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  • - [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.

- [Instructor] We're told that a 10-liter cylinder

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