Low-pressure phase equilibria: Measurement of VLE

Fluid Phase Equilibria, 29 (1986) 193-207

193

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

LOW-PRESSURE

MICHAEL

PHASE EOUILIBRIA:

MEASUREMENT

OF VLE

M. ABBOTT

Department Polytechnic

of Chemical Engineering and Environmental Engineering, Institute, Troy, New York 12180 (U.S.A.)

Rensselaer

ABSTRACT Techniques

for measurement

on developments

of low-pressure

with emphasis

Modern static and dynamic devices allow

of the past decade.

the speedy collection

VLE are surveyed,

of good data, and current output of isotherms

appears to

exceed that of isobars by a healthy margin.

Special interest in limiting

vity coefficients

of methods

has spurred the perfection

for measurement

acti-

of VLE

in dilute systems.

INTRODUCTION The usual goal of a low-pressure cients or excess Gibbs energies application

xiyi+pisat

of the equilibrium

= yieiP

perature

T.

activity

Quantity

coefficient

nonidealities

In evaluating coefficients,

term virial equation working

T

definitions

reactive mixtures

037873812/86/$03.50

corrections

and for pressure effects on the liquid-phase (1982).

an equation of state for the vapor mixtures

activity

of species i at temperature

&i is i factor of order unity which contains

see e.g. Van Ness and Abbott

mixtures.

(1)

N)

pressure P+; P.sat is the vapor pressure of pure liquid i at tem-

for vapor-phase cities:

coeffi-

This is done by

equations

(i=l , 2 ,...,

Here, yi + is the liquid-phase and reference

VLE study is to obtain activity

for the liquid phase.

Rigorous evaluation and volumetric

fuga-

of oi requires

data for the liquid

oi, one usually ignores the effect of pressure on the

and assumes that the vapor phase is described

These assumptions may in fact be used as

in pressure. of -low-pressure

up to pressure

by the two-

VLE; they are appropriate

levels of about 5 bar.

0 1986 Elsevier Science Publishers B.V.

for most non-

194 A complete VLE data set is a collection peratures,

Most low-pressure

and pressures.

mal or at isobaric conditions, constitute

{xi,yi,T,P} of compositions,

tem-

studies are done either at isother-

and for these cases either {xi,yi,P} or {xi,yi,T} Since liquid-phase

complete data sets.

more strongly on T than on P, isothermal

excess properties

data are generally

depend much

preferred to iso-

baric data because they are more easily reduced and interpreted. Liquid-phase

activity coefficients

are interrelated

through the Gibbs-Duhem

equation: lxidenyi = i

HE

dT +

$

dP

RT2

Any set of activity coefficients

obtained from a complete VLE data set must If Eq. (2) is satisfied

satisfy Eq. (2), both globally and locally. some standard of comparison, sistent, and therefore

possibly correct.

There is a vast literature

sistency testing; the work of Dohnal and Fenclovh contemporary

The Gibbs-Duhem

(1985a,b) is representative

equation may instead be incorporated

as a constraint

in a VLE experiment.

Thus, for isothermal

of the activity coefficients.

Similarly,

HE data are available

for the liquid phase.

Experimental

have been

The most popu-

in which xi and P are the

variables.

Determination partial

experiment,

provided that

procedures

devised which provide most of these types of partial data sets. lar of these is the total-pressure

for

for isobaric conditions

the partial data sets {xi,T}, {yi,T), or {xi,yi) are sufficient,

measured

on the

the partial data sets [xi,P}, {yi,P}, or {xi,yi} are sufficient

determination

of

in which case one may reduce by one the number of vari-

(xi,yi,T, or P) to be measured

conditions

con-

on VLE con-

efforts in this area.

activity coefficients, ables

relative to

the VLE data set is judged thermodynamically

of the activity coefficients,

VLE data set, is an exercise

reduction

procedure

(isothermal by the-level

is conditioned

vs. isobaric),

Skjold-Jorgensen Much chemical

in data reduction.

sophistication

literature;

Here too there

(1983) are good examples of current work. processing

occurs at conditions

region.

of high dilution

specifications

for one or

inevitably

involve the

Hence there are special needs for activity coeffi-

cients at infinite dilution. conventional

deemed necessary.

the studies of Kemeny et al. (1982) and

more of the species present; environmental infinitely-dilute

The nature of a data-

by the type of VLE data being treated

by whether the data set is complete or partial, and

of statistical

is a voluminous

whether from a complete or a

VLE experiments

These quantities may of course be obtained from by extrapolation

of the raw data, or as limiting

195 features of the correlated techniques

are available

excess Gibbs energies.

special experimental

which are capable of good precision,

for high dilution,

and which offer considerable

However,

savings in time and cost over conventional

proce-

dures.

