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Worked example: Calculating partial pressures

AP.Chem:
SAP‑7 (EU)
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SAP‑7.A (LO)
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SAP‑7.A.1 (EK)
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SAP‑7.A.2 (EK)
In a mixture of ideal gases, each gas behaves independently of the other gases. As a result, we can use the ideal gas law to calculate the partial pressure of each gas in the mixture. Once we know the partial pressures of all of the gases, we can sum them using Dalton's law to find the total pressure of the mixture. Created by Sal Khan.

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  • leaf green style avatar for user Nelson.Horsley
    I don't understand how the masses of the particles don't effect the pressure. Doesn't pressure come from the momentum of the particles? Why are # of particles and speed the only thing that matter?
    (50 votes)
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    • blobby green style avatar for user malvidin
      The kinetic theory of gases answers your question. The average pressure exerted by a particle is the same, whether large or small. If it is a small particle, it will have a higher average speed. If it is a large particle, it will have a lower average speed. Still, the average energy and the pressure on the container from each particle will be the same.
      It more like throwing a golf ball at a bowling ball. After the collision, the golf ball may have transferred all of its kinetic energy to the bowling ball, but the bowling ball won't be moving at the same speed the golf ball was.
      (80 votes)
  • blobby green style avatar for user Jeffrey Thomas
    I'd imagine that if a balloon were filled with one mole of hydrogen (H2) gas and one mole of, say, neon gas, that each neon atom would contribute to the total pressure more than each hydrogen molecule since the momentum of a neon atom would be 10 times greater than a hydrogen atom moving at the same speed (a neon atom is 10 times more massive than an H2 molecule), and when a neon atom bounces off the balloon wall, I imagine it would produce a greater impact than an H2 would. Can someone explain?
    (20 votes)
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    • blobby green style avatar for user malvidin
      The kinetic theory of gases answers your question. The average pressure exerted by a particle is the same, whether large or small. If it is a small particle, it will have a higher average speed. If it is a large particle, it will have a lower average speed. Still, the average energy and the pressure on the container from each particle will be the same.
      It more like throwing a golf ball at a bowling ball. After the collision, the golf ball may have transferred all of its kinetic energy to the bowling ball, but the bowling ball won't be moving at the same speed the golf ball was.
      Yes, I copied this answer from a previous question I answered.
      (28 votes)
  • mr pants teal style avatar for user Anthony
    If F=ma and P=F/A, then why doesn't the mass of the particle matter?
    (8 votes)
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    • mr pink red style avatar for user Carson Barlow
      I was wondering the same thing. But then I believe Sal answered the question a bit later at .

      If I'm not mistaken, each particle has the same amount of energy as defined by the term: temperature (average kinetic energy). That means that the bigger particles are going to have a lower acceleration than the smaller particles because they all have the same amount of energy, but applied to a higher mass. Although the acceleration is lower in the bigger particles, the pressure contribution upon impact of the surface is the same as a smaller particle because its higher mass then makes up for its lack of acceleration.
      (22 votes)
  • blobby green style avatar for user Clevella Hill
    why is oxygen gas usually stored under pressure in metal cylinders?
    (6 votes)
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    • male robot johnny style avatar for user Jimmy Yue
      Oxygen gas, like all gases are stored under pressure. This is because gases are compressible and are more efficent to store large amounts in a small area. Furthermore as NIGEL 1994 said, by doing so, you'll be able to get out the gas, through diffusion , where areas of high concentration would go to low concentration to acheive an "isotonic" state. Another thing is, if you didn't pressurize the gas, It would take up a large volume, as gas particles disperse from each other. Imagine carrying an oxygen tank underwater that was the size of a humvee!
      (12 votes)
  • piceratops ultimate style avatar for user THX 1138
    So let me get this straight. The O2 and H2 and N2 molecules are all moving at the same velocity, but because the H2 molecules are less massive, they exert less pressure.
    (5 votes)
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    • piceratops ultimate style avatar for user Just Keith
      No. The molecules have the same average kinetic energy, they are not all moving at the same velocity. The more massive molecules move more slowly than the lighter molecules.

      If temperature and volume are constant, then the pressure that each type of gas in mixture of gases exerts is proportional to the number of molecules of each kind, not the size of the molecules. Thus, the average pressure per molecule is the same no matter the mass of the molecule.
      (11 votes)
  • spunky sam blue style avatar for user Manav Rajvanshi
    hey a question just striked my mind when sal said about hydrogen at ..
    as we know that in most of the cases a hydrogen atom consists of an electron revolving around the proton(as there are no neutrons).. so my question is that.. IF WE TOOK AN ELECTRON NEAR A ISOLATED PROTON THEN WILL I BE ABLE TO CREATE HYDROGEN ATOM?
    (4 votes)
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  • male robot hal style avatar for user SHARVAI PATIL
    What is partial pressure and is it specific for a particular gas?
    (3 votes)
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  • aqualine ultimate style avatar for user Joanna S
    Suppose you have a 300 mL sample of He at 32oC. Assuming the volume of the container can vary so that the gas pressure is held constant, to what temperature would you have to heat the gas to increase its volume to 475 mL?
    (2 votes)
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  • piceratops ultimate style avatar for user anmolseth00
    At , Sal scrolls down to show us the three types of "R"s. My high school offers this Chemistry course in high school so I am doing a little prep work by watching Chemistry videos before starting the course. My question is, when tests come up regarding this topic, do we generally have to memorize these "R"s or are they given to us. I am asking since these look very daunting if we have to memorize these. I know I will be going to a different school but I want to know in your case what happened. Thanks.
    (2 votes)
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  • leaf yellow style avatar for user Raisin5488
    At , why is it that we don't care about the mass, but the amount of molecules when reguarding pressure? Because isn't hydrogen molecules so much smaller than say oxygen molecules ?
    (2 votes)
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    • old spice man green style avatar for user Joe
      Ideal gas equation is based on the assumption that there is no forces of attraction or repulsion between the particles. So if we have bigger molecules, they take up space, they have more density. So the molecules will be "closer" to each other such that the forces of attraction or repulsion can't be ignored. This fact is ignored when we deal with ideal gases where the size or mass of the particles are considered to be significantly less. The assumption is made so that people can grasp the concept better. That's why we don't care about the mass. Hope this helps
      (2 votes)

