How much P-V work does a gas system do on its surroundings at a constant pressure of 1.00 atm if the volume of gas triples from 250.0 mL to 750.0 mL? Express your answer in joules (J).

50.65J

The P-V work done by a gas on its surrounding at constant pressure is given by;

W = | -PΔV |     (i)

Where;

P = Pressure of the gas

ΔV = Change in the volume of the gas = final volume of the gas(V₂) - initial volume of the gas(V₁)

i.e

ΔV = V₂ - V₁

Therefore, equation (i) could be re-written as;

W = P (V₂ - V₁)        (ii)

From the question;

V₂ = 750mL

V₁ = 250mL

P = 1.00atm

Substitute these values into equation(ii) as follows;

W = 1.00 (750 - 250)

W = 1.00(500)

W = 500 atm.mL

Convert the result to Joules as follows;

(i) first convert to atm.L;

500 atm. mL = 500 atm.mL x 10⁻³L / mL = 0.5atm.L

(ii) then convert to Pa.L

0.5atm.L = 0.5 atm.L x 1.013 x 10⁵Pa / atm = 0.5065 x 10⁵Pa L

(ii) now convert to Pa.m³ (which is equivalent to 1 Joule)

0.5065 x 10⁵Pa.L = 0.5065 x 10⁵ Pa.L x m³ / 1000L = 50.65 Pa.m³

Therefore, the work done is 50.65J

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