Ideal gas laws
Ideal Gas Example 4 Figuring out the molar mass of a mystery molecule at STP.
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- I think it makes sense to keep doing a few more problems just
- so you really get intimately comfortable with PV equals
- nRT, or the ideal gas equation.
- So we have 98 milliliters of an unknown gas.
- They say weighs in the problem, but I'll use mass.
- Its mass is 0.081 grams. You shouldn't say weighs 0.081
- grams. This is mass.
- Weight would be in newtons if we're in the metric system at
- standard temperature and pressure.
- Calculate the molar mass of the gas.
- So they want to know the mass per mole.
- So the molar mass, or the mass per mole.
- Now, we could just substitute this into PV is equal to nRT.
- We know what standard temperature and pressure are.
- Standard temperature is 273 degrees Kelvin.
- Standard pressure is 1 atmosphere.
- And then, of course, they're giving us 98 milliliters.
- And then you can just solve for how many moles we have.
- And actually, maybe I'll do that.
- But the other way to think about it is that at standard
- temperature and pressure, an ideal gas-- and we did this
- two videos ago.
- We said 1 mole of an ideal gas at standard temperature and
- pressure will fill up a volume of 22.4 liters.
- And I'm normally not a big fan of memorizing things, but this
- might be something handy to memorize if you want to get
- through your chemistry test fast. But you can always
- derive this if you know what standard temperature and
- pressure is by PV equals nRT.
- But if you know that 1 mole is going to take up that much
- space, so one mole is to 22.4 liters, as how many moles,
- let's say x moles in this question.
- We want to figure out how many moles of the gas we have and
- we know we are at 98 milliliters, so 0.098, so we
- set up this proportional equation and we could figure
- out how many moles we're dealing with.
- If 1 mole takes up 22.4 liters, then our number of
- moles are going to take up 0.098, and this is an ideal
- gas in both circumstances.
- So we could say 22.4x is equal to 0.098.
- And then we have x is equal to 0.098 divided by 22.4.
- And this, of course, is in moles.
- So 0.098 divided by 22.4 is equal to 0.004375 moles.
- And they're telling us that this amount has a mass of
- 0.081 grams. So let me get the number.
- So how many grams are there per mole?
- So we take 0.081 grams and we just did the math to figure
- out that we're dealing with 0.004375 moles.
- So how many grams do we have per mole?
- Let's take the calculator out.
- So we have 0.081 divided by 0.004375 is equal to 18.51.
- So it's equals 18.5 grams per mole.
- So now this is an interesting question.
- So we figured out the molar mass of our mystery substance
- that took up 98 milliliters and had a mass of 0.081 grams
- at standard temperature and pressure, and we figured out
- its molar mass, or its mass per mole, is 18.5 grams. So
- any guess as to what molecule we're dealing with?
- 18.5 grams.
- And probably it's not going to be exact, but at least in my
- brain, water seems to be a good candidate.
- Water is H20.
- Maybe I should do it in blue because it's water.
- The mass of each hydrogen is 1.
- Remember, hydrogen, at least in its most standard form,
- doesn't have a neutron, so it's really just a proton and
- and an electron, so it has an atomic mass of 1 or a molar
- mass of 1 gram.
- And oxygen has a molar mass of 16 grams. So you have two
- hydrogens, so it's 2 plus 16 is equal to 18.
- So it looks like our mystery substance is water.
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