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## AP®︎/College Chemistry

### Unit 3: Lesson 4

Ideal gas law- The ideal gas law (PV = nRT)
- Worked example: Using the ideal gas law to calculate number of moles
- Worked example: Using the ideal gas law to calculate a change in volume
- Gas mixtures and partial pressures
- Worked example: Calculating partial pressures
- Ideal gas law

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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?

- At3:30why is the total pressure 2.5atm, where did that number come from and how did you calculate it?(10 votes)
- 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.(26 votes)

- Hello. When you add molecules of oxygen gas to the nitrogen gas, why does the number of moles (n) stay the same?(10 votes)
- 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.(11 votes)

- 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?(6 votes)
- 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.(12 votes)

- 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?(4 votes) - 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?(2 votes)- 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.(6 votes)

- 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?(2 votes)
- 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(4 votes)

- 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..(3 votes)- 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.(2 votes)

- At5:20the Partial pressure of Nitrogen should change as the volume it can occupy is reduced due to the introduction of oxygen which takes up half of the space, right?(1 vote)
- Actually, Kinetic Molecular Theory (KMT) tells us that since gas molecules take up almost no space in comparison to any container we could put them in, we can think of them as having no volume. If the (oxygen) molecules have no volume, then they can't take away any of the volume that the N2 is occupying, which itself is much less than "half" the volume of the box. As the teacher says at about3:42, gases act independently of each other.

Hope this helps!(2 votes)

- Wait, so if we say partial pressure of N2 is 2.0 atm for example, and at the time there are 4 molecules of that N2, does that mean that the pressure exerted from all those four molecules combined is 2.0 atm? Is partial pressure of a gas (e.g. N2) in a mixture represents the pressure of all the molecules of that N2 gas combined, or is it the pressure of individual
**MOLECULE**of the N2 gas?(1 vote)- The partial pressure of a gas is the pressure that arises from
*all*the molecules of that gas that are present. Remember that in many practical situations the number of molecules of a gas that are present will be around 10^23.(2 votes)

- A sample of unknown gas is collected above a closed rigid container of water

at 80o C, the total pressure above the container is 125 kPa. What is the

pressure due to the unknown gas?(1 vote)- I usually don't like answering obvious homework questions since it's the easy way out, but I don't like hanging people out to dry either so I guess you're in luck.

You have to use Dalton's law of partial pressures which states that the total pressure of mixture of gases is the combination of the component gases' partial pressures added together. Partial pressures being the pressure exerted by a single gas compound.

Here you have two gases, an unknown gas and water vapor (gaseous water) in a rigid container. It's rigid so the gases won't expand the container and the pressure remains constant. The total pressure is 125 kPa and is composed of the partial pressures of the unknown gas and water vapor. So the formula looks like this so far using Dalton's law: Ptotal = 125 kPa = Punknown +Pwater. So you have two variables, the Punknown and Pwater, and they want to eventually solve for the Punknown which means they gave you a way to determine the Pwater in the problem. We can determine the Pwater from the temperature which gives us the vapor pressure of water. The vapor pressure is the pressure of the evaporated gaseous water above liquid at a certain temperature in a closed container. So the vapor pressure of water for a temperature is a constant you can look up in a table anywhere. Using Wikipedia is acceptable here which tells us the vapor pressure for water at 80 degrees Celsius is 47.3730 kPa. So 47.3730 kPa is your Pwater for the equation from before. Therefore, 125 kPa = Punknown + 47.3730 kPa. Using algerbra to solve for Punknown yields us 77.627 kPa. Acconting for sig figs, the final answer is 78 kPa.

