Prediction of Salt Effect on Vapor-Liquid Equilibria by Solvation Model

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 CaCl₂to methanol is 15.395 and that to water is 18.7844.

【Solution】

From the given liquid compositions

x_i'＝ 0.6, x_salt＝ 0.04, x_{total,solvent}＝ 0.96

then compositions at salt basis are calculated as x_１= 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; 　S_i= S_io×x_i'　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

x_1a'　= (0.576 - 9.237･0.04) / (1- 0.04 - 9.237･0.04 - 7.514･0.04)

　　　= 0.7122　

Similarly,　x_2a' = 0.2878.

　

Activity coefficients g₁^' and g₂^'　for effective liquid compositions: x_1a', x_2a' 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 (x_1a' Λ12 x_2a') x_2a' [Λ12 / ( x_1a' Λ12 x_2a') -Λ2１ / (Λ2１x_1a' x_2a')]

　 ln g₂^'　= -ln (x_2a' Λ2１ x_1a') - x_1a' [Λ12 / ( x_1a' Λ12 x_2a') -Λ2１ / (Λ2１x_1a' x_2a')]

to the compositions x_1a' and x_2a' , 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　g_mix,solvent . From the solvation number for each pure solvent S₁₀, S₂₀, Eq. (2) estimates activity coefficients for respective components: g_1,solventand g_{2,
solvent}.

g_1,solvent　= (0.96 - 0.04・15.395) / (1 - 0.04・15.395) / 0.96　= 0.9332

g_{2,
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.