COMPREHENSIVE

VLE MEASUREMENT

Stills and Cells We use the label "comprehensive"

to describe VLE data sets, whether complete

or partial, which span the range of phase compositions Reduction

of a comprehensive

VLE data set provides one with an expression

valid for the entire range of liquid compositions. have been proposed quently

for'providing

comprehensive

fall into one of two categories:

equilibrium

In circulation

Compositions

Those used most frestills, and static

is charged to a distilling

Evolved vapors are condensed

flask, where it mixes with the boiling liquid.

steady values.

change with time,

In a properly functioning

liquid and vapor compositions.

and temperature

flask and

into a receiver; the vapor con-

of the boiling liquid and the vapor condensate

attaining

the true equilibrium manostat,

VLE data.

dynamic circulation

stills, a liquid mixture

returns to the distilling

eventually

still, these are

Pressure is controlled

an up-to-date

operation

equilibrium determination tion.

methods,

and weaknesses

the minimization

of pressure

of true values of the equilibrium a well-designed

(1982a)

stressing principles

of

of the various designs.

concern with these devices are the establishment

conditions,

Nevertheless,

quickly

survey of circulation

and the relative strengths

Areas of potential

by a

is measured.

Hila et al. (1967) review still designs through 1965, and Malanowski presents

for GE

Scores of apparatus designs

cells.

brought to a boil. densate

0 4 xi ( 1 and 0 < yi 6 1.

fluctuations,

temperature

of true and the

and vapor composi-

still can often provide good VLE data as

and cheaply as can a static apparatus.

The modified Rogalski apparatus

Swietoslawski

and Malanowski, of good design.

of vapor condensate. which a continuous into an equilibrium

ebulliometer

as perfected by Malanowski

1980) is an example of a modern dynamic circulation This device provides

recirculation

of both liquid and

Liquid is boiled in an electrically-heated

stream of vapor and liquid is delivered

the vapor and liquid phases disengage, The vapor passes into a condenser,

the liquid draining

reservoir,

well.

return to the boiler, completing

Here

into a mixing chamber.

from which the vapor condensate

the mixing chamber where it recombines with the disengaged

from

via a Cottrell pump

chamber where it impinges upon a thermometer

of the mixing chamber

(see e.g.

liquid.

the cycle.

returns to The contents

196 Malanowski equilibrium

has developed two designs, one allowing for sampling of the

liquid and vapor condensate

(thus providing, with T and P, complete

data sets), and another -- a simpler apparatus -- in which no such provision made.

In the latter case, equilibrium

overall compositions

liquid compositions

are determined

via material balance and the equilibrium

equations.

is

from The

data set is in this case of course incomplete. Pressure control is provided by a manostat; for isothermal

runs by introduction

response to pressure variations more difficult

than isobaric.

samples without disrupting

or removal of an inert gas.

compositions

The design permits introduction

nique.

If compositions

mixtures),

to about k 0.002 K.

Pressures Accuracies

of

(a particular

and by the accuracy of the analytical

are calculated,

the molar vapor-to-liquid

procedures

is little

or removal of

the boiling action in the ebulliometer.

are limited by sample-handling

problem for wide-boiling

Temperature

is fast, so that isothermal operation

are precise to about + 3 Pa and temperatures measured

the system pressure can be varied

tech-

one needs a good estimate of f I V/L,

ratio ("coefficient

of evaporation").

This quantity

varies little from system to system, and is not a strong function of temperature or pressure. between

Malanowski's

ebulliometers

operate satisfactorily

5 and 300 kPa, and at temperatures

tative study, illustrating

the efficiency

at pressures

between 300 and 500 K. and versatility

A represen-

of the technique,

is

that of Gierycz et al. (1985), in which are reported 21 isotherms for 13 binary systems containing

N-methylpyrrolidone

as a common compound.

In static methods, a liquid mixture is charged to an evacuated equilibrium cell immersed in a constant-temperature phases is brought about by stirring. bath, and pressure

bath.

Equilibration

Temperature

of vapor and liquid

control is provided by the

is measured; hence static methods are inherently

isothermal

techniques. There are two major drawbacks

to the static methods,

The first is serious:

one is dealing with a closed system, and small amounts of gases dissolved charged liquids can render the measured mixture Thus the liquids must be thoroughly mation

degassed.

(Bell et al., 1968) or by distillation

second drawback

relates to sampling.

in the

vapor pressures meaningless. This can be done by vacuum subli-

(Van Ness and Abbott, 1978).

The

At low pressures, the vapor density is

small, as is the total vapor volume in most cell designs; hence a vapor sample must be extremely of the sample. vapor sampling

small in order that equilibrium

Although

(Inoue et al,, 1975), practically

tunity and content themselves T.

not be disturbed

on withdrawal

at least one design has been proposed to allow for all workers forgo the oppor-

with a partial data set, viz,, P vs. x at constant

Thus the phrase "total pressure method" has become practically

synonymous

197 with "static method",

although dynamic techniques

can also provide isothermal

P-x data. Liquid compositions

are established

in various ways.

