Assuming an ideal gas for the vapor phase only, estimate the pressure and vapor phase composition of a liquid mixture of toluene (1) and methyl ethyl ketone (2) at 323 K and 31 % (by mole) of component 1.

Question

The experimentally determined infinite dilution activity coefficient for component 1 is 1.2189 and the experimentally determined infinite dilution activity coefficient for component 2 is 1.4506. (Hint: Use those values to determine Gibbs Excess model parameters)

Note the vapor pressure for toluene at 323 K is 92.12 mmHg while the vapor pressure of methyl ethyl ketone at 323 K is 267.77 mmHg.

Answer 1

SOLUTION:

For an infinitely dilute solution:

ln?(?_1^? )=-ln?(?_12 )+1-?_21

ln?(?_2^? )=-ln?(?_21 )+1-?_12



Which gives two equations and two unknowns:

ln?(1.2189)=-ln?(?_12 )+1-?_21

ln?(1.4506)=-ln?(?_21 )+1-?_12



When solved simultaneously:

?_12=1.4138

?_21=0.45576



For the Wilson Model:



Using Raoult’s Law for each component:



Results in two equations with two unknowns:



(1.13813)(0.31)(92.12 mmHg)=y_1?P

(1.01390)(0.69)(267.77 mmHg)=(1-y_1)?P



Therefore:

y_1=0.148

y_2=0.852

P=219.8 mmHg