Video transcript

- [Instructor] We're told that a 10-liter cylinder contains 7.60 grams of argon, in gas form, and 4.40 grams of molecular nitrogen, once again in gas form, at 25 degrees Celsius. Calculate the partial pressure of each gas and the total pressure in the cylinder. All right, so pause this video, and see if you can work through this on your own before we work through it together. All right, so you might imagine that the ideal gas law is applicable here, and it's applicable whether we're just thinking about the partial pressures of each gas or the total. So the ideal gas law tells us that pressure times volume is equal to the number of moles times the ideal gas constant times temperature. And in this case, we're trying to solve for pressure, whether it's partial pressure or total pressure. So to solve for pressure here, we can just divide both sides by V, and you get pressure is equal to the number of moles times the ideal gas constant times the temperature divided by the volume. And so we can use this to figure out the partial pressure of each of these gases. So we can say that the partial pressure of argon is going to be equal to the number of moles of argon times the ideal gas constant times the temperature, both gases are at the same temperature over here, divided by the volume. And then we can also say that the partial pressure of our molecular nitrogen is equal to the number of moles of our molecular nitrogen times the ideal gas constant times the temperature divided by the volume. So we already know several of these things. We can look up the ideal gas constant with the appropriate units over here. They've given us the temperature, at least in terms of degrees Celsius. We'll have to convert that to kelvin. And they've also given us the volume. So all we really have to do is figure out the number of moles of each of these. And to figure out the number of moles, they give us the mass, we just have to think about molar mass. So let's look up the molar mass of argon, as well as the molar mass of molecular nitrogen. So the molar mass of argon, getting out our periodic table of elements, we look at argon right over here, and it has an average atomic mass of 39.95, which also gives us our molar mass. So a mole of argon will have a mass of 39.95 grams per mole. And then if we want to figure out the same thing for our molecular nitrogen, we look up nitrogen here, we see an average atomic mass of 14.01. So we might be tempted to say that the molar mass of molecular nitrogen is 14.01 grams per mole, but we have to remind ourselves that molecular nitrogen is made up of two nitrogen atoms. So the molar mass is going to be twice this, or 28.02 grams per mole. So this is equal to 28.02 grams per mole. And then we can apply each of these equations. So the partial pressure of argon, let me give myself a little extra space here, partial pressure of argon is going to be equal to the number of moles of argon. Well, that's just going to be, let me do this in another color, so you can see this part of the calculation. That's going to be the grams of argon, so let me write that down, 7.60 grams, times one over the molar mass, so times one over 39.95 moles per gram. And you can see that the units work out. Grams cancel with grams, and this is just going to give you the number of moles of our argon. And then we multiply that times our ideal gas constant. and we have to pick which one to use. In this case, we're dealing with liters, so both of these cases deal with that. And the difference between these is how they deal with pressure. The first is in terms of atmospheres. The second is in terms of torr. So if we want our partial and total pressures in terms of torr, we could use this second one. So let's do that. So in this case, let's use this second ideal gas constant. So that's going to be times 62.36 liter torr per mole kelvin. And then we need to multiply that times the temperature. So 25 degrees Celsius in kelvin, we add 273 to that, so that's 298 kelvin. And all of that is going to be divided by our volume, which is 10.0 liters, 10.0 liters. And we can validate that the units work out. We already talked about these grams canceling out. This mole cancels with this mole. This kelvin cancels with that kelvin. And then this liters cancels with this liters. And we're just left with torr, which is what we care about. We're thinking about a pressure, in this case, a partial pressure. We have 7.60 divided by 39.95 times 62.36 times 298 divided by 10.0 is equal to this business. And now we just have to think about our significant figures here. So we have three here, four here, three here, and three here. So when we're multiplying and dividing, we'll just go to the fewest number of significant figures we have, so it's three. So we'll want to go round to 354 torr. So the partial pressure of argon, 354 torr. And now we can do the same thing for the molecular nitrogen. And let me get myself a little more space here. So the partial pressure of our molecular nitrogen is going to be equal to, I will do this in a different color as well, when I figure out the number of moles, that is going to be the mass of molecular nitrogen, which is 4.40 grams, times one over the molar mass, so that's one over 28.02 grams per mole. And then that is going to be times our ideal gas constant, so we can really just copy the rest of this right over here, times 62.36 liter torr per mole kelvin times 298 kelvin. All of that is going to be over 10.0 liters. And once again, the units work out. Grams cancel with grams. Moles cancel with moles, liters with liters, kelvin with kelvin, and we're just left with torr. And this gets us to 4.40 divided by 28.02 times 62.36 times 298 divided by 10.0 is equal to this. And once again, the lowest significant figures we have here are three, so we'll round this to 292. So this is equal to 292 torr. And so we've figured out the partial pressure of each of these. And if we want to figure out the total pressure, the total pressure, that's just going to be the sum of the partial pressures. So it's going to be the partial pressure of the argon plus the partial pressure of the molecular nitrogen. And so this is going to be, let's see, I think I can do this in my head, 646 torr. And we are done.