(1963) sampled the liquid phase directly. liquid degassing

can be done -in situ.

here as always a potential Some workers quantitatively brium cell.

liquid compositions

This procedure

has the advantage that

On the other hand, sample handling is

source of error, especially distill degassed

The known compositions

Hermsen and Prausnitz

for wide-boiling

liquids directly

systems.

into the equili-

in this case are overall mole fractions

xi are found from the zi as part of the data-reduction

zi; pro-

(Here, one requires the total vapor and liquid volumes; the smaller the

cedure.

vapor volume, the smaller the difference experiment, loading,

In this kind of

cell loadings are usually one-time affairs, and so, for a given

total pressures

ponding to different

are often measured

bath temperatures

results of such a study are multiple volumetric

between xi and zi.)

metering

scheme developed

of degassed

at several temperatures,

P-x isotherms.

liquids directly

A third procedure

others

(e.g. Tomlins and Marsh, 1976). and dilatometric

This procedure,

dilution techniques,

The

involves

into the evacuated cell, a

by Gibbs and Van Ness (1972) and subsequently

metric

corres-

(see e.g. Van Ness et al., 1967).

elaborated

by

like similar calori-

has the considerable

advantage

of

If the liquids are properly degassed, the main limitation of the method

speed.

is the accuracy with which one can establish overall compositions liquid volumes.

stored in and metered species.

from commercial

piston injectors,

The cell volume and piston-injector

complete

from metered

In the Gibbs and Van Ness apparatus, degassed liquids are

binary VLE experiment

one injector for each

volume are each about 100 cm3; a

covering the entire liquid-composition

requires two runs, which can be done in one or two days. adapted to ternary systems

range

The method is easily

(one merely adds a third piston-injector),

and can

also be applied to systems which form two liquid phases (Loehe et al,, 1983). The apparatus device, time,

of Maher and Smith (1979) is an example of a modern static

specially designed to produce large quantities

of binary data in a short

It consists of fifteen small cells (approximately

charged with the two pure components positions

are established

25 cm3 each) which are

and with thirteen mixtures.

gravimetrically.

Overall com-

After loading, the cells are con-

nected via vacuum fittings to 15 bellows valves mounted in a ring and connected to a manifold.

The contents of the cells are degassed -in situ by freezing/ cycles. After degassing is completed (a seven- to nine-hour

evacuation/thawing effort),

the manifold

with the attached cells is placed in a constant-temper-

ature bath (controlled to f 0.003 K) and connected to a pressure transducer. The P-x isotherm is obtained by sequentially

opening each cell to the trans-

198 Isotherms

ducer.

measurements

at other temperatures

at other bath temperatures.

are approximately

Estimated

?r 0.03 K for T, approximately

+ 0.0005 for the (calculated)

produces

accuracies

in a week three or four complete

of the cells, it is imperative be virtually

studied must be extremely

stable and the mixtures

formation

leaktight.

for experiments Additionally,

nonreactive,

make interpretation

J. Chem. Eng. Data appear in 14 papers; they comprise systems.

Noteworthy

Low-pressure

mental

are the data of Srivastava

mixtures

of the condensed

molecularly-based

goal here is to accumulate

simplest

liquid mixtures:

introduced,

Results published 139 isotherms

theories

of the liquid state.

in the sense that as molecular

one step at a time.

The simplest

are those of the noble gases Ar, Kr, and Xe, and the properties stances

exemplify

for such systems. peratures

the problems

temperatures

of pairs of candidate

VLE.

study of low-pressure

VLE for mixtures

liquid mixtures,

thus obtaining

ments.

are prepared

Mixtures

pycnometer

enclosed

substance

at its triple

(Staveley

et al., 1981).

techniques. Rowlinson

tem-

the triple and critical

have liquid ranges that overlap.

of condensed

vapor pressures

by condensation

gases.

in the experimental They use a special

and molar volumes of cryogenic

of the component

gases into a

in a special cryostat which incorporates

Vapor pressures

the apparatus;

VLE

both GE and VE from a single series of experi-

or with a quartz spiral pressure

results obtained

of these sub-

are low, so that cryogenic

Secondly,

is

of all mixtures

point to provide precise and reproducible

data-reduction

of the

complexity

species are often far apart, making it diffi-

whose components

to measure

of

The experi-

who would measure

at Oxford and Calado at Lisbon have pioneered

static device designed

calibrated

temperatures

for low-pressure

cult to choose mixtures Staveley

facing the experimentalist

First, critical

are required

apparently

have an immense importance

precise data for the excess functions

"simple"

it is introduced

at 398.6 K.

lighter gases, although community,

in

for 48

and Smith (1985) for the

system, which show a rare double azeotrope

little direct interest to the industrial to those developing

else the long-

volume of low pressure

VLE data, all taken on the Maher and Smith apparatus.

binary

of this

the compounds

of the results impossible.

