Answer to Question #133071 in General Chemistry for Frederick Jude Evangelista

Question

A sample of nitrogen gas expands in volume from 1.6 L to 5.4 L at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of 0.80 atm, and (c) against a constant pressure of 3.7 atm.

Answer 1

Work done by the gas in isothermal expansion w = -p. DV

p = pressure, DV = final volume (V₂) - initial volume (V₁)

(a) When expand against vacuum then p= 0 atm

      W = -0 atm×(5.4-1.6) L = 0 L.atm = 0 J

(b) Here, p = 0.80 atm  

       V₂-V₁ = ( 5.4-1.6) L = 3.8 L

1 L.atm = 101.325 J

w = - 0.80×3.8  L.atm

     = -3.04 L.atm

     = -3.04×101.325 J

    = -308.03 J

(c) Here, p = 3.7 atm  

       V₂-V₁ = ( 5.4-1.6) L = 3.8 L

1 L.atm = 101.325 J

w = - 3.7×3.8  L.atm

     = -14.06  L.atm

     = -14.06×101.325 J

  = -1424.63 J