Question

2- The vapor pressure of pure benzene (M=78.12 amu) and pure toluene (M=92.14 amu) at 298.15 K are 103.1 Torr and 28.4 Torr, respectively. A solution is prepared from a mixture of 100.0 g each, under 1.000 atm pressure and equilibrium is established. i- What would be the composition of the vapor assuming the solution to be an ideal one? (5 pts) ii- What are the changes in the chemical potentials of the liquid and gaseous benzene and toluene upon formation of the solution? (10 pts) iii- Calculate the activity and the activity coefficient of benzene in the solution, if the experimentally found vapor pressure of benzene was 60.23 Torr. (10 pts) iv- Without doing explicit calculations, predict the activity coefficient of toluene in the solution. (5 pts)

Answer 1

• Benzene and toluene form ideal solution:

  Vapour pressure of pure substances :

  P^o (benzene ) = 103.1 Torr

  P^o (Toluene ) = 28.4 Torr

  Moles of Benzene in mixture : 100 g/ 78.12 g/mol   = 1.28 moles

  Moles of Toluene in mixture : 100 g/ 92.14 g/mol   = 1.08 moles

  Mole fraction (xB) = 1.28 mol/ 2.36 mol = 0.54

  xT = 0.46

  (a) Composition of Vapour phase :

  Solution P = xB*P^o (benzene ) + xT*P^o (Toluene )= 0.54*103.1 Torr+ 0.46*28.4 Torr = 68.74 Torr

  Thus In vapor phase mole fraction :

  yB = 0.54*103.1 Torr / 68.74 torr = 0.81

  yT = 0.46*28.4 Torr / 68.74 Torr = 0.19

  (xA is the mole fraction in the liquid and yA the mole fraction in the vapour.)

  (b) For an ideal solution, it follows
  μA = μA* + RT ln xA :                      (at 298 K)

  Assuming ideal solution formation :

  μB(l) = μB(l)* + RT ln xB

  thus, μB(l) - μB(l)* + RT ln 0.54 = -1.53 kJ/mol

  similarly, μT(l) - μT(l)* + RT ln 0.46 = -1.92 kJ/mol

• μB(g) - μB(g)* + RT ln 0.81 = -0.52 kJ/mol

  similarly, μT(g) - μT(g)* + RT ln 0.19 = -4.12 kJ/mol

  (c)

  Experimentally found that : P(b) = 60.23 torr

  aB = P(b)/P^o (benzene ) = 60.23 Torr / 103.1 Torr = 0.584

  we have, aB = xB*γB

  Thus,    γB= aB / xB = 0.584 / 0.54 = 1.08

  (d)     without explicit calculation

• Since, equilibrium between liquid and vapour phases of a solution at 298 K at 1.00 atm, thus

  P(T) > xT*P^o (Tolu )

  thus, aT > xT

  and γT > 1.