Since 1979, Smith's group has reported a prodigious

diethylamine/methanoT

of the variables

+ 0.1 96 for P, and approximately

length that the apparatus

term effects of product

the pressure

Since all data for a system are obtained

for a single binary system.

from single loadings

by repeating

liquid mole fractions.

The Maher and Smith apparatus isotherms

are obtained

are measured

transducer,

and GE is obtained

for this important

(1982) summarize class of mixtures.

values of T

with a dead-weight

Calado et al. (1980) describe

and Swinton

a pure

gage

by standard

a current version of

systems studied and

199 Special

Methods

Although

most comprehensive

circulation

low-pressure

stills or with static cells,

VLE experimentation

special techniques

is done with

are also available.

We note here a few of these. Dew point/bubble

In its idealized assembly

immersed

(UPBP) methods

is introduced

mined

as function

to the apparatus, of volume.

of the coexisting

high-pressure McGlashan

suggested

is not measured,

reduction.

The major drawback

amounts

bubble

of dissolved

also measured, McGlashan

pressure

VLE.

Christian balance,

is required; equation.

liquid

Tucker

isothermal

measurements

of their extreme

Dew-pressure

this technique

compositions

and Christian P-z data.

vered to the system through

Brewster

a

No sampling

of the Gibbs-Duhem

an automated

quantities

valve.

low-

incorporating

P-y data.

apparatus

and when successive

a chromatography

is

and

at low pressures.

is computer-activated;

reproducible

about half the liquid-composition method

to systems

isothermal

(1979) devised

0.7 Pa, accurately

The isopiestic

if the composition

procedure.

are found by integration

are made every three minutes,

agree to within

to even small

novel ways of measuring

(in effect)

Sample addition

of accurately

sensitivity

et al. (1960) used a static method

obtaining

in which the

as part of the data

determinations,

have explored

for

Dixon and

procedure,

is the difficulty

a related but alternative

and his coworkers

vapor-density

covering

of the method

because

are used primarily

have been proposed.

on the idealized

but is instead calculated

gases.

constitute

of known composi-

of the system is deter-

DPBP methods

applications

(1973, 1977) have applied

Christian

duces

pressures,

A mixture

1982b).

piston/cylinder

of the breaks define the molar

Although

a variation

composition

measuring

bath.

and the pressure

the coordinates

phases.

VLE, low-pressure

(1965)

(Malanowski,

of a calibrated

The dew point and the bubble point are found from

in the P vs. V trace;

volumes

have a long history consists

in a constant-temperature

tion

breaks

point

form, a DPBP apparatus

which pro-

pressure

measurements

of a liquid are deli-

A complete

experiment,

range, takes about two hours.

can be used for mixtures

containing

a single

volatile

component.

An apparatus

sentative.

It consists of five silver cups placed in holes drilled in a large

copper

plate.

cited paper) triethylene

by Herskowitz

and Gottlieb

Three cups are loaded with a nonvolatile and two with the nonvolatile

glycol).

some volatile cups.

described

Weights

substance

substance

of the non-volatile

(here, water)

and the entire At equilibrium,

assembly

allowed

the chemical

substance

in a desiccator,

to equilibrate

potential

standard

being studied

(LiCx in the (here,

are determined,

is added gravimetrically

The copper plate with cups is placed

(1984) is repre-

to each of the air is pumped out,

in a constant-temperature

of the volatile

and

substance

bath.

is the same in

the sample solutions as in the standard solutions; giavimetric equilibrium

compositions

determination

allows one to compute (from the known behavior of the

standard solutions) the activity of the volatile substance in the samples.

No

are required, but the nonvolatile substances must be truly

pressure measurements nonvolatile.

of

Equilibration

times can be very long; Herskowitz

and Gottlieb

allowed one to three days for each of their determinations. The development

of gas chromatography

as a quantitative

analytical tool has

inspired a few recent apparatus designs in which the vapor phase is sampled directly.

In GC headspace analysis, precisely reproducible

sampled from a closed container containing phase.

Liquid compositions

measured.

are determined

volumes of vapor are

vapor in equilibrium gravimetrically,

with a liquid

and peak areas are

Provided that the detector is operated in a linear range and that

sampling procedures

and operating conditions are carefully reproduced, the acti-

vity of species i in the liquid phase is approximately peak areas Ai/Aj, where Ai is determined pure liquid i.

equal to the ratio of

for a vapor sample in equilibrium

To the extent that vapor-phase

nonidealities

with

can be ignored in

the data reduction, the liquids need not be degassed.

Sample sizes are small,

and a complete binary system can be studied in a day.

