Hello, Bob,
We can use a gas law relationship in a case where there in 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 P2. The temperature remains constant in this problem, so T1 = T2
P2 = P1*(V1/V2)*(T2/T1) = P1*(V1/V2)
Set up a table and enter the data into the equation. Pay attention to see if the units cancel to leave kiloascals. Also be certain that temperatures are in Kelvin in problems where temperature doesn't cancel..
Before we do the calculation, make a prediction as to what should happen. We are compressing a fixed volume of gas in a closed chamber. Dangerous! I'll bet the pressure goes up. How much? Well, by the ratio of the two volumes.
We go from 5.4 to 1.36 liters, a ratio of a little less than 4. So I would guestimate a pressure increase of around 4 times the original, or about 4*2.17 atm = almost 9 atm.
Now we are ready to judge whether our answer is headed in the right direction and by the correct amount.
P2 = P1(V1/V2)
P2 = 2.17 atm(5.4 L/1.36 L) = 8.61 atm
We guesstimated 9, so I'm happy and moving on,
Bob
