (named Vishal Jain, who has a degree from the best college in India, IIT-B). If you could formulate your reasoning, such that it aligns with the answer given, and answers my question, I'd gladly upvote and mark it as an answer $\endgroup$
    – Bongo Man
    Oct 15, 2023 at 7:30
  • $\begingroup$ @BongoMan That is not how science works. $\endgroup$
    – Karsten
    Oct 15, 2023 at 13:06
  • $\begingroup$ @ Karsten. Please explain. How does science work, according to you ? $\endgroup$
    – Maurice
    Oct 15, 2023 at 13:56

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