Oh I told you that two most important thing you should know in thermo dynamics but it will get you most of you weight through most exams is that the pressure times the volume is equal to a constant. And the pressure times the volume divided by the temperature is equal to constant. And so they're all change such that, you know, the initial pressure times the volume divided by initial temperature is equal to the final pressure times volume divided by the final temperature. Assuming that you're not changing the energy of the system and we’ll do more of that later.
And the other thing you should remember is that pressure times volume is equal to n where n is the number of mole, mole like a number like dozen but most a huge number six times 10(23) × r, r was the universal gas constant that’s 8.31 joules per mole Kelvin times the temperature and remember whenever just to be safe always convert to Kelvin first. So let see if we can do a problem that I can make up and apply of this situation.
Let say I have a balloon and the volume of the balloon is one meter cube so this is a big balloon, that’s fairly large if you imagine a cube like a meter. So the volumes at cubic meter the pressure is equal to—I don’t know, let say there's not a lot pressure in it. So the pressure is equal to 5 PASCAL’s and that’s the Newton’s per meter squared. And we have a reasonably warm temperature so temperature is equal to 20º Celsius. So my question to you is how and let say that balloon is filled up with helium. So my question to you is how many molecules of helium do I have in the balloon?
Well let just substitute into the equation so we have pressure which is 5 Newton’s per meter squared times the volume one meter cube is equal to my number of moles n times the universal gas constant 8.31 joules per mole Kelvin times temperature and remember I can't repeat this enough always convert the temperature to Kelvin. So whenever our Celsius temperature is add 273 so add 273 to that you get 293 Kelvin, so let see. I get 5 × 1 and meter squared, meters cube this cancels out this is comes in meter Newton meters joules, five joules is equal to n moles times 8.31 joules per mole Kelvin. Well this Kelvin and this Kelvin cancel so 8.31 × 293.
So let see, 8.31 × 293 is equal to 2434.83 × 2434.83 joules per mole and so to get the number of moles we just divide both sides that’s the equation by that and the unit should work out so you get so n is equal to five joules times one over that, one over 2434.83 and then since we’re dividing by this flips moles per joule instead of course this joules cancel with this joules so this action divide five by this and we’ll get the number of moles. So let's take the inverse of what I had there times five, so I get 0.002 moles. So this equals 0.0021 moles.
Now that might seem like a small number to you. But let's figure out how many molecules that is. So we’re already said we knew that—alright Avogadro’s number. All right, did I even say what Avogadro number is? Avogadro’s number is a number of molecules per mole is that number so number Avogadro is equal to 6.022 × 10(23 molecules per more). So the top is molecules the bottom is mole. I know you can read that.
So if I have 0.021 moles how many molecules I have? Well I just multiplied that, 0.0021 times—how many moles per molecule because this is mole times Avogadro’s number molecules per mole—that’s molecules this is mole. Molecules per mole so then the moles will cancel out and Avogadro’s number is 6.022 × 10(23) let's just remember that and let's just multiply that times 0.0021 it equals 0.2 so this equals 0.0126 × 10(23) right, we have to remember that—molecules.
And let see this is 0.0126 that’s the same thing as 1.26 × 0.01 and then of course times 10(23). And what's 0.01? That’s 10(-2), right. So then we get 1.26 10(-2) × 10(3) we add the exponents times 10to the 21st power. So roughly 126 and then another 19 zeros or roughly one followed by 21 zeros is how many molecules or in this helium we had in the balloon. So not too difficult the hard part is really just remembering Avogadro’s number, remembering the universal gas constant is 8.31 per joules per mole Kelvin, remembering to always convert your temperature to Kelvin and then just making sure all your units match up, I mean sometimes that might be tricky, they might give volume and leaders and you have to especially in this case you have to convert it to meters cube before you do it or they might pressure on atmospheres in which or bars and then you should know the conversion and then converted to Pascal’s or Newton’s per meter square.
But other than that is just substituting and just doing the hairy math and the scientific notation. Anyway, hopefully that was bigly clarifying. See you in the next video.
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