Prediction of the Salt Effect on

Vapor-Liquid Equilibria by the Solvation Method

Shuzo Ohe, Ph.D. Prof. Sci. Univ. Tokyo

 

 

 

【Prediction Example】

Calculate vapor-liquid equilibria for the methanol water CaCl2 (4 mole %) system at 1 atm by solvation method when the liquid composition of methanol is 60 mole % at salt free basis and the solvation number of CaCl2 to methanol is 15.395 and that to water is 18.7844.

【Solution】

From the given liquid compositions

xi'= 0.6, xsalt= 0.04, xtotal,solvent= 0.96

then compositions at salt basis are calculated as x= 0.6・0.96 = 0.576, x2= 0.4・0.96 = 0.384, respectively. The solvation number for each volatile component is given as

     S10 = 15.395,  S20 = 18.7844

therefore, from relation;  Si = Sio×xi' they are estimated as

S1= 15.395・0.6 = 9.237, S2= 18.7844・0.4 = 7.514, respectively.

Next, effective liquid compositions of each volatile component from Eq. (4) is, calculated as

x1a' = (0.576 - 9.237・0.04) / (1- 0.04 - 9.237・0.04 - 7.514・0.04)

   = 0.7122 

Similarly, x2a' = 0.2878.

 

Activity coefficients g1' and g2' for effective liquid compositions: x1a', x2a' are calculated by the Wilson equation, using the following parameters for the methanol water system:

   Λ12 = 0.5515 and Λ21 = 0.8978.

By applying the Wilson equation:

  ln g1' = -ln (x1a' Λ12 x2a') x2a' [Λ12 / ( x1a' Λ12 x2a') -Λ21 / (Λ21x1a' x2a')]

  ln g2' = -ln (x2a' Λ21 x1a') - x1a' [Λ12 / ( x1a' Λ12 x2a') -Λ21 / (Λ21x1a' x2a')]

to the compositions x1a' and x2a' , we get

ln g1'= 0.0418, ln g2' = 0.3142

then g1' = 1.0427, g 2' = 1.3692.

 

Second, determine the activity coefficient for vapor pressure lowering gmix,solvent . From the solvation number for each pure solvent S10, S20, Eq. (2) estimates activity coefficients for respective components: g 1,solvent and g2, solvent.

g 1,solvent = (0.96 - 0.04・15.395) / (1 - 0.04・15.395) / 0.96 = 0.9332

g2, solvent = (0.96 - 0.04・15.395) / (1- 0.04・18.7844) / 0.96 = 0.8741

Eq. (3) calculates activity coefficients of solvent mixture g mix, solvent.

  g mix, solvent = 0.9332・0.6 0.8741・0.4 = 0.9096

Total activity coefficients for each volatile component are calculated from Eq. (7) as 

  g1 = 1.0427・0.9096・0.7122・0.96 / 0.576 = 1.1257

  g2 = 1.3692・0.9096・0.2878・0.96 / 0.384 = 0.8961.

 

Calculate the vapor pressures for each volatile component from the Antoine equation. Antoine constants for methanol and water are

A1 = 8.07919、B1 = 1581.341、C1 = 239.65

A2 = 8.02754、B2 = 1705.616、C2 = 231.405.

The Equilibrium temperature can be determined by bubble point calculation as 72.58 ℃.

Then the methanol vapor pressure is

P1 = 10 ( 8.07919 - 1581.341 / (72.58 239.65) ) = 1034.01 mmHg

and that of water is

P2 = 10 ( 8.02754 - 1705.616 / (72.58 231.405) ) = 261.03 mmHg.

Therefore, methanol and water partial pressures are

p1 = 1034.01・1.1257・0.576 = 670.46 mmHg

p2 = 261.03・0.8961・0.384 = 89.82 mmHg.

The total pressure is then  π = p1 p2 = 760.28 mmHg.

Vapor compositions for the components y1, y2 are

y1 = p1 /π = 670.46 / 760.28 = 0.882, y2 = 0.118.

The observed bubbling point is 72.6 ℃、and the vapor phase composition of methanol is 0.884 mole fraction. Absolute errors are 0.02 ℃ and 0.002, which indicate a high degree of accuracy.

©, Shuzo Ohe, 2003-2010, All rights reserved.