Hope that helps.(1 vote)

## Video transcript

- [Instructor] In this video, we're going to introduce
ourselves to the idea of partial pressure due to ideal gases. And the way to think about it is imagine some type of a container, and you don't just have one
type of gas in that container. You have more than one type of gas. So let's say you have gas one
that is in this white color. And obviously, I'm not
drawing it to scale, and I'm just drawing those
gas molecules moving around. You have gas two in this yellow color. You have gas three in this blue color. It turns out that people
have been able to observe that the total pressure in this system and you could imagine that's being exerted on the inside of the wall, or if you put anything in this container, the pressure, the force per
area that would be exerted on that thing is equal to the sum of the pressures contributed
from each of these gases or the pressure that each
gas would exert on its own. So this is going to be equal to the partial pressure due to gas one plus the partial pressure due to gas two plus the partial pressure
due to gas three. And this makes sense mathematically from the ideal gas law
that we have seen before. Remember, the ideal gas law tells us that pressure times volume is
equal to the number of moles times the ideal gas constant
times the temperature. And so if you were to
solve for pressure here, just divide both sides by volume. You'd get pressure is equal to nR times T over volume. And so we can express both
sides of this equation that way. Our total pressure, that would
be our total number of moles. So let me write it this way, n total times the ideal gas constant times our temperature in kelvin divided by the volume of our container. And that's going to be equal to, so the pressure due to gas one, that's going to be the
number of moles of gas one, times the ideal gas constant
times the temperature, the temperature is not going
to be different for each gas, we're assuming they're all
in the same environment, divided by the volume. And once again, the volume
is going to be the same. They're all in the same
container in this situation. And then we would add that to
the number of moles of gas two times the ideal gas constant,
which once again is going to be the same for all of the gases, times the temperature
divided by the volume. And then to that, we could add the number
of moles of gas three times the ideal gas constant times the temperature
divided by the volume. Now, I just happen to
have three gases here, but you could clearly keep going and keep adding more
gases into this container. But when you look at it
mathematically like this, you can see that the right-hand side, we can factor out the RT over V. And if you do that, you
are going to get n one plus n two plus n three, let me close those parentheses, times RT, RT over V. And this right over here
is the exact same thing as our total number of moles. If you say the number of moles of gas one plus the number of moles of gas two plus the number of moles of gas three, that's going to give you
the total number of moles of gas that you have in the container. So this makes sense
mathematically and logically. And we can use these mathematical ideas to answer other questions or to come up with other
ways of thinking about it. For example, let's say that we knew that the total pressure in our container due to all of the gases is four atmospheres. And let's say we know that
the total number of moles in the container is equal to eight moles. And let's say we know that the number of moles of gas three is equal to two moles. Can we use this information to figure out what is going to be the partial
pressure due to gas three? Pause this video, and
try to think about that. Well, one way you could think about it is the partial pressure due to gas three over the total pressure, over the total pressure
is going to be equal to, if we just look at this
piece right over here, it's going to be this. It's going to be the number
of moles of gas three times the ideal gas constant times the temperature
divided by the volume. And then the total pressure, well, that's just going
to be this expression. So the total number of moles
times the ideal gas constant times that same temperature, 'cause they're all in
the same environment, divided by that same volume. They're in the same container. And you can see very clearly
that the RT over V is in the numerator and the denominator, so they're going to cancel out. And we get this idea that the, I'll write it down here, the partial pressure due to gas three over the total pressure is equal to the number of moles of gas three divided by the total, total number of moles. And this quantity right over here, this is known as the mole fraction. Let me just write that down. It's a useful concept. And you can see the mole
fraction can help you figure out what the partial pressure is going to be. So for this example, if we
just substitute the numbers, we know that the total pressure is four. We know that the total
number of moles is eight. We know that the moles, the number of moles of gas three is two. And then we can just solve. We get, let me just do
it, write it over here, I'll write it in one color, that the partial pressure
due to gas three over four is equal to two over
eight, is equal to 1/4. And so you can just pattern match this, or you can multiply both sides by four to figure out that the partial
pressure due to gas three is going to be one. And since we were dealing
with units of atmosphere for the total pressure, this
is going to be one atmosphere. And we'd be done.