Shaw and Anderson

(1983)

applied the procedure to five binary systems and a few ternary mixtures; they conclude that the technique

is especially suited to mixtures of relatively non-

volatile components. Trends for the Past Decade To assess trends in comprehensive detailed examination

low-pressure

VLE data measurement,

of results published in three journals

(Fluid Phase

Equilibria, J. Chem. Eng. Data, and J. Chem. Thermodynamics) through 1985.

we did a

for the years 1976

Although these journals contain only a portion of the world's

data published during that time, the number of articles is large (almost 300), and we therefore

believe the sample to be representative.

this search are summarized

Selected results of

in Tables 1 and 2.

It is interesting to note the increase over time of the number of isothermal studies relative to isobaric studies (Table 1). increased appreciation ment of efficient

of the advantages

and reliable techniques

One might attribute this to

of isothermal data, or to the developfor producing such data, or to both.

Of the isotherms, most are P-x data taken on static devices; however, there seems to be a relative increase in the amount of reported data taken on circulation

stills.

Publication

rates are increasing slowly (Table 1).

However, the numbers of

reported isotherms or isobars per system vary little from year to year (Table

201

TABLE 1 Comprehensive

Year

VLE studies reported in three journals No. of papers

No. of svstems

No. of isotherms

No. of isobars

1976

25

68

57

31

1977

19

57

44

32

1978

20

47

64

19

1979

25

55

82

14

1980

40

99

155

31

1981

29

79

109

36

1982

22

53

55

35

1983

30

107

211

7

1984

36

64

75

41

1985

50

141

223

39

Total

296

770

1075

285

TABLE 2 Publishing

Year

trends for three journals

Isotherms per system

Isobars per system

Isotherms per paper

Isobars per paper 2.4

1976

1.5

1.0

4.8

1977

1.2

1.5

5.5

2.7

1978

2.1

1.1

5.3

2.4

1979

2.0

1.0

4.1

2.3

1980

2.0

1.1

5.2

2.4

1981

1.6

2.3

4.8

4.5

1982

1.7

1.7

5.0

3.2

1983

2.1

1.2

7.8

2.3

1984

1.7

2.2

3.4

2.9

1985

1.9

1.6

6.0

2.8

Average

1.8

1.5

5.2

2.8

202 The number of systems per publication

2).

the isothermal enthalpies calorimetry

constant.

Many of

papers in which are reported excess

reflecting continuing

experimental

activity

in

and densimetry.

HIGH-DILUTION

TECHNIQUES

Gas/liquid activity

VLE studies have companion

and/or excess volumes,

is also relatively

elution chromatography

coefficients

(GLEC) is a popular method for determining In this technique,

at infinite dilution.

a small amount

of solute species 1 is injected into a carrier gas stream, which passes through a column in which solvent species 2 is distributed The solute absorbs

packing.

the carrier gas, resulting in a measurable For negligibly

species.

as a liquid on the column

into the liquid solvent and then desorbs back into net retention time tN for the solute

small solute concentrations,

and assuming local equi-

librium in the column, one can develop the following expression n2a

for tN:

/;o(xI/yI)mPvdP

tN=F

(3)

P' J ' pVdP 'i

Here, n2 a is the molar loading of solvent on the column, I? is the molar flow rate of the carrier gas, pv is the molar vapor density, and outlet column pressures.

Connection

for VLE, and on the specification

and Pi and PO are inlet

with yI OD is made through an equation

of an equation of state for the vapor phase.

The simplest case obtains when one assumes ideal-gas behavior and ignores the effect of pressure on liquid properties. n:RT -

YIrn =

In this case, we find that

(4)

sat

‘NPl where VN

VN

f

3 2

(5)

Here, F, is the volumetric Equations ments

flowrate, determined

(4) and (5), although approximate,

needed in a GLEC experiment:

indicate the kinds of measure-

gas flowrate,

loading,

pressures,

estimate

of the vapor pressure of the solute.

incorporated,

and temperature.

at column outlet conditions.

net retention time, column

In addition, one requires an independent

second virial coefficients

If

vapor-phase

are needed as well.

nonidealities

are

203 Advantages reduction

of GLEC include its relative speed and the simplicity The experimental

process.

ment is commercially separation

available.

is achieved

through

Surface adsorption

is essential.

Depending

of the detector.

GLEC can provide values of yIm with accuracies

1965; Cruickshank

(1978) survey applications GLEC are exemplified

et al., 1966, 1969).

in

direct measurements

stream of inert carrier gas is continuously liquid mixture

The offgas is intermittently areas AI are recorded libration

a non-volatile

contained analyzed

technique

of ym.

solvent the following

equilibrium

by gas chromatography, Assuming

Poynting corrections expression

a steady

with a highly dilute

in a thermostated

small solute concentrations,

and liquid-phase

of

which, like GLEC,

By this procedure,

contacted

as a function of time t.

and negligibly

nonidealities

of modern

consisting

(1982b),

34 solvents.

