# 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

• It's quite unclear as to what you are asking exactly. However, the volume of a gas will be the volume of the container but the pressure and temperature will change as the number of moles is changed. Similarly, if you change P,T or n at a constant volume, the other two state variables will change. In a mathematical sense V(n,T,p) – RobChem Jan 2 '15 at 17:56
• I suspect that doesn't completely answer your question, if at all. Please try to make your question more coherent. – RobChem Jan 2 '15 at 17:58
• What exactly is your question? – RobChem Jan 2 '15 at 17:58
• Question: why are volumes of gases in a container in direct proportion STP? – most venerable sir Jan 2 '15 at 17:59
• If they are constant throughout. – most venerable sir Jan 2 '15 at 18:06

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

We have Avogadros Law, which applies for an 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: $$pV = nRT \quad\Rightarrow\quad \frac{p_1V_1}{n_1T_1} = \frac{p_2V_2}{n_2T_2}$$

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 pressures, but no demixing.

A relevant question was posted on physics.SE, that may help you if you have to dive deeper into this topic.

• Regarding that post on physic SE, I didn't really learn how to combine c(degree of freedom into the gas law, it maybe more complicated than the one I'm learning). But thanks anyways – most venerable sir Jan 2 '15 at 18:52
• Sorry I should have state that there is only one question to answer. I thought answering those sub-question may help me understand this. – most venerable sir Jan 2 '15 at 18:53
• I don't mean gas demixing. I just want to know why they will have proportional volumes at STP( t and p are constant). If p and t are not constant they will mix. This is what I was told in my previous OP. – most venerable sir Jan 2 '15 at 18:55

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.