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In class, I was taught that 1 mole of an ideal gas occupies a set volume eg 22.4 L at STP. Why does the gas only occupy a certain volume and not just keep expanding forever, having limitless volume?

Ideal gases neglect inter-molecular forces so shouldn't they just keep expanding?

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  • $\begingroup$ As you mentioned yourself, the relationship holds at STP (273.15 K, 100 kPa). Decrease the (outer) pressure and your gas will expand accordingly. $\endgroup$
    – Klaus-Dieter Warzecha
    Commented Oct 8, 2016 at 7:45
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    $\begingroup$ "At STP" implies that there is some pressure (namely 1 bar) pressing on the gas from the outside, right? If there was no such pressure, then the gas is effectively in a vacuum, and yes it would keep expanding. $\endgroup$
    – orthocresol
    Commented Oct 8, 2016 at 8:10
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    $\begingroup$ Please note that the value $V_\mathrm m=22.4\ \mathrm{l/mol}$ for the molar volume of an ideal gas corresponds to the old definition of standard temperature and pressure (STP), which is a temperature of $T=273.15\ \mathrm K$ and a pressure of $1\ \mathrm{atm}$. Since 1982, $p=1\ \mathrm{bar}=100\,000\ \mathrm{Pa}$ is used as the standard pressure for tabulating thermodynamic data. At this pressure, the molar volume of an ideal gas actually is $V_\mathrm m=22.710\,947(13)\ \mathrm{l/mol}$. $\endgroup$
    – user7951
    Commented Oct 8, 2016 at 8:39
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    $\begingroup$ Because the volume is set. $\endgroup$
    – Todd Minehardt
    Commented Oct 13, 2016 at 3:32
  • $\begingroup$ Say you don't wonder how restraining volume can be any different from restraining pressure. Putting into a vessel (volume) per se amounts to putting on pressure. "Volume. you must assume". Don't put it on ... $\endgroup$
    – Peter Bernhard
    Commented Nov 3, 2022 at 12:39

2 Answers 2

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The reason the gas doesn't expand to infinity is because it is in a vessel.

Or, to be more precise, the ideal gas equation defines the relationship between temperature, pressure and volume for a fixed amount of gas.

What is normally done to understand the relationship is to put the gas into a vessel of fixed volume and measure the pressure it exerts at a given temperature. The pressure changes with temperature according to the formula (real gases may deviate slightly).

Alternatively, we can use a more complex apparatus that allows us to measure the volume occupied by the gas as we vary the temperature while maintaining a constant pressure (say atmospheric pressure). Same equation, different constraint.

Your misunderstanding is that you have not thought through the conditions under which you are applying the rules. The thought experiment you are doing is releasing the gas in the vacuum of space where there is no external pressure. In those circumstances the gas will expand to infinity but this doesn't violate the ideal gas equation as there is no constraining volume (you could say volume is infinite).

When applying the rules you have three variables (you usually keep the amount of gas, the number of moles, fixed) and you have to constrain two of them. If you don't, are an infinite range of possible combinations of the variables (e.g. constrain temperature and there is still nothing that tells you what the volume and pressure are as they can vary together over any values that satisfy the equation).

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  • $\begingroup$ For beginners, you rarely find such good advice: "... you have three variables (you usually keep the amount of gas, the number of moles, fixed) and you have to constrain two of them. ... " - The question seems to set volume on infinite, and if the gas "keeps expanding" it seems to do exert pressure - just measure pressure trying to stop it in the universe. Then, infinite volume seems to demand extreme temperatures to begin with. $\endgroup$
    – Peter Bernhard
    Commented Nov 3, 2022 at 12:47
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That is based on the equation pV=nRT for ideal gases, where p is pressure, V is volume, n is amount, R is a constant, and T is the absolute temperature in kelvin.

The derivation of this equation can be found from many sources, so I am not going to include it here.

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  • $\begingroup$ I understand that PV=nRT can be derived from Boyle's, Avagadro's, Guy-Lussac and Charle's law but I asking specifically about Avogadro's law and the volume-mole relationship. $\endgroup$
    – Simon
    Commented Oct 8, 2016 at 7:40
  • $\begingroup$ The temperature and pressure and amount are all fixed, so the volume is fixed as well. By the way, it is assumed that they are in a closed container, for obvious purposes. $\endgroup$
    – DHMO
    Commented Oct 8, 2016 at 7:42
  • $\begingroup$ Okay I understand this but I still feel as though it is not answered fully. I am asking specifically why gas only occupies a set amount of space and does not keep expanding forever, if ideal gases neglect inter-molecular forces $\endgroup$
    – Simon
    Commented Oct 8, 2016 at 7:44
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    $\begingroup$ This doesn't actually answer anything. $\endgroup$
    – matt_black
    Commented Oct 8, 2016 at 10:53

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