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We say that pressure due to gas is constant throughout the container. Pressure is created by molecules present in it. When there are many molecules I agree that they can apply the same pressure all over.

But when there are very few or just one molecule in the container, how can that single molecule create a uniform pressure in the container. I mean pressure will be created (say in a manometer) when a molecule applies force on it (Hg). If we take a very large container and place just one molecule and also keep two manometers at the two extremes. Then how can that single molecule create the same pressure or apply the same force on both the manometers at the same time (container is very large)?

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    $\begingroup$ Well, not quite at the same time, but you are probably aware that molecules fly pretty fast. $\endgroup$ – Ivan Neretin Apr 4 at 17:37
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    $\begingroup$ Well, that's pretty much so. Moreover, even for smaller containers and more molecules, pressure is measured only statistically. $\endgroup$ – Ivan Neretin Apr 4 at 17:44
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    $\begingroup$ You're right. One molecule can't exert uniform pressure. But in reality the pressure isn't from the molecule, but the nearly perfect vacuum. // The gas laws are based on overall statistical behavior. Having just few gas molecules doesn't give such statistical information. $\endgroup$ – MaxW Apr 4 at 17:48
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    $\begingroup$ If you're using mercury manometers you'd never get to one molecule of gas. Mercury itself has a vapor pressure. $\endgroup$ – MaxW Apr 4 at 17:55
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    $\begingroup$ A vessel containing only one molecule of gas is way better than the most perfect vacuum we have ever been able to create. So there is really no need to worry about correcting for the situation. Even "empty" interstellar space contains between 1 and 1,000 atoms per cubic centimetre. Most concepts from equilibrium thermodynamics fall apart at such densities simply because there are too few molecular collisions to establish equilibrium. $\endgroup$ – matt_black Apr 4 at 18:19
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What happens to the pressure of gas when only one molecule of it is placed in a very large container?

I think you have forgotten what pressure represents in terms of the kinetic theory of gases. When studying gas kinetics, you start by understanding the behavior of a single molecule/atom moving around a container and colliding with the surface and bouncing in random directions. Then you add a few more molecules/atoms so that now there are collisions and as long as the mean free path of the gas is less than the dimensions of your vessel you still have motion that acts in random diffusion-like behavior. Once sufficiently many atoms have been added that a given amount of area experiences a regular number of collisions per unit of time, then you have something that can be given as an average rather than a count of collisions. This is what pressure represents, an average force on a surface per unit area of molecular collisions on that surface. The instantaneous force can change for a given spot nanosecond to nanosecond, but averaging all spots over a span of microseconds will give an average force per area can be resolved which we call pressure.

The problem here that gives you a misunderstanding is that you have taken a behavior of an aggregation of many molecules and tried to apply it to a single molecule. This approach will disappoint. But to summarize and actually answer the question, pressure cannot describe a system of only one gas molecule, and is therefore undefined.

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The gas pressure, the same as temperature, are statistical quantities. A single molecule has no temperature and no pressure.

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