A sample of gas occupies a volume of 59.9 mL. As it expands, it does 126.2 J of work on its surroundings at a constant pressure of 798 torr. What is the final volume of the gas?
a. 61.1 mL
b. 1,250 mL
c. 218 mL
d. 1,490 mL
e. None of the above
I used the work function w = -PΔV and I performed the following conversions:
-126.6 J = -1.2458 L*atm
798 torr = .9524 atm
I plugged these values in to the equation:
-1.2458 L*atm = (.9524 atm)(ΔV)
ΔV = 1.30806 L
I then added the original volume of 59.9 mL to this value to get around 1,367 mL for the final volume, but this is apparently incorrect. I found if I subtracted 59.9 mL from 1.30806 L I got the correct answer, but I didn't know if this was the proper way to reach the answer.
So long story short, is subtracting the value of the original volume from ΔV correct, and if so, why?
And according to this solution I have here the correct answer is b. 1,250 mL~
Never mind, I just found my error; I incorrectly converted between Torr and atm, I should've gotten 1.05 atm instead.
Yes, subtracting the value of the original volume from ΔV is the correct approach in this case. Let me explain why.
Given that the work done by the gas on its surroundings is 126.2 J, and the pressure is 798 torr (which is equivalent to 0.9524 atm), we can use the formula for work done in a constant-pressure process:
w = -PΔV
In this case, we want to find the final volume, so we rearrange the equation to solve for ΔV:
ΔV = w / (-P)
Substituting the given values:
ΔV = 126.2 J / (-0.9524 atm)
Now, notice that the original volume is given in milliliters (mL), so we need to convert the final volume to the same unit for comparison.
To convert ΔV from liters (L) to milliliters (mL), we multiply by 1000:
ΔV = (126.2 J / (-0.9524 atm)) * 1000 mL/L
Calculating this value gives us:
ΔV = -132,280.89 mL
Now, since the initial volume is 59.9 mL, the final volume can be found by adding the initial volume to ΔV:
Final volume = initial volume + ΔV
Final volume = 59.9 mL + (-132,280.89 mL)
Final volume = -132,220.99 mL
However, we cannot have a negative volume. This indicates that our assumption of the gas expanding was incorrect. In reality, the gas must have undergone compression. Therefore, we should take the absolute value of the final volume:
Final volume = |-132,220.99 mL|
Final volume = 132,220.99 mL
The closest answer option to this is "None of the above."
So, to summarize, the value of the original volume should not be subtracted from ΔV. Instead, you should add the original volume to ΔV to find the final volume. In this case, since the final volume is negative, it indicates that the gas underwent compression, not expansion.