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Gas in a Balloon

Patrick Ford
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Hey everybody. So let's work on this problem together here. So I've got a spherical balloon that I'm told some information about. So I'm gonna just draw this out real quickly. So I've got this spherical balloon and we're told that the volume is four times 10 to the third meters cubed and the pressure is 1.2 atmospheres. Now, remember whenever we're given units of atmospheres, we can always convert this to pascal's by using this conversion factor over here. Now we're told here also that the average kinetic energy of the particles inside the balloon is this number over here and ultimately we want to figure out is the number of moles of gas inside the balloon, basically how many how much gas do we have? So the variable for that number is going to be little end. So which equation do we start off with? Well remember we have one equation involving and it's going to be PV equals NRT. Alright, so let's go ahead and start off there. So we've got PV equals N. R. T. So if you want to figure out N then we just have to move everything over to the other side and we've seen this before. So basically what happens is you end up with PV divided by R. T. Is equal to N. Alright, so now what I'm gonna do is just gonna start plugging in some numbers here. So the pressure before I plug it in, I can't plug it in as 1.2. I'm gonna have to convert this really quickly here. So this 1.2 atmospheres, I can use this conversion factor to get it in terms of pascal's basically what I'm gonna do is I want to divide by units of atmospheres on the bottom so that it cancels. Well, the conversion factor is one atmosphere and this is 1.1 times 10 to the fifth pascal's. So this unit will cancel what you'll end up with here is 21.21 times 10 to the fifth pascal's. Alright, so, that's just the number that I'm gonna plug in here. 1.21 Times 10 to the 5th. Now, I've got the volume which is four times 10 to the minus three. Now, I'm gonna divide by the R which is the gas constant 8.314. And now, finally, I'm going to look at the temperature. So, what is the temperature? Well, actually, I'm not really told in this problem what the temperature is. So, I can't just go ahead right away and plug it in. So, I'm gonna have to figure this out. The only other information that I know about this problem is that the average kinetic energy is just this number over here. So, basically what they're giving me in this problem is they're actually giving me K average. Remember this equation here for k average is related to the temperature. So, that's how we figure out what T is equal to. All right. So, basically, I'm gonna go over here. So, I've got that K average is equal to three halves and this is gonna be K. B. T. Alright, so basically this just says that the average kinetic energy is related to the temperature. So that's the sort of relationship. But that's the link of how we get the temperature. Okay? So here's what we're gonna do, we're gonna do the uh this K average and I'm gonna just divide by this other stuff over here to get the temperature. So this is gonna be 7.2 times 10 to the minus 21 divided by uh This is gonna be three halves. And this is gonna be 1.38 times 10 to the minus 23. That's just the bolts, one constant, which is list right over there, That's equal to the temperature. And if you work this out, what you're gonna get here is you're gonna get 347.8 Kelvin. Alright, so this is the number here that we plug in for this over here. So now we're just gonna multiply by 347.8 or sorry, divide And that's going to give you your final answer for moles. And if you work this out, what you're gonna get is 1 0.1 Six moles. Actually it thinks this is a this is going to be seven or 168 moles. Alright, so that's it for this one. Guys, let me know if you have any questions