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# Thermodynamics part 5: Molar ideal gas law problem

## Video transcript

well I told you that the the two most important things you should know in thermodynamics and that'll get you most of your way through most exams is that the pressure times the volume is equal to a constant and that the pressure times the volume divided by the temperature is equal to constant and so they all change such that you know the initial pressure times volume times the initial divided by the 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 on that later and the other thing you should remember is that pressure times volume is equal to n where n is the number of moles right moles like a number like dozen but moles a huge number six times ten to the 23 times R R was the universal gas constant that's eight point I always forget eight point two one I think times let me let me see what I just forgot it I think it's eight point two one times eight point three one this is eight point three one eight point three one joules per mole Kelvin times the temperature and we'll remember whenever just to be safe always convert to Kelvin first so let's see if we can do a problem that I can make up on the fly of this situation let's say I have a balloon I have a balloon and the volume the volume of the balloon is let's say it's one let's say it's one meter cube so this is a big balloon that's that's fairly large if you imagine a cubic meter so the volume is a cubic meter let's say the pressure is equal to I don't know let's say there's not a lot of pressure in it so it's the pressure is equal to five Pascal's that's Newton's per meter squared right and let's say we're at a reasonably let's say a reasonably warm temperature so temperature is equal to twenty degrees Celsius so my question to you is how and let's say that balloon is filled of with helium helium so my question to you is how many molecules of helium do I have in the well let's just substitute into the equation so we have pressure which is 5 and actually write the unit's I never do it but you should and you should always do in an exam 5 Newton's per meter squared times the volume 1 meter cubed is equal to my number of moles n times the universal gas constant 8.314 mole Kelvin times temperature and remember I can't repeat this enough always convert the temperature to Kelvin so whatever our Celsius temperature is at 273 so at 273 to that you get 293 Kelvin so let's see I get 5 times 1 and meter squared meters cubed this cancels out this just becomes a meter Newton meters joules 5 joules is equal to n moles times 8.314 well this Kelvin and this Kelvin cancel out so 8.3 1 times 293 so let's see 8.3 1 times 293 is equal to two four three four point eight three so let me write that down times two four three four point eight three four Yul's per mole and so to get the number of moles we just divide both sides of this equation by that and the unit's should work out so you get five so n switch colors for to ease the monotony n is equal to five joules times one over that one over two four three four point eight three and then since we're dividing by this the this flips moles per Joule and said of course this jewel cancel out with this jewel so we just have to divide five by this and we'll get the number of moles so let's take the inverse of what I had there so I get point O two moles so this equals equals 0.002 one moles now that might seem like a small number to you but let's let's figure out how many molecules that is so we already said we knew that let me let me make some space free because alright some Avogadro's number down so I can let me get rid of all of this stuff okay now I have space so Avogadro's number what did I even say what Avogadro's number is Avogadro's number is the number of molecules per mole it's that number so number of a Gaudreau is equal to six point oh two two times ten to the 23 molecules per mole so that's the top is molecules the bottom is well I know you can't read that so if I have Oh to one moles how many molecules I have well I just multiply that 0.002 one times how many moles per molecule right because this is moles let me write that moles times Avogadro's number Avogadro's number molecules per mole I know that that's molecules this is mole maybe I should write the whole thing molecules per mole so then the moles will cancel out and Avogadro's number is 6.022 times 10 to the 23 let's just remember that and let's just multiply that times 0.002 one it equals 0.02 so this equals let's see point oh one two six times 10 to the 23 right I have to remember that molecules let's see this is 0.01 to six that's the same thing as that's the same thing as one point two six times 0.01 right and then of course times 10 to the 23 and what's point oh one that's 10 to the negative 2 right 10 to the negative 1 is point 1 so this is 10 to the negative 2 so then we get 1 point 2 6 10 to the negative 2 times 10 to the negative 3 we add the exponents times 10 to the 21st power so roughly one to six and then another 1900 flee 1 followed by 2100 many molecules of in this case 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 8.314 joules per mole Kelvin remembering to always convert your your temperature to Kelvin and then just making sure all your units match up I mean sometimes it might be tricky they might give volume in liters and you have to especially in this case you have to convert it to meters cubed before you do it or they might give pressure and atmospheres in which or bars and then you should know the conversion and convert it to Pascal's or Newtons per meter squared but other than that it's just substituting and just doing the hairy math and the scientific notation anyway hopefully that was vaguely clarifying see in the next video