A sample of gas occupies a volume of 63.1 mL. As it expands, it does 130.4 J of work on its surroundings at a constant pressure of 783 torr. What is the final volume of the gas?
I know that P= 1.03 ATM when converted. I think I'm supposed to use the equation w= -PdeltaV and solve for deltaV? Then add the initial volume to deltaV to get the final volume? Please explain, I'd really appreciate it! (:
I would convert 130.4 J to L*atm then use w = -pdV as you've indicated. I think the answer is about 1300 mL or so.
To find the final volume of the gas, you can indeed use the equation w = -PΔV, where w represents the work done by the gas, P is the pressure, and ΔV is the change in volume.
In this case, you are given the initial volume, V1, as 63.1 mL, the work done by the gas, w, as 130.4 J, and the pressure, P, as 783 torr (which is equivalent to 1.03 atm when converting).
First, let's convert the initial volume to liters to maintain consistent units:
V1 = 63.1 mL = 63.1 mL * (1 L / 1000 mL) = 0.0631 L
Now you can rearrange the equation w = -PΔV to solve for ΔV:
ΔV = -w / P
Plug in the given values:
ΔV = -130.4 J / (1.03 atm) = -126.6 L·atm
Keep in mind that since the initial volume V1 is positive, the change in volume ΔV will be negative since the gas is expanding.
Finally, calculate the final volume V2 by adding the change in volume ΔV to the initial volume V1:
V2 = V1 + ΔV
V2 = 0.0631 L + (-126.6 L·atm) = -126.537 L
Since volume cannot be negative, it appears there may be an error or discrepancy in the given information or calculations. Please double-check the numbers to ensure accuracy.