CHM 5414 Thermodynamics

Your browser must support super and subscripts to view this page!

Quiz #4 Solutions

5 November 1996

  1. Being below its critical point, carbon dioxide is famous for subliming at atmospheric pressure; it does so at - 78°C. So what? Everything sublimes below its melting point. A case in point is water which has the following vapor pressures at its own fusion point and when in contact with solid carbon dioxide:

    T, °C P(H2O), Pa
    0 611
    - 78 0.079

    Estimate water's heat of sublimation assuming that it is reasonably independent of temperature over this range.

ln(P2/P1) = - ( Delta Hfus/R)×(T2-1 - T1-1)
or
Delta Hfus = - R ln(P2/P1) ÷ (T2-1 - T1-1)
and with our data
Delta Hfus = - 8.314 J/mol°K ln(0.079/611) ÷ [ (273. - 78.)-1 - (273.)-1) ] K
or
Delta Hfus = - 8.314 J/mol°K ln(1.29×10 -4) ÷ [ 1.47×10 -3 ] K
= 5.08×104 J/mol = 50.8 kJ/mol

  • Methylbenzene and butanone form mixtures which are approximately ideal. The data below is the total vapor pressure (in kPa) above two different mixtures of these liquids at 303.15 K. Estimate their separate (pure) vapor pressures at that temperature.

    Xmethylbenzene P(total), kPa
    0.25 30.9
    0.80 18.6

    • Both substances have appreciable vapor pressure. If they form ideal liquids, they act as one another's ideal solute; hence:

    Pmethylbenzene = P°methylbenzene Xmethylbenzene
    and
    Pbutanone = P°butanone Xbutanone

    Since the vapor is an ideal gas (naturally),

    Ptotal=Pmethylbenzene+Pbutanone ,

    and we have two equations in two unknowns like:

    Ptotal; 1 = P°AX A; 1 + P°BX B; 1
    and
    Ptotal; 2 = P°AX A; 2 + P°BX B; 2

    Solving by substitution (or determinants or Cramer's rule or whatever you remember),

    P°B(utanone) = [ (Ptotal; 1/X A; 1) - (Ptotal; 2/X A; 2) ] ÷ [ (X B; 1/X A; 1) - (X B; 2/X A; 2) ]

    P°Butanone = [ (30.9)/(0.25) - (18.59/0.80) ] ÷ [ (0.75/0.25) - (0.20)/(0.80) ] = 36.5 kPa

    P°A = (Ptotal; 1/X A; 1) - (X B; 1/X A; 1) P°B

    P°methylbenzene = (30.9/0.25) - (0.75/0.25) 36.5 = 14.1 kPa

    (The actual values are 36.1 and 12.3 kPa, respectively; so ideality wasn't too far off.)
    Last modified 30 October 1996