How is the notion that gases expand to the containing volume fit with the concept of molar volume? [duplicate]








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[If a gas always occupies the volume of its container, will its volume always be 22.4L at STP?](/questions/82085/if-a-gas-always-occupies-the-volume-of-its-container-will-its-volume-always-be)

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I have a question about the concept of molar volume of a gas, which is defined as the volume occupied per mole of molecules of the gas.


I don't know details about what a gas is at a deep level, but from high school level knowledge, gases expand to fill the volume they are contained in.


If we have one mole of a gas in a balloon in a huge room at sea level at a location at some standard temperature (0 degrees C), and we release the gas from the balloon, what can we say about the volume the gas will occupy? Is it really the molar volume?


How does that go with the notion that a gas expands because molecules are moving very fast and chaotically at a relatively large distance from each other?


I can understand intuitively, from everyday experience, what a molar volume of a liquid would be (at specific conditions of temperature and atmospheric pressure), because I can see the liquid and how much volume it occupies.


Does the same thing occur with gases? If we have a gas that is red, will it have a fixed volume (the molar volume)?




**The gas laws define relationships under fixed conditions: molar volume is defined when all the other variables are fixed**


The confusion you have seems to result from failing to consider the conditions under which molar volume is defined.


The ideal gas laws define the relationship between 4 things: the volume, the pressure, the temperature and the amount of molecules of the gas. Al sorts of combinations of those variables are possible. If the amount of gas molecules is constant (say 1 mole of the gas molecules) there are still 3 variables to play with. So there are plenty of combinations of volume, pressure and temperature are possible. Even if temperature is fixed, there are still a range of combinations of volume and pressure where the law will be satisfied.


But if the pressure is also fixed, there is only one possible volume where the law works. This is the *molar volume* (the volume occupied when everything else if fixed).


There is no contradiction between this definition and the fact that a gas whose volume is *unconstrained* will fill all the space available. But that case has too many free variable for a single volume to make sense (both the volume and the partial pressure can vary freely).


The case where molar volume does make sense is one where the *pressure* is held constant (imagine a vessel with a plunger that exerts a constant pressure in the vessel's contents. If that pressure is fixed, then the volume of a mole of gas released into the (empty) vessel will be the molar volume. And that volume will be the same for any gas (if far enough away from the point where it ceases to be an ideal gas).


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For the air as mixture, one may consider the molar volume as the volume containing $\pu{1 mol}$ of any molecules $$V\_\mathrm{M, air}=\frac{RT}{p\_\mathrm{air}}.$$


For just the $\pu{1 mol}$ of the gas from the balloon, the molar volume is determined by the partial pressure of the gas $$V\_\mathrm{M,gas}=\frac{RT}{p\_\mathrm{gas}}.$$


And


$$p\_\mathrm{gas} = \frac{n\_\mathrm{gas}RT}{V\_\mathrm{container}},$$


as the gas molar volume is equal to the container volume


In both cases, we can assume ideal gas behavior with negligible errors.


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