Hey everyone. So now that we've talked about how we're able to derive different types of formulas from the ideal gas law formula, let's put it into action with the following example question. Here it says, a sample of sulfur hexachloride gas occupies 8.30 liters at 202 degrees Celsius. Assuming that the pressure remains constant, what temperature in degrees Celsius is needed to decrease the volume to 5.25 liters? Alright. So, step 1 tells us that we need to begin by writing out the ideal gas formula. Remember that is PV=nRT. Step 2, circle the variables in the ideal gas law formula that have 2 sets of different values. So in the question, we have 2 volumes, and let's see. Pressure is being held constant. That means it's not changing. There wouldn't be 2 values. They're giving us one temperature and asking for another.
Alright. So our 2 sets of values deal with volume and temperature. Now, step 3, cross out the variables in the ideal gas law formula that are not discussed or are remaining the same or constant. Since the R constant will be the same value you can also ignore it. So pressure is being held constant, you never mention moles because it's being held constant, and R is our constant. Next step 4, algebraically move all the circled variables to the left side of the ideal gas law. So now we have V/T. Make these circled variables equal to the second set of identical variables in order to derive a new formula. So it becomes V/T=V/T. And since we're dealing with 2 sets of data, it's Vt1/Tt1=Vt2/Tt2. If temperature is involved in the calculation, it must be in the units in the SI unit of Kelvin. So they want the answer in degrees Celsius, but don't fall for that. When we're doing our calculations, temperatures still need to be done in Kelvin.
Once we've gotten our final answer in Kelvin, then we change it to degrees Celsius. Alright. So, in the question, they're giving us 202 degrees Celsius so you're going to add 273.15 to this. Doing that is gonna give us our Kelvin which is 475.15 Kelvin. Okay. So that is gonna be T1. So let's come over here. We're told that our initial volume is 8.30 liters. T1 is 475.15 Kelvin. We know our second volume is 5.25 liters. And we don't know what our T2 is. That's what we need to find. To solve this, just cross multiply. So we're going to cross multiply these 2. Cross multiply these 2. So we're gonna get 8.30liters×t2=5.25liters×475.15Kelvin. Divide both sides now by 8.30 liters. Liters cancel out. I'll get T2 in Kelvin which comes out to 300.55 Kelvin. But, again, we want the answer in degrees Celsius. So, subtract 273.15 from this. When I do that, I get T2 equals 27.40 Kelvin. So, this would be my final answer.
Again, as long as you know the Ideal Gas Law, that's the first step. Next, look and see what are the 2 sets of data in relation to those variables of the ideal gas law formula. Focus on them. Once you've determined which ones are changing, ignore all the other ones that are being held constant. Move everything over to the left side and then it becomes a simple math problem to isolate the one missing variable. Doing that will ensure that you get the correct answer at the end. And always remember, when dealing with calculations of temperature, make sure that you're doing it in units of Kelvin. Even if they ask for degrees Celsius at the end, still change everything to Kelvin as you're doing your calculations. And change that Kelvin to Celsius at the very end. Right? So just keep that in mind. You'll be able to tackle any type of ideal gas law, derivation type of question.
