Why two ( or more) gases have proportional volumes at constant pressure and temp.? (Avogadro's Law)

I am in real confusion over Avogadro's Law..


In some of the problems I did on gas laws, there are the number of moles of the gas, the temperature. and the pressure. And it expects me to find the volume of gas.


But then in other problems there everything else is given including the volume of the container ( instead of the gas itself) and then something else is expected to be found. 


The confusion starts here. If any gas occupy the volume of volumes, always, then why will volume change according the combined gas law?


In one of my previous post, I learned that volumes of different gases won't be proportional (meaning all of them will occupy equal space) unless the condition of constant tempt and pressure is reached. 


But what really happen when constant tempt and pressure are reached? Do individual gases just separate themselves from one another? Because in order for their volume ratio to be equal to anything other than 1, their volume must be different.


**you only have to answer the question in the title, the others questions are intended to help you understand what I mean. Sorry for the possible confusion**


[a link to my previous post](https://chemistry.stackexchange.com/questions/18957/volume-of-different-gas-in-a-container)




So, there are many questions, and I'm not sure if I understand you 100 %:


We have [Avogadros Law](http://en.wikipedia.org/wiki/Avogadro%27s_law), which applies for an [ideal gas](http://en.wikipedia.org/wiki/Ideal_gas) at constant pressure and temperature:
$$\frac{V}{n} = k \quad\Rightarrow\quad \frac{V\_1}{n\_1}=\frac{V\_2}{n\_2}$$
With $k$ as a constant.


And we have the [ideal gas law](http://en.wikipedia.org/wiki/Ideal_gas_law): 
$$pV = nRT \quad\Rightarrow\quad \frac{p\_1V\_1}{n\_1T\_1} = \frac{p\_2V\_2}{n\_2T\_2}$$


And this is probably what your first question is about. There are problems when you have a state $1$ and a state $2$, which differ. 


For example: You have a container where everything ($p\_1,V\_1,T\_1,n\_1$) is given. Now you double the temperature - and the task is to calculate the pressure. Since the volume and amount of substance is fixed ($V\_1 = V\_2$, $n\_1 = n\_2$), you can just rearrange everything and calculate the pressure $p\_2$.


In the ideal gas-model, gases do not seperate. I may be misunderstanding you, but if you put 1 mol $\ce{N2}$ and 2 mol oxygen in a container, you will have different [partial pressure](http://en.wikipedia.org/wiki/Partial_pressure)s, but no demixing.


A relevant question was [posted on physics.SE](https://physics.stackexchange.com/questions/96089/mixing-of-ideal-gas-thermodynamic-equilibrium), that may help you if you have to dive deeper into this topic.


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I think some of your confusion arises from the way your questions have been posed. The laws state a relationship among pressure, volume, temperature and the number of molecules of gas (which is what moles of gas tells you).


The only reason we know the volume is because the gas is in a container. You may not be told this volume in the question, but gases expand to fill whatever container they are in (unless you are doing something on a planetary scale where gravity starts to count and you aren't going to get questions involving this in basic chemistry). So if volume is the unknown, you are being asked to calculate the volume of a container. Or the volume may be known and you need to calculate another of the 4 factors.


It is worth understanding the basis of the laws. They are a high level summary of the consequences of some simple behaviour which can be understood from simple principles. One is that all molecules in an ideal gas (which means anything not close to liquefying from cold or pressure) behave like small objects that don't interact. At a constant temperature and pressure a mole of any gas will occupy the *same* volume. This means that, if we can control the pressure and temperature, we can count the molecules (the number of moles of objects making up the gas) by measuring the volume. Since we can also weigh the gas, we know what the objects consist of, or, at least, their mass). 


Because the molecules making up a gas don't interact, a mixture of different molecules will simply mix and we can adjust the gas equations to pretend that the components have *partial* pressures depending on their proportions in the mixture. So air (simplifying and rounding to make the numbers easier) is 75% nitrogen and 25% oxygen. 1 atmosphere of air will contain oxygen with a partial pressure of 0.25 atmosphere and nitrogen of .75 atm. You can apply the equations to the components using these numbers.


Remember the principles and you will be able to work out how to apply the laws.


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