In this example question, it says a sample of sulfur hexachloride gas occupies 8.30 liters at 202�C. Assuming that the pressure remains constant, what temperature degrees Celsius is needed to decrease the volume to 5.25 liters? All right, so how do I know I'm dealing with an ideal gas derivation? Remember we said that you're going to have to derive a new formula anytime a variable from the ideal gas law has two different values associated with it. If we look, we have two volumes and we have one temperature here and they're asking for a second temperature here. So we're dealing with two temperatures.
Again, if you're dealing with two pressures, 2 volumes, 2 moles or two temperatures, we're dealing with an ideal gas derivation. So these are the steps we're going to have to use to find our answer, begin by writing out the ideal gas law formula. So we're going to do that. We're going to say PV=nRT. Now we're going to circle the variable in the ideal gas law formula, then have two sets of different values. So we had again 2 volumes being discussed, two temperatures being discussed.
Next we're going to cross out the variables in the ideal gas law formula that are not discussed or remaining the same. So they weren't discussing pressure because it's being held the same. They weren't discussing moles. Since the R constant will have the same value, can also ignore it. Now we're going to say algebraically move all the circled variables to the left side of the ideal gas law formula. Oi need to move temperature to the other side so I have to divide it out. So now my equation becomes VT.
At this point, realize you're going to have to make these circled variables equal to the second set of identical variables in order to arrive a new formula, and this is important. If the temperatures is involved in the calculation, it must use the SI unit of Kelvins. All right. So what did that last line mean? Well, we have VT here, which is great. But remember we have two volumes and two temperatures, so we'll make this one V1 and T1 and they will equal the second set of volume and temperature. So we've just derived the formula we're going to have to utilize in order to find our answer.
So now what we do is we just bring down the numbers that we had. So if we look, we had 8.30 liters, 5.25 liters. Ince this liter is set first, we're going to say it's V1. Since this temperature set first, this is T1. They're asking for a second temperature. So this is T2. Since this is the second volume being discussed, this is V2, all right? So I'm just going to bring this formula up here. So V1T1=V2T2. Plug in our numbers. So 8.3 liters for V1 and then 525 liters for V2.
Remember we just said that your temperature in Kelvin, that your temperature has to be in Kelvin even though they want the answer in Celsius. When we're doing calculations, we first have to convert the temperature into Kelvin. So we have 202�C + 273.5, so it's going to give us 475.5 Kelvin. And then T2 is what we're looking for. We don't know what it is, so just solve for T2. We're going to cross multiply these two, cross multiply these two. So when we do that, we're going to have here 8.30 liters times T2 equals 475.15 Kelvin times 5.25 liters.
Divide both sides by 8.30 liters. Leaders cancel out and initially I'll have my temperature in Kelvin. So T2 initially equals 300.5 5 Kelvin, but we want our answer in degrees Celsius, so subtract out 273.15 and when we do that we're going to get our degrees Celsius, so that comes out two when we work it out 17.40�C as our final answer.
