Ideal gas laws
Ideal Gas Equation: PV=nRT Intuition behind the ideal gas equation: PV=nRT.
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- Let's say I have a balloon
- and in that balloon i have a bunch of particles bouncing around
- they're gas particles
- so they're floating freely
- and they all have, they each have some velocity
- some kinetic energy
- and what I care about
- what I care... let me just draw a few more
- what I care about is the pressure that is exerted
- on the surface of the balloon
- so I care about the pressure
- and what's pressure? it's force per area
- force per area
- so the area here, you can think of it as
- the inside surface of the balloon
- and what's going to put force,
- what's going to apply force to that?
- at any given moment i only drew what, 6 particles here
- but in a real balloon you would have
- you know, gazillions of particles, you know
- we could talk about how large, but more particles
- than you could really, probably imagine
- but at any given moment some of those particles
- are bouncing off the wall of the container
- that particle is bouncing there, this particle
- is bouncing there, this guy's bouncing like that
- and when they bounce, they apply a force to the
- container, an outward force, that's what keeps
- the balloon blown up.
- So let's think about what the pressure
- is going to be dependent on.
- So first of all the pressure, the faster these
- particles move, the higher the pressure, right?
- Faster particles
- faster particles would imply pressure would go up
- right? slower particles you're gonna be bouncing
- into the container less
- and when you do bounce into the container
- there is going to be less of a ricochet,
- or less of a change in momentum
- so slower particles
- you're gonna have pressure go down
- now it's practically impossible to measure
- the kinetic energy, or the velocity
- or the direction of each individual particle
- as especially you have gazillions of them
- in the balloon
- so what we do is we think of
- the average energy of the particles
- and the average energy of the particles
- you might say oh, Sal's about to introduce us
- to a new concept
- well I might, well it's a new of looking at a
- probably very familiar concept to you
- and that's temperature
- temperature can and should be viewed
- as the average energy of the particles in the system
- so i'll put a little squiggly line
- cause it's, you know, there's a lot of ways to
- think about.. Average energy
- or, you know... some, and mostly kinetic energy
- right? because these particles are moving and bouncing
- the higher the temperature, the more
- the faster that these particles move
- and the more that they're going to
- bounce into the side of the [sic]particle
- into the side of this container
- but temperature is average energy
- it tells us energy, energy per particle
- right, if you wanted to know the total, so you know
- obviously if we only had one particle in there
- with super high temperature
- that's going to have less pressure
- then if we have a million particles in there
- let me draw that
- if i have.. if i have..
- let's take two cases right here
- one is: i have a bunch of particles with
- a certain temperature
- moving in their different directions
- and in the other example i have one particle
- right?
- and maybe they have the same temperature
- on average they have the same kinetic energy
- the kinetic energy per particle is the same
- cleary this one is going to be applying
- more pressure to its container
- cause at every given moment
- more of these particles are gonna be bouncing
- off the side
- then in this example, this guy is gonna
- bounce —bam— and gonna go and move and bounce bam
- so he's gonna be applying less pressure
- even though his temperature might be the same
- because temperature is kinetic energy, or you
- can view it as kinetic energy per particle
- or it's a way of looking at kinetic energy per particle
- so if we wanted to look at the total energy
- in the system, we would want to
- multiply the temperature
- times the number of particles
- and just since we are dealing on the molecular scale
- the number of particles can often be represented
- as moles, remeber, moles is just the number of particles
- so we're saying that pressure
- pressure, is well I'll say, it's proportional
- so it's equal to let's say, some constant
- let's call that R times
- (cause we've got to make all the
- units work out in the end
- I mean temperature's in Kelvin
- but we eventually want to get back to Joules
- so let's just say it's equal to some constant
- or it's proportional to temperature
- times the number of particles
- we could do that a bunch of ways
- but let's think of that in moles
- but if I say they're 5 mole particles there
- you know that's 5 times 6 times 10 to the 23 particles
- so this is a number of particles (n)
- this is the temperature (T)
- and this is just some constant (n)
- constant, right there.
- now what else is the pressure dependent on?
- we gave these two examples
- obviously it's dependent on the Temperature
- the faster each of these particles move,
- the higher pressure it will have
- it's also dependent on the number of particles
- the more particles we have
- the more pressure we'll have
- what about the size of the container?
- the volume of the container?
- if we took this example, but we shrunk the container somehow maybe by pressing on the outside
- so this container looked like this, but we still had the same four particles in it
- the same four particles with the same average
- kinetic energy, with the same temperature
- so that number of particles is the same,
- the temperature's the same
- but the volume has gone down
- now these guys are gonna bump into
- the sides of the container more frequently
- and there's less area, right?
- so at any given moment, you have more force
- and less area
- so when you have more force and less area
- the pressure's gonna go up
- so when the volume went down
- your pressure went up
- so pressure is going to be, is going to be
- we could say, we could say
- pressure is inversely proportional to volume
- so let's think about that
- let's put that into our equation
- we said that pressure
- sorry, not ressure
- pressure is proportional, and I'm just saying
- some proportionality constant, let's call that R
- to the number of particles times the temperature
- (this gives us the total energy)
- and it's inversely proportional to the volume
- and so if we multiply both sides of this
- times the Volume
- we get the pressure, times the volume is proportional
- to the number of particles times the temperature
- and then you know
- so PV is equal to R n t
- and just to switch this around a little bit
- so it's in a form that you are more likely to see
- in your chemistry book, if we just switch
- the n and the R term
- you get P (pressure) times volume is equal to
- n (the number of particles you have)
- times some constant times temperature
- and this right here is the ideal gas equation
- ideal gas equation
- and hopefully makes some sense to you
- ideal gas (not not gass) equation
- they say ideal gas is based on
- this little mental exercise I did to come up with this
- i made some implicit assumptions when I did this
- one is I assumed, I essentially I assumed that
- that we are dealing with an ideal gas
- and so you say, what Sal, what is an ideal gas?
- an ideal gas, is one where the molecules
- they're not too concerned with each other
- they're just concerned with their own kinetic energy
- and bouncing off of the walls
- so they don't attract or repel each other
- don't attract or repel....
- cause let's say they are attracted to each other
- then as you increased the number of particles,
- maybe they'd want to not go to the side
- maybe they'd all gravitate towards the center a little bit more
- if they did attract each other
- and if they did that, they would bounce into the walls less and the pressure would be a little bit lower
- so assuming that they don't attract or repel each other
- and we're also assuming that the actual volume
- of the individual particles are inconsequential
- which is a pretty good assumption
- because they're pretty small
- altough if you start putting a ton of particles
- into a certain volume then at some point,
- especially if they are big molecules
- it will start to matter in terms of their size
- but we're assuming that for the purposes of
- our mental exercise that the molecules have
- inconsequential volumes
- and they don't attract or repel each other
- and in that situation we can apply the ideal gas
- equation, right here.
- Now we've established the ideal gas equation
- but we're like oh,oh what's R, how do I deal with it, and how do I do math problems
- and solve chemistry problems with it
- and how do the units all work out
- we'll do all of that in the next video, where i will solve a ton of equations, or a ton of exercises
- with the ideal gas equation
- but the important thing, the important take away from this video
- is just to have the intuition, as to why this actually does make sense
- and frankly once you have this intuition, you should never forget it
- you should be able to maybe even derive it on your own.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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