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# Gas mixtures and partial pressures

AP.Chem:
SAP‑7 (EU)
,
SAP‑7.A (LO)
,
SAP‑7.A.1 (EK)
,
SAP‑7.A.2 (EK)
For a mixture of ideal gases, the total pressure exerted by the mixture equals the sum of the pressures that each gas would exert on its own. This observation, known as Dalton's law of partial pressures, can be written as follows:  P (total) = P ₁ + P ₂ + P ₃ + ... where P ₁, P ₂, and P ₃ are the partial pressures of the different gases in the mixture, and P (total) is the total pressure of the mixture.. Created by Sal Khan.

## Want to join the conversation?

• At why is the total pressure 2.5atm, where did that number come from and how did you calculate it?
• The number 2.5atm was just made up as a starting value for the question, and wasn't calculated from anything. The part that was calculated was "what is the partial pressure of the oxygen in the container, since the pressure changed from 2.0atm to 2.5 atm when we added oxygen in with the nitrogen?"

Hope that helps.
• Hello. When you add molecules of oxygen gas to the nitrogen gas, why does the number of moles (n) stay the same?
• Yes, when we added O2 molecules, we did change the number of moles in the container. However, in the video, She is saying that the number of moles of N2 didn't change since we only added some molecules of O2. Pressure is dependent on 3 factors. (i.e. T, V and n) Since we didn't change any of these factors for N2, n of N2 stays the same.
• Does it not make a difference wether the particles are colliding with each other and so the temperature increases which leads to the change in pressure?
• It is an assumption made that the collisions between the particles are completely elastic and that is the reason the avg. energy of particles remains constant, hence there is no change in temperature too.
Hope that helps.
• Air is made up of different types of gases and all these gases considered to be ideal.
They all are in same space so the factor V is same for all.
They are at the same temp, and being similar in mass, volume since they are "ideal" they all would have same average KE. So T is also same for all.
The only thing however is different is n.
So doesn't that mean just knowing n of each gas can give us their Partial pressure?
• there was initially 4 nitrogen molecules exerting a P of 2 atm then we added 4 oxygen molecules but the total P wasn't 4 atm.
This means O and N have different P, and since V and n is same, then they must be different in terms of T.
But won't the temperature of both N and O be same after a while? If that is so then after a while N and O won't have the same Partial pressure we calculated it has just after adding them together?
• You're taking the diagrams in the video too literally. They are meant to be symbolic and they don't accurate represent the amounts of each gas.

Although the diagrams suggest that the number of molecules (or moles) of nitrogen equal those of oxygen, this cannot be the case for an ideal gas, given the pressures referred to in the video. For the total pressure to be 2.5 atm after adding the oxygen, then there must be four times the amount of nitrogen than there is oxygen.
• Why is R the same? Don't different gases have different gas constants? Or is R the same for simplicity, to make the problem easier to answer?
• The gas constant, R, is the same for all gases.

Anytime you here that is something is proportional to something else, like x is proportional to y, then another way to say that is that x = ky where k is some constant.
In physics & chemistry we figure out that we have proportional relationships: but then we need to figure out how exactly they are proportional, which we figure out through experimentation.

Remember that the gas law was discovered using 3 observations of 3 people:
Boyle's Law --> V ∝ 1 / P,
Charles's Law --> V ∝ T,
Avogadro's law --> V ∝ n

Then, we wanted to find some way to combine these 3 proportional relationships, and so we did that using the gas law.
V = nRT/P

Note that we are really just combining the 3 said relationships, and we put the constant there to define the proportionality. Also it is often seen as PV = nRT.

Hope this helps,
- Convenient Colleague
• I know according to the Ideal Gas Equation, pV=nRT, the removal or addition of gases from a mixture does not affect its partial pressure. But if we see the formula for partial pressure which is mole fraction multiplied by the total pressure. And mole fraction is the number of moles of a particular molecule divided by the total number of moles.

By removing or adding any gases, wouldn't the total number of moles change? Hence causing the mole fraction and partial pressure to change as well..
• I think you have a conceptual misunderstanding. Adding or decreasing gasses does affect the partial pressure. The exception is when adding an INERT gas which doesn't change anything.
• If i am given the total pressure, how can i get the partial pressure of the individual gases that make the gas mixture since the gases apply different pressure on the container
(1 vote)
• You can use the mole fraction of each gas in the mixture to find their partial pressures if you're given total pressure and the moles of gas present. Sal shows this at .
• My question is what would you do if they only gave you the total pressure and asked you to find the partial pressures of the other gases. That's what has me confused.
(1 vote)
• Total pressure is just a sum you cannot find partial pressure of 2 gases from it just like x+y=8 now x&y can be 6,2 or 4,4 or any other number you need to know one to be able to find out the other
Now to be able to find it the partial pressure of any gas the question must give the either the partial pressure of one gas and the total pressure or it should give the total pressure and total number of moles of in a container as well as the individual number of moles of gases involved if moles are given we use
P1=(N1/Nt)Pt here p1 is the partial pressure of gas 1 N1 is the number of moles of gas 1 and Nt and Pt is the total number of moles and total pressure of gas