Hello, Brandy,
I've been answering many gas law questions lately. I guess many classes have reached the chapter at the same time. I believe a couple were for you, and I hope they helped.
I'll repeat some of what I had explained in a response I just finished in answer to a question you posted, but please let us know what portion of the calculation is the most difficult, so that we may work on that, instead of explaining the entire process. It would be appreciated.
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We can use a gas law relationship in a case where there is no gain or loss of the number of moles of the gas. It is:
P1V1/T1 = P2V2/T2
Where P, V, and T are pressure, volume and temperature (in Kelvin), respectively. The subscripts 1 and 2 mean initial and final.
Make a table with the values and rearrange the equation to solve for the unknown, In this case, the unknown is V1, the initial volume. We quickly see that no temperatures are given, so we must assume the temperatures are constant. I'll enter a simple 100K into the equation just to make me feel good, but the T1 and T2 terms cancel, so the temperature makes no difference in this calculation.
V1 = V2(P2/P1)(T1/T2)
Please note that I’ve rearranged the equation to demonstrate that the initial volume is the final volume adjusted by the ratio of initial and final values for both temperature and pressure. (T1/T2) tells us that as temperature is increased, the initial volume must be smaller. In this case, that ratio is "1." (P2/P1) tells us that as pressure increases, the initial volume must be reduced.
Set up a table and enter the data. Pay attention to see if the units cancel to leave liters. Also be certain that temperatures are in Kelvin, in the gas law calculations where it appears.
Before we do the calculation, make a prediction as to what should happen. The final volume is nearly 71 liters, after the gas more than doubled in pressure. In fact, the (P2/P1) term (527.82/192.58) is almost a factor of 3.
Since the pressure increased, the final volume will be small than the initial, by around a factor of around 2.7. If V2 = 70.925L, then V1 would be about 2.7X that, or, just guessing, about 200L.
Now we are ready to plug in the numbers from the table
V1 = V2(P2/P1)(T1/T2)
V1 = (70.925L)(527.82kPa/192.58kPa)(T1/T2)
V1 = 194.4L
We guesstimated 200L.
Bob
