WEBVTT

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I think it makes sense to keep doing a few more problems just

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so you really get intimately comfortable

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with PV equals nRT, or the ideal gas equation.

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So we have 98 milliliters of an unknown gas.

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They say weighs in the problem, but I'll use mass.

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Its mass is 0.081 grams.

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You shouldn't say weighs 0.081 grams. This is mass.

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Weight would be in newtons if we're in the metric system

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at standard temperature and pressure.

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Calculate the molar mass of the gas.

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So they want to know the mass per mole.

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So the molar mass, or the mass per mole.

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Now, we could just substitute this into PV is equal to nRT.

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We know what standard temperature and pressure are.

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Standard temperature is 273 degrees Kelvin.

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Standard pressure is 1 atmosphere.

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And then, of course, they're giving us 98 milliliters.

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And then you can just solve for how many moles we have.

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And naturally we'll do that.

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But the other way to think about it is that

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at standard temperature and pressure, an ideal gas

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-- and we did this two videos ago.

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We said 1 mole of an ideal gas at standard temperature and pressure

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will fill up a volume of 22.4 liters.

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And I'm normally not a big fan of memorizing things,

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but this might be something handy to memorize

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if you want to get through your chemistry test fast.

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But you can always derive this if you know

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what standard temperature and pressure is by PV equals nRT.

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But if you know that 1 mole is going to take up that much space,

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so one mole is to 22.4 liters, as how many moles,

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let's say x moles in this question.

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We want to figure out how many moles of the gas we have

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and we know we are at 98 milliliters, so 0.098,

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so we set up this proportional equation

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and we could figure out how many moles we're dealing with.

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If 1 mole takes up 22.4 liters,

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then our number of moles are going to take up 0.098,

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and this is an ideal gas in both circumstances.

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So we could say 22.4x is equal to 0.098.

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And then we have x is equal to 0.098 divided by 22.4.

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And this, of course, is in moles.

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So 0.098 divided by 22.4 is equal to 0.004375 moles.

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And they're telling us that this amount has a mass of 0.081 grams.

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So let me get the number.

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So how many grams are there per mole?

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So we take 0.081 grams and we just did the math

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to figure out that we're dealing with 0.004375 moles.

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So how many grams do we have per mole?

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Let's take the calculator out.

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So we have 0.081 divided by 0.004375 is equal to 18.51.

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So it's equals 18.5 grams per mole.

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So now this is an interesting question.

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So we figured out the molar mass of our mystery substance

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that took up 98 milliliters and had a mass of 0.081 grams

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at standard temperature and pressure, and we figured out

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its molar mass, or its mass per mole, is 18.5 grams.

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So any guess as to what molecule we're dealing with?

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And probably it's not going to be exact,

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but at least in my brain, water seems to be a good candidate.

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Water is H20.

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Maybe I should do it in blue because it's water. H2O.

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The mass of each hydrogen is 1.

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Remember, hydrogen, at least in its most standard form,

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doesn't have a neutron, so it's really just a proton

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and an electron, so it has an atomic mass of 1

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or a molar mass of 1 gram.

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And oxygen has a molar mass of 16 grams.

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So you have two hydrogens, so it's 2 plus 16 is equal to 18.

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So it looks like our mystery substance is water.