(IGS) is an unsteady-state

can provide more-or-less

solute/solvent

Locke (1976) and Letcher

The speed and versatility

by results reported by Thomas et al.

stripping

Inert-gas

between about 1 and 10%.

in a series of papers by the Bristol

and technique.

584 values of ym, for 35 solutes

of

on the nature of the

and the details of the data-reduction

The refined theory of GLEC is presented (Everett,

of solute must be

The latter effect can be mitigated

system, the extent of the experiments,

group

On the

of the carrier gas with solvent, at the expense

reducing the sensitivity

process,

and equip-

because

Solute sample sizes are small.

as must solvent stripping.

presaturation

are well-established,

Solute purity is not critical,

in the column.

other hand, solvent purity minimized,

techniques

of the data-

cell.

and solute peak

instantaneous

equi-

and ignoring vapor-phase

, one obtains for the case of

relating

vimto

measurable

quan-

tities:

n2'RT

Ylrn

-.

=

sat

en(AI,O/AI) Ft-VQn(AI,O/AI)

p1 Here, n2a is the amount of solvent carrier

in the cell, F is the volumetric

gas, and V is the volume of the vapor space in the cell.

solute peak area AI,0 is found by back-extrapolation The Ecole des Mines group (Leroi et al., al.,

flowrate

of

The zero-time

of AI vs. t data to t=O.

1977; Richon et al., 1980; Richon et

1985) have developed IGS as a research tool, and they have studied the

effects tility

of solvent viscosity, on the reliability

ditions,

they estimate

a complete

experiment

Infinite-dilution

carrier-gas

of the results.

accuracies (producing

activity

flowrate,

and solute and solvent vola-

Under favorable

experimental

for yIm as good as l-2%.

con-

For most systems,

a single value of y,") takes one to two hours.

coefficients

can be determined

from the limiting

204 slopes

of mixture

binary

isobaric

Ylrn =

- sat p1

“lW

QIW sat

curves

or mixture

vapor-pressure

Thus, for

curves.

VLE,

Lv

sat

dP2sat

- "2

'2

dT

(dT)_ dxl P

(7)

I

and, for binary

Ylrn= -

boiling

[

isothermal

VLE,

(8)

p2

p1 Here, as in

quantity

Eq. (I),

ties and for pressure

effects

compressibility-factor

change

The limiting accurate

derivatives

evaluation

"I contains

corrections

on liquid properties; of vaporization

for vapor-phase

for the pure solvent.

in Eqs. (7) and (8) are found by extrapolation;

of these quantities

requires

very precise

for small values of x1.

Although

experiments

on stills or static cells, better accuracy

able through

direct measurement

for these quantities

In differential

sers to a common

solution

pressure

are boiled by separate temperatures ments

(dT/dxl)-.

pressure,

fluctuations

cel in the measured

ym.

region;

providing

the 2-10%

range.

and the difference

provides

conden-

of the ebulliometers

A series of measure-

the information

both ebulliometers

pure solvent

separate

AT between the equilibrium

thermometry.

have promoted

at all times

necessary

for

"see" the same in P tend to can-

the use of differential

In a recent publication capable

of producing

to f 0.01 - 0.05 kPa.

for four solutes

are connected

Solute compositions

increments

to an accuracy

values of ym depend

ebulliometry

(Thomas et al., 1982a), they ym values

Five ebulliometers

volume-fraction

AT can be determined

in the reported

through

in T and T sat due to small fluctuations

in an 8-hour day.

P is controlled

injection,

(one containing

AT.

an apparatus

mon solvent which

Because

from

is attain-

techniques.

The liquid contents

by differential

and his coworkers

for determining describe

twin ebulliometers

solute compositions

computing

Eckert

heaters,

in principle

AT E T-T2Sat or AP : P-P2sat.

by differential

of 1 in 2) are connected

reservoir.

is determined

for various

of the differences

are provided

ebulliometry,

2, the other a dilute

such data can be obtained

P-x or T-x data

conventional

Values

nonideali-

AZ~~" is the

in a com-

to a manifold

in

are varied by

of 0.003 to 0.015 in the dilute

of about + 0.001 K.

Uncertainties

upon the system type, but generally

lie in

205 Differential

is the isothermal analog of differential

Here, twin cells (one containing

ebulliometry. solution

tensimetry

pure solvent, the other a dilute

of 1 in 2) are immersed in a common constant-temperature

difference

AP between the equilibrium

ential pressure transducer.

vapor pressures

Solute composition

(dP/dxl)" is found from the trace of BP vs. of the total-pressure

bath, and the

is measured with a differ-

is varied by injection, and Since this iS merely a variant

x1.

static method, one must take the usual precautions

to

ensure thorough degassing of the liquids. Hutchings producing

and Van Hook (1985a) describe a differential

an extremely

capable of

high density of points in the dilute region, as many as

25 up to a solute mole fraction of 0.025. K, and AP is measured with a differential made for absolute accuracy, in cyclohexane

tensimeter

is controlled transducer.

to ?r0.0005

No claims are

but 0.3% agreement with referee results for benzene

is cited as "typical".

