Question

A vapor stream that is 65.0 mole% styrene and 35.0 mole% toluene is in equilibrium with a liquid mixture of the same two species. The pressure in the system is 150 mmHg absolute. Use Raoult’s law to estimate the composition of the liquid and the system temperature.

Answer 1

From Raoults law

y1P=x1p1sat

0.65*150 = x1p1sat = 97.5, x1= 97.5/p1sat

x2= 0.35*150/p2sat

but x1+x2= 1

97.5/p1sat +52.5/p2sat= 1 (1)

p1sat and p2sat has to be choosen so that x1+x2=1

p1sat and p2 sat are dependent on temperature

for styrene log P(bar)= 4.0593- 1459.9/(T-59.551 ) (2)

T in K

for toluene

log P (bar)= 4.23679 - 1424.448/ (T-45.997)   (3)

T in K

assume a temperature. Calculate p1sat and p2sat from Eq.2 and Eq.3 and see that whether they satisfty eq.1

This trial and error is done in excel and at T= 358.6 K P1sat= 112.876m Hg and p2sat= 359.03mm Hg

x1=97.5/112.876 =0.86 and x2=1-0.86= 0.14