Question

A sample of gas occupies a volume of 55.5 mL. As it expands, it

does 148.6 J of work on its surroundings at a constant pressure of
783 Torr . What is the final volume of the gas?
=

Answer 1

To find the final volume of the gas, we can use the equation:

Work = Pressure * Change in Volume

Given:
Initial volume (Vi) = 55.5 mL
Work (W) = 148.6 J
Pressure (P) = 783 Torr

We need to rearrange the equation to solve for the change in volume (ΔV):

ΔV = W / P

Now, we can substitute the given values into the equation to find the change in volume:

ΔV = 148.6 J / 783 Torr

To convert Torr to atm, we divide by 760:

ΔV = 148.6 J / (783 Torr / 760 Torr/atm)

Simplifying:

ΔV = 148.6 J / (0.9969 atm)

Calculating:

ΔV ≈ 149 mL

Now, we can find the final volume by adding the change in volume to the initial volume:

Vf = Vi + ΔV

Vf = 55.5 mL + 149 mL

Calculating:

Vf ≈ 204.5 mL

Therefore, the final volume of the gas is approximately 204.5 mL.

Step by step solutions:
1. Use the equation ΔV = W / P to find the change in volume.
2. Substitute the given values into the equation.
3. Convert Torr to atm if necessary.
4. Calculate the change in volume.
5. Find the final volume by adding the change in volume to the initial volume.