Activity Coefficients at Infinite Dilution Activity Coefficients at Infinite Dilution

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Activity Coefficients at Infinite Dilution Activity Coefficients at Infinite Dilution

using the Dilutor Method using the Dilutor Method

**Kyu-Jin Han, Jong-Hyeok Oh*, So-Jin Park**

^†

Dept. of Chemical Engineering,

Dept. of Chemical Engineering, Chungnam Chungnam National University National University

* Korea Atomic Energy Research Institute

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Introduction

Activity Coefficient (γ)

Definition : the ratio of activity Definition : the ratio of activity to some convenient to some convenient measure of the

measure of the concentration concentration in the liquid mixture in the liquid mixture

Important relation with excess Gibbs energy Important relation with excess Gibbs energy

s i i

i i

i i i

i

x P

P y f

x f x

a = =

≡

₀

γ

∑

=

i

i i

E

RT x

g ln γ ^Binary

mixture x

¹

ln γ

¹

x

²

ln γ

²

RT

g

^E

+

=

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Introduction

Activity Coefficient at Infinite dilution (γ ^∞ )

Characterizing the behavior of a single solute Characterizing the behavior of a single solute molecule

molecule completely surrounded by solvent completely surrounded by solvent

A maximum non A maximum non - - ideality(excess property) : ideality(excess property) : solute

solute- -solvent interactions solvent interactions in the absence of in the absence of solute

solute- -solute interactions solute interactions

Prediction of the phase behavior of a mixture Prediction of the phase behavior of a mixture over over the entire concentration range

the entire concentration range

Separation factor in extractive distillation column : Separation factor in extractive distillation column : used for the selection of selective solvents

used for the selection of selective solvents

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Introduction

Determination methods for γ ^∞

Indirect measurement Indirect measurement

Extrapolation of VLE data in whole or highly Extrapolation of VLE data in whole or highly dilute composition region

dilute composition region

Dilutor method Dilutor method

Direct measurement Direct measurement

Differential Differential ebulliometry ebulliometry method method

Differential static technique Differential static technique

In this work : Dilutor Method In this work : Dilutor Method

Based on the inert gas flow in the highly dilute Based on the inert gas flow in the highly dilute solution

solution

Possible to measure Possible to measure γ γ

^∞^∞

in solvent mixtures in solvent mixtures

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Scope

Activity coefficients at infinite dilution for the solutes of

Activity coefficients at infinite dilution for the solutes of nn-heptane-heptane and benzene in the solvent of DMF and DMF/water mixtures(10 wt%

and benzene in the solvent of DMF and DMF/water mixtures(10 wt%

of water) were measured with the help of the dilutor technique a

of water) were measured with the help of the dilutor technique at the t the temperature of 30, 40 and 50

temperature of 30, 40 and 50 °°C. C.

Activity coefficients at infinite dilution for methanol+

Activity coefficients at infinite dilution for methanol+dimethyl dimethyl cabonate

cabonate(DMC), and the solutes of 1(DMC), and the solutes of 1-propanol-propanol and toluene in the and toluene in the solvent of DMC were measured with the help of the dilutor techni

solvent of DMC were measured with the help of the dilutor technique que at the temperature of 20, 30, 40 and 50

at the temperature of 20, 30, 40 and 50 °°C.C.

The measured values for benzene in DMF were compared with the The measured values for benzene in DMF were compared with the reference data, and all experimental data were compared with the reference data, and all experimental data were compared with the estimated values using modified UNIFAC(Dortmund) at the same estimated values using modified UNIFAC(Dortmund) at the same conditions.

conditions.

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Theory

Basic relation for the highly dilute component Basic relation for the highly dilute component

Solute i :

Pure solvent :

P y

Poy P

x

_i

γ

_i

ϕ

_i^s _i^s _i

=

_i

ϕ

_i^v

P y

Poy P

x

_solv

γ

_solv

ϕ

_solv^s _solv^s _solv

=

_solv

ϕ

_solv^v

At the condition of infinite dilution

( )

1 1

solv solv solv

solv solv

≈

=

^∞

v s

i i i

Poy Poy

x

ϕ ϕ γ

γ γ

P y

P

P y P

x

s

i s

i s i i i

solv solv

=

∞

ϕ =

γ

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Theory

Calculation of Calculation of γ γ

^∞^∞

in Dilutor method in Dilutor method

( )

t A a ln A

ⁱ

/

⁰

=

Slope of decrease of solute :

From the material balance in the cells and thermodynamic relations

( )

RT F RT

n

V n P

P t

A A

s i s i i

i in

solv

g solv

0

1 /

ln &

 





 



 +

−

=

^∞ _∞

ϕ γ

( )

 

 



 + +

−

∞

=

solv g He

solv

/

1 V

a

P P

P F

RT n

s s i s i

i

&

ϕ

γ

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Experiment

Figure. Picture of the dilutor system for measuring γ

^∞

.

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Experiment

Figure. Schematic diagram of the dilutor system.

