A sample of gas occupies a volume of 72.0 mL . As it expands, it does 141.2 J of work on its surroundings at a constant pressure

Question

1 year ago

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of 783 Torr . What is the final volume of the gas?

1 answer:

bagirrra123 [75] · Answer 1 · 2023-10-26T07:55:44+03:00

The final volume of the gas is 73.359 mL

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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 $ext$ :

$P ext$ = 783 torr × $\frac{1 atm}{760 torr}$

$Pext$ = 1.03 atm

The work done W = $Pext V$

The change in volume ΔV= $\frac{W}{Pext}$

ΔV = $\frac{141.2 J \frac{1 L atm}{101.325 J} }{1.03 atm}$

ΔV = $\frac{0.0014}{1.03}$

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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