The final volume of the gas is 73.359 mL
Given :
A sample gas has an initial volume of 72.0 mL
The work done = 141.2 J
Pressure = 783 torr
The objective is to determine the final volume of the gas.
Since, the process does 141.2 J of work on its surroundings at a constant pressure of 783 Torr. Then, the pressure is external.
Converting the external pressure to atm; we have
External Pressure P[tex]ext[/tex]:
[tex]P ext[/tex] = 783 torr × [tex]\frac{1 atm}{760 torr}[/tex]
[tex]Pext[/tex] = 1.03 atm
The work done W = [tex]Pext V[/tex]
The change in volume ΔV= [tex]\frac{W}{Pext}[/tex]
ΔV = [tex]\frac{141.2 J \frac{1 L atm}{101.325 J} }{1.03 atm}[/tex]
ΔV = [tex]\frac{0.0014}{1.03}[/tex]
ΔV = 0.001359 L
ΔV = 1.359 mL
The initial volume = 72.0 mL
The change in volume V is ΔV = V₂ - V₁
- V₂ = - ΔV - V₁
multiply both sides by (-), we have:
V₂ = ΔV + V₁
= 1.359 mL + 72.0 mL
= 73.359 mL
Therefore, the final volume of the gas is 73.359 mL .
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