# Does a mixture of gases contain equal volume to that of the container they're in? Why?

In my textbook, the derivation of Dalton's Law of Partial Pressure is done by keeping the volume of a mixture of gas in a container constant which is equal to the volume of container itself.

How can this be so? Let's say we have 100 moles (fairly large) of Nitrogen and 1 mole of hydrogen gas taken in a container of a certain volume. Then is the volume still considered equal to that of the container in this case? Because this is what is done when deriving Dalton's law of partial pressure?

Also, if we have 100 moles of a gas and another just a single molecule then what happens?

## 1 Answer

Well, the word "container" means a fixed volume. Let's look at your room for example (don't take into account any openings, like doors or windows, just the walls). It has some amount of gas in it at this moment. Now, if someone decided to "push in" let's say 100 extra moles of O2 gas, then that would not change the volume of your room. The volume of the containter remains constant, no matter how much gas we put into in.

This is also true for each component of the mixture. The oxygen in the original air of your room had the volume of your whole room, and even when we "push in" that 100 extra moles, it still has the same volume - because your room did not change. What can change then? Obviously, the pressure or the temperature can change.

• but when we run PV=nRT for each gases,shouldn't we consider V for the particular gas we are dealing with?Why would we take the volume of entire container? Jan 28, 2017 at 15:48
• The assumption is that the gas is completely homogeneously diffused. You can think about this assumption by checking that you can not really find either of the components in one place or another, but you can find every single component in the whole container - every component by itself takes the entire volume.
– user23638
Jan 28, 2017 at 15:50
• Let's say there is a single molecule of oxygen gas in the container very large.Now how will you statement compensate this?Please help Jan 28, 2017 at 15:52
• The huge oxygen molecule still can be found in any place of the container with the same probability - it is not sitting still in a room, but moving all around, like all other gas molecules. Think about volume as not the size of the molecules, but rather the space where they can move.
– user23638
Jan 28, 2017 at 16:21
• @SurazB In that case that single gas molecule will move in the entire room,changing directions after hitting walls Jan 28, 2017 at 16:22