Hello, Molly,
A handy formula to remember when doing gas laws in which the number of moles of gas remains constant (nothing added or removed) is:
P1V1/T1 = P2V2/T2
where P, V, and T are Pressure, Volume, and Temperature. The subscripts 1 and 2 refer to the starting and ending conditions, respectively. Say it out loud and it becomes easier to remember: Pee One Vee One Over Tee One Equals Pee Two Vee Two Over Tee Two. Well, you get the idea.
Rearrange to isolate the unknown, in this case V2.
V2 = (P1V1T2)/(T1P2)
We are told P1 = P2, so they will cancel out.
V2 = (V1T2)/(T1)
or
V2 = (T2/T1)*V1 (we can see that the volume change is proportional to the temperature change.
Remember that the gas laws require Kelvin in the calculations. If Centigrade were allowed, there would be problems with 0 C, since the mathematicians say we cannot divide by zero. And 0C does not mean there is no energy (heat). K is an absolute temperature, not one invented by freezing and boiling water. Don't get me started on Fahrenheit.
Then create a table to keep things straight:
Before we do the calculation, let's predict what we might expect. We are heating the gas in a "flexible" container (think balloon) and increasing it by over 160K, which is a little more than 50% higher than the initial temperature of 293K. Without wasting too much time, I'll guessimate that the volume will go up by around 50%, from let's say 50 to make it easy, to 75L. So we know to look for sometime around this figure.
The actual calculation:
V2 = (T2/T1)*V1
V2 = (458K/293K)*(47L)
V2 = 73.5 L
74 liters to 2 sig figs. Hey - that's pretty close to our wild estimate of 74 liters. AND, the units cancel to leave just Liters. I'm happy, on to the next problem.
Bob