1985b) apply the technique

Temperature capacitance

The same authors

to binary mixtures

(Hutchings and Van Hook,

of n-alkanes

in which the differ-

ence in carbon number is small.

CLOSURE The area surveyed in this paper -- measurement matured

considerably

in the last decade.

of VLE at low pressures -- has

We note the following trends, some of

which can be expected to continue: l

Dual emphases on accuracy and on speed;

l

Increasing numbers of isothermal

l

Special focus on the dilute

l

Use of chromatography

l

Accumulation

as an analytical

of really comprehensive

(e.g. ethanol/water) High-precision

studies;

region; tool; and

sets of data on selected mixtures

and classes of mixtures

data on multicomponent

(e.g. UNIFAC and TOM sys,ems).

systems are still relatively

scarce; one

hopes in the next decade to see such data collected with the same enthusiasm devoted to binary studies.

ACKNOWLEDGEMENT Support for preparation Science Foundation

of this manuscript

was provided by the National

under Grant No. CPE-8311785.

REFERENCES Bell, T.N., E.L. Cussler, K.R. Harris, C.N. Pepela and P.J. Dunlop, 1968. An apparatus for degassing liquids by vacuum sublimation. J. Phys. Chem., 72: 4693 - 4695.

now

206 Determination of excess Gibbs funcBrewster, E.R. and M.L. McGlashan, 1973. tions of binary liquid mixtures from measurements of dew pressure and comJ. Chem. position of vapor. Test of the method on benzene + cyclohexane. Sot. Far. I, 69: 2046 - 2053. The properties of binary mixtures of Brewster, E.R. and M.L. McGlashan, 1977. _ tetramethylmethane, tetramethylsilane, and tetramethylstannane. II. EXCeSS J. Chem. Thermodynamics, 9: 1095 - 1099. Gibbs functions. Thermodynamic Calado, J.C.G., E.J.S. Gomes de Azevedo and V.A.M. Soares, 1980. properties of binary liquid mixtures of ethane and ethylene with methane and Chem. Eng. Commun., 5: 149 - 163. the rare gases. Christian, S.D., E. Neparko and H.E. Affsprung, 1960. A new method for the determination of activity coefficients of components in binary liquid mixtures. J. Phys. Chem., 64: 442 - 446. Cruickshank, A.J.B., M.L. Windsor and C.L. Young, 1966. The use of gas-liquid chromatography to determine activity coefficients and second virial coefI. Theory and verification of method of data analysis. ficients of mixtures. Proc. Roy. Sot. (London), A295: 259 - 270. Cruickshank, A.J.B., B.W. Gainey, C.P. Hicks, T.M. Letcher, R.W. Moody and C.L. Gas-liquid chromatographic determination of cross-term second Young, 1969. virial coefficients using glycerol. Trans. Far. Sot., 69: 1014 - 1031. Dixon, D.T. and M.L. McGlashan, 1965. A new method for the precise determination of the excess Gibbs function of a liquid mixture. Nature, 206: 710. Verification of the accuracy of complete Dohnal, D. and 0. Fenclova', 1985a. binary vapor-liquid equilibrium data. Fluid Phase Equilibria, 19: 1 - 12. Dohnal, D. and D. Fenclovh, 1985b. A new procedure for consistency testing of Fluid Phase Equilibria, 21: 211 - 235. binary vapour-liquid equilibrium data. Effect of gas imperfection on G.L.C. measurements: a Everett, D.H., 1965. refined method for determining activity coefficients and second virial coefficients. Trans. Far. Sot., 61: 1637 - 1645. Gibbs, R.E. and H.C. Van Ness, 1972. Vapor-liquid equilibria from totalpressure measurements. A new apparatus. I & EC Fundam., 11: 410 - 413. Gierycz, P., M. Rogalski and S. Malanowski, 1985. Vapour-liquid equilibria in binary systems formed by N-methylpyrrolidone with hydrocarbons and hydroxyl Fluid Phase Equilibria, 22: 107 - 122. derivatives. HCla, E., J. Pick, V. Fried and 0. Vilim, 1967. Vapour-Liquid Equilibrium, Pergamon, Oxford. Hermsen, R.W. and J.M. Prausnitz, 1963. Thermodynamic properties of the benzene and cyclopentane system. Chem. Eng. Sci., 18: 485 - 494. Herskowitz, M. and M. Gottlieb, 1984. Vapor-liquid equilibrium in aqueous solutions of various glycols and poly(ethylene glycols). 1. Triethylene glycol. J. Chem. Eng. Data, 29: 173 - 175. Hutchings, R.S. and W.A. Van Hook, 1985a. A new continuous dilution vapor liquid equilibrium apparatus: the activity coefficients of benzene and water in cyclohexane at 50°C. J. Solution Chemistry, 14: 13 - 26. Hutchings, R.S. and W.A. Van Hook, 1985b. Excess molar Gibbs free energies of pairs of n-alkanes, the two n-alkanes differing by one or two carbon atoms. J. Chem. Thermodynamics, 17: 531 - 538. Inoue, M., K. Azumi and N. Suzuki, 1975. A new vapor pressure assembly for static vapor-liquid equilibrium. I & EC Fundam., 14: 312 - 314. Kemeny, S., J. Manczinger, S. Skjold-Jorgensen and K. Toth, 1982. Reduction of thermodynamic data by means of the multi-response maximum likelihood principle. AIChE J., 28: 20 - 30. Leroi, J.-C., J.-C. Masson, H. Renon, J.-F. Fabries and H. Sannier, 1977. Accurate measurement of activity coefficients at infinite dilution by inert gas stripping and gas chromatography. I & EC Process Des. Dev., 16: 139 -

