![]() ![]() Of course, I have toĭo that on both sides. This, this cancels with that, so I have just V two Multiplying it times this is so that this cancels with ![]() And so we have everything we need in order to solve for V two, in fact, we can solve for V two before we even put in these numbers, if we multiply both sides of this equation times T two over P two, and the reason why I'm Subtract, it's going to be in my head, 229 Kelvin. Is going to be 296 Kelvin, and then what is T two? Well, T two is negativeĤ4 degrees Celsius, if we add 273 to that, let's see, that's going to be, if we In terms of Kelvin, so to convert 23 degreesĬelsius into Kelvin, you have to add 273, so this More of an absolute scale, and deal with temperatures Starting temperature is at 23 degrees Celsius, but you have to think on Least, what is T one? Well, they tell us the Want us to figure out, what is the volume of theīalloon just before it bursts? So I'll put a little question mark there. Now, what is V two? Well, that's what they 6.51 Torr, now, what is V one? Well, they tell us that right over there, that is 1.85 times 10 to the third liters. Torr, much lower pressure, which makes intuitive sense, 765 Torr, and what's P two? That's the pressure just before it burst, and they tell us it's 6.51 And so what are these different variables? Well, let's first think about P one, so pressure at time one That P one times V one over T one is equal to P To the number of moles times the ideal gas constant, which also needs to beĮqual to your pressure right before it bursts times the volume right before it bursts,ĭivided by the temperature right before it bursts, or you could just say Over your starting temperature is going to be equal Or another way to think about it, you could say your starting pressure times your starting volume Temperature could change, but because this wholeĮxpression on the left has to be constant, that could So one way to think about it is that PV over T has to be constant. And in this example, as this balloon goes to higher and higher altitudes, the number of moles does not change, and the ideal gasĬonstant does not change. And so one way to thinkĪbout it is if we divide both sides by T, you get These variables changing, and how that might affect other variables. Now, what's different about this example is that they aren't just giving us several of these variables and asking us to solve one of them, they're talking about Us a bunch of pressures, volumes, and temperatures, and the ideal gas law deals with that, it tells us that pressure times volume is equal to the number of moles times the ideal gasĬonstant times temperature. All right, so you mightĪlready have an intuitive sense that this has something toĭo with the ideal gas law, because they're giving What is the volume of theīalloon just before it bursts? So pause this video and see Negative 44 degrees Celsius and the pressure is 6.51 Torr. The balloon travels for two hours before bursting at anĪltitude of 32 kilometers, where the temperature is That a weather balloon containing 1.85 timesġ0 to the third liters of helium gas at 23 degreesĬelsius and 765 Torr is launched into the atmosphere. Then through some algebra rearrangements we arrive at an equation that solves for the final volume. So if these two equations are equal to the same constant, then through the transitive property these two equations are equal to each other. ![]() And this equation is true for both the initial and final states so we essentially have two versions of the same equation, just with different subscripts to denote the state. ![]() So Sal's equation: PV/T = nR, has the changing variables on the left and the constants in the right. In this problem we don't know what the exact value of n is, but we know this it is unchanging is not gaining or losing gas so n is a constant in addition to R. The idea with Sal's equation is that we rearrange the ideal gas law to that all the changing variables are on one side of the equation and the unchanging variables (the constants essentially) are on the other side. However the problem gives no information about the number of moles, for either the initial or final state. The problem with you equation is that it requires us to know the temperature, pressure, and moles of the gas to solve for the volume. However this use with just using this equation is that we don't just want to calculate volume at a single state, we want to calculate the volume at a new second state. So if we began with the ideal gas law and wanted to solve for volume, that would indeed be the equation we would use: V = (nRT)/P. ![]()
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