A : carrier gas B : elec. flowmeter C : heating coil D : saturation cell E : equilibrium cell F : septum

G : stirring motor H : transfer line I : sampling valve J : GC

K : PC

L : bubble flowmeter TH1, TH2 : thermostats

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DMF (C

₃

H

₇

NO)

A : 7.10850 B : 1537.78 C : 210.390 Antoine Constants

0.9440 g/cm

³

Density (25

^o

C)

153

^o

C Normal Boiling Point

73.10 g/mol Molecular Weight

Experiment

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DMC (C

₃

H

₆

O

₃

)

A : 7.09722 B : 1285.21 C : 214.536 Antoine Constants

1.0694 g/cm

³

Density (20

^o

C)

90.3

^o

C Normal Boiling Point

98.08 g/mol Molecular Weight

Experiment

CH

₃

H

₃

C O O

C

O

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Figure. Comparison of the experimental γ^∞

values with the reference data for n-heptane in DMF at various temperatures.*

[ Popescu, R. et al., Rev.Roum.Chim., 18, 746 (1967)]*

Results

1000/T

2.9 3.0 3.1 3.2 3.3 3.4

2.1 2.4 2.7 3.0 3.3

experimental data reference data*

modified UNIFAC(Dortmund) y=1.2365x-1.0503

r²=0.9999

1000/T

2.9 3.0 3.1 3.2 3.3 3.4

2.1 2.4 2.7 3.0 3.3

experimental data reference data*

r²=0.9999

γ

∞

ln

γ

^∞ ln

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Figure. Activity coefficients at infinite dilution for benzene as a function of temperature in DMF.

Results

1000/T

3.0 3.1 3.2 3.3 3.4

0.0 0.2 0.4 0.6 0.8

experimental data

modified UNIFAC(Dortmund)

modified UNIFAC(Dortmund-Unpublished) y=0.1473x+0.0199 r²=0.9893

1000/T

3.0 3.1 3.2 3.3 3.4

0.0 0.2 0.4 0.6 0.8

experimental data

modified UNIFAC(Dortmund)

modified UNIFAC(Dortmund-Unpublished) y=0.1473x+0.0199 r²=0.9893

γ

∞

ln

γ

^∞ ln

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Figure. Activity coefficients at infinite dilution for n-heptane as a function of temperature in the solvent mixture DMF/water(10wt%).

Results

γ

∞

ln

γ

^∞ ln

1000/T

3.0 3.1 3.2 3.3 3.4

3.0 3.5 4.0 4.5 5.0

experimental data

r²=0.9651

1000/T

3.0 3.1 3.2 3.3 3.4

3.0 3.5 4.0 4.5 5.0

experimental data

r²=0.9651

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Results

γ

∞

ln

γ

^∞ ln

Figure. Activity coefficients at infinite dilution for benzene as a function of temperature in the solvent mixture DMF/water(10wt%).

1000/T

3.0 3.1 3.2 3.3 3.4

0.6 0.9 1.2 1.5 1.8

experimental data

modified UNIFAC(Dortmund) y=0.3935x+0.0996

r²=0.9990

1000/T

3.0 3.1 3.2 3.3 3.4

0.6 0.9 1.2 1.5 1.8

experimental data

modified UNIFAC(Dortmund) y=0.3935x+0.0996

r²=0.9990

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1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 0.6

0.9 1.2 1.5 1.8 2.1

experimental data

modified UNIFAC(Dortmund) y = 0.9989x + 1.839 r² = 0.9994

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 0.6

0.9 1.2 1.5 1.8 2.1

experimental data

modified UNIFAC(Dortmund) y = 0.9989x + 1.839 r² = 0.9994

γ

∞

ln

γ

^∞ ln

Figure. Activity coefficients at infinite dilution for methanol as a function of temperature in DMC.

Results

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1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 1.6

1.8 2.0 2.2

2.4 y = -1.2997x + 6.2507

r² = 0.9959

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 1.6

1.8 2.0 2.2

2.4 y = -1.2997x + 6.2507

r² = 0.9959

γ

∞

ln

γ

^∞ ln

Figure. Activity coefficients at infinite dilution for DMC as a function of temperature in methanol.

Results

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1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 2.0

2.2 2.4 2.6 2.8

y = 1.1537x -1.5089 r² = 0.9025

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 2.0

2.2 2.4 2.6 2.8

y = 1.1537x -1.5089 r² = 0.9025

γ

∞

ln

γ

^∞ ln

Figure. Activity coefficients at infinite dilution for 1-propanol as a function of temperature in DMC.

Results

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1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 0.4

0.6 0.8 1.0

1.2 y = 0.8615x -2.0186 r² = 0.9965

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 0.4

0.6 0.8 1.0

1.2 y = 0.8615x -2.0186 r² = 0.9965

γ

∞

ln

γ

^∞ ln

Figure. Activity coefficients at infinite dilution for toluene as a function of temperature in DMC.

Results

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Conclusions

Activity coefficients at infinite dilution for the solutes of

Activity coefficients at infinite dilution for the solutes of n-n-heptaneheptane and benzene in the solvent of DMF and DMF/water mixtures(10 wt%

and benzene in the solvent of DMF and DMF/water mixtures(10 wt%

of water) were determined experimentally using the dilutor metho of water) were determined experimentally using the dilutor method d at various temperatures. And the

at various temperatures. And the γγ^∞^∞ data were measured for the data were measured for the system of methanol+DMC and the solutes of 1

system of methanol+DMC and the solutes of 1--propanolpropanol and and toluene in the solvent of DMC at the same conditions

toluene in the solvent of DMC at the same conditions

The experimental results show good agreements with the reference The experimental results show good agreements with the reference data and the calculated values using modified UNIFAC(Dortmund).

data and the calculated values using modified UNIFAC(Dortmund).

The dilutor method is excellently suitable for the measurement o The dilutor method is excellently suitable for the measurement of f activity coefficients at infinite dilution not only in pure solv

activity coefficients at infinite dilution not only in pure solvent but ent but also in solvent mixture.

also in solvent mixture.

Activity Coefficients at Infinite Dilution Activity Coefficients at Infinite Dilution