Activity Coefficients at Infinite DilutionActivity Coefficients at Infinite Dilutionusing the Dilutor Methodusing the Dilutor Method

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

Dept. of Chemical Engineering, Dept. of Chemical Engineering, Chungnam Chungnam National UniversityNational University* Korea Atomic Energy Research Institute* Korea Atomic Energy Research Institute

Introduction

Activity Coefficient (γ)

Definition : the ratio of Definition : the ratio of activityactivity to some convenient to some convenient measure of the measure of the concentrationconcentration in the liquid mixturein the liquid mixture

Important relation with Important relation with excess Gibbs energyexcess Gibbs energy

sii

i

ii

i

i

ii Px

Pyfxf

xa

==≡ 0γ

∑=i

iiE xRTg γln Binary

mixture 2211 lnln γγ xxRTg E

+=

Introduction

Activity Coefficient at Infinite dilution (γ∞)

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

moleculemolecule completely surrounded by solventcompletely surrounded by solvent

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

solutesolute--solvent interactionssolvent interactions in the absence of in the absence of

solutesolute--solute interactionssolute interactions

Prediction of the Prediction of the phase behavior of a mixturephase behavior of a mixture over over

the entire concentration rangethe entire concentration range

Separation factor in extractive distillation column : Separation factor in extractive distillation column :

used for the selection of selective solventsused for the selection of selective solvents

Introduction

Determination methods for γ∞

Indirect measurementIndirect measurement

Extrapolation of VLE data in whole or highly Extrapolation of VLE data in whole or highly

dilute composition regiondilute composition region

Dilutor methodDilutor method

Direct measurementDirect measurement

Differential Differential ebulliometryebulliometry methodmethod

Differential static techniqueDifferential static technique

In this work : In this work : Dilutor MethodDilutor Method

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

solutionsolution

Possible to measure Possible to measure γγ∞∞ in solvent mixturesin solvent mixtures

Scope

Activity coefficients at infinite dilution for the solutes of Activity coefficients at infinite dilution for the solutes of nn--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 measured with the help of the dilutor technique aof 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

cabonatecabonate(DMC), and the solutes of 1(DMC), and the solutes of 1--propanolpropanol and toluene in the and toluene in the

solvent of DMC were measured with the help of the dilutor technisolvent 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 thereference 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.

Theory

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

Solute i :

Pure solvent :

PyPoyPx viii

si

siii ϕϕγ =

PyPoyPx vsssolvsolvsolvsolvsolvsolvsolv ϕϕγ =

At the condition of infinite dilution

( )

1

111

solv

solvsolv

solvsolv

≈

≈≈=

= ∞

v

si

ii

Poy

Poyx

ϕϕ

γγγ

PyP

PyPxs

is

isiii

solvsolv =

=∞ϕγ

TheoryCalculation of Calculation of γγ∞∞ in Dilutor methodin Dilutor method

( )t

AAa i 0/ln=Slope of decrease of solute :

From the material balance in the cells and thermodynamic relations

( )RTF

RTnVP

n

Pt

AAs

isii

si

siii in

solv

gsolv

0

1

/ln &

+

−=∞

∞

ϕγϕγ

( )

+

+−=∞

gsolvHe

solv

/1 Va

PPFP

RTns

si

si

i &ϕ

γ

Experiment

Figure. Picture of the dilutor system for measuring γ∞.

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

DMF (C3H7NO)

A : 7.10850

B : 1537.78

C : 210.390

Antoine Constants

0.9440 g/cm3Density (25 oC)

153 oCNormal Boiling Point

73.10 g/molMolecular Weight

Experiment

DMC (C3H6O3)

A : 7.09722

B : 1285.21

C : 214.536

Antoine Constants

1.0694 g/cm3Density (20 oC)

90.3 oCNormal Boiling Point

98.08 g/molMolecular Weight

Experiment

CH3H3CO O

C

O

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 datareference data*modified UNIFAC(Dortmund)

y=1.2365x-1.0503r2=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 datareference data*modified UNIFAC(Dortmund)

y=1.2365x-1.0503r2=0.9999

∞γln∞γln

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 3.40.0

0.2

0.4

0.6

0.8

experimental datamodified UNIFAC(Dortmund)modified UNIFAC(Dortmund-Unpublished)

y=0.1473x+0.0199r2=0.9893

1000/T

3.0 3.1 3.2 3.3 3.40.0

0.2

0.4

0.6

0.8

experimental datamodified UNIFAC(Dortmund)modified UNIFAC(Dortmund-Unpublished)

y=0.1473x+0.0199r2=0.9893

∞γln∞γln

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

Results

∞γln∞γln

1000/T

3.0 3.1 3.2 3.3 3.43.0

3.5

4.0

4.5

5.0

experimental datamodified UNIFAC(Dortmund)

y=1.5227x-0.4592r2=0.9651

1000/T

3.0 3.1 3.2 3.3 3.43.0

3.5

4.0

4.5

5.0

experimental datamodified UNIFAC(Dortmund)

y=1.5227x-0.4592r2=0.9651

Results

∞γln∞γln

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 3.40.6

0.9

1.2

1.5

1.8

experimental datamodified UNIFAC(Dortmund)

y=0.3935x+0.0996r2=0.9990

1000/T

3.0 3.1 3.2 3.3 3.40.6

0.9

1.2

1.5

1.8

experimental datamodified UNIFAC(Dortmund)

y=0.3935x+0.0996r2=0.9990

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.350.6

0.9

1.2

1.5

1.8

2.1

experimental datamodified UNIFAC(Dortmund)

y = 0.9989x + 1.839r2 = 0.9994

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.350.6

0.9

1.2

1.5

1.8

2.1

experimental datamodified UNIFAC(Dortmund)

y = 0.9989x + 1.839r2 = 0.9994

∞γln∞γln

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

Results

1000/T

3.05 3.10 3.15 3.20 3.25 3.30 3.35

1.6

1.8

2.0

2.2

2.4y = -1.2997x + 6.2507r2 = 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

2.4y = -1.2997x + 6.2507r2 = 0.9959

∞γln∞γln

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

Results

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 -1.5089r2 = 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 -1.5089r2 = 0.9025

∞γln∞γln

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

Results

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

1.2y = 0.8615x -2.0186r2 = 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

1.2y = 0.8615x -2.0186r2 = 0.9965

∞γln∞γln

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

Results

Conclusions

Activity coefficients at infinite dilution for the solutes of Activity coefficients at infinite dilution for the solutes of nn--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 methoof 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 1system of methanol+DMC and the solutes of 1--propanolpropanol and and

toluene in the solvent of DMC at the same conditionstoluene in the solvent of DMC at the same conditions

The experimental results show good agreements with the referenceThe 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 oThe dilutor method is excellently suitable for the measurement of f

activity coefficients at infinite dilution not only in pure solvactivity coefficients at infinite dilution not only in pure solvent but ent but

also in solvent mixture.also in solvent mixture.