144.

207 Letcher, T.M., 1978. Activity coefficients at infinite dilution from gas-liquid In: Chemical Thermodynamics, vol. 2, A Specialist Periodical chromatography. Report, The Chemical Society, London, chapter 2. In: Locke, D.C., 1976. Physicochemical measurements using chromatography. Advances in Chromatography, vol. 14, Marcel Dekker, New York, chapter 4. Loehe, J.R., H.C. Van Ness and M.M. Abbott, 1983. Vapor/liquid/liquid equilibrium. Total-pressure data and GE for water/methyl acetate at 50°C. J. Chem. Eng. Data, 28: 405 - 407. Maher, P.J. and B.D. Smith, 1979. A new total pressure vapor-liquid equilibrium apparatus. The ethanol + aniline system at 313.15, 350.81, and 386.67 K. J. Chem. Eng. Data, 24: 16 - 22. Malanowski, S., 1982a. Experimental methods for vapour-liquid equilibria. Part I. Circulation methods. Fluid Phase Equilibria, 8: 197 - 219. Malanowski, S., 1982b. Experimental methods for vapour-liquid equilibria. II. Fluid Phase Equilibria, 9: 311 - 317. Dew- and bubble-point method. Richon, D., P. Antoine and H. Renon, 1980. Infinite dilution activity coefficients of linear and branched alkanes from Cl to C9 in n-hexadecane by I & EC Process Des. Dev., 19: 144 - 147. inert gas stripping. Richon, D., F. Sorrentino and A. Voilley, 1985. Infinite dilution activity coefficients by inert gas stripping method: extension to the study of I & EC Process Des. Dev., 24: 1160 - 1165. viscous and foaming mixtures. Rogalski, M. and S. Malanowski, 1980. Ebulliometers modified for the accurate determination of vapour-liquid equilibrium. Fluid Phase Equilibria, 5: 97 - 112. Rowlinson, J.S. and F.L. Swinton, 1982. Liquids and Liquid Mixtures, 3rd Edition, Butterworths, London, pp. 140 - 145. Shaw, D.A. and T.F. Anderson, 1983. Use of gas chromatographic headspace analysis in vapor-liquid equilibrium data collection. I & EC Fundam., 22: 79 - 83. Skjold-Jorgensen, S., 1983. On statistical principles in reduction of thermodynamic data. Fluid Phase Equilibria, 14: 273 - 288. Srivastava, R. and B.D. Smith, 1985. Total-pressure vapor-liquid equilibrium data for binary systems of-diethylamine with acetone, acetonitrile. and methanol. J. Chem. Eno. Data. 30: 308 - 313. Staveley, L.A.K., L.Q. Lobo and J.C.G. Calado, 1981. Triple-points of low melting substances and their use in cryogenic work. Cryogenics, 21: 131 144. Thomas, E.R., B.A. Newman, G.L. Nicolaides and C.A. Eckert, 1982a. Limiting activity coefficients from differential ebulliometry. J. Chem. Eng. Data, 27: 233 - 240. Thomas, E.R., B.A. Newman, T.C. Long, D.A. Wood and C.A. Eckert, 1982b. Limiting activity coefficients of nonpolar and polar solutes in both volatile and nonvolatile solvents by gas chromatography. J. Chem. Eng. Data, 27: 399 - 405. Tomlins, R.P. and K.N. Marsh, 1976. A new apparatus for measuring the vapor pressure of liquid mixtures. Excess Gibbs free energy of octamethylcyclotetrasiloxane + cyclohexane at 308.15 K. J. Chem. Thermodynamics, 8: 1184 - 1194. Tucker, E.E. and S.D. Christian, 1979. Rapid determination of liquid-vapor equilibria. 2,2,2-trifluoroethanol + tetrahydrofuran at 298.15 K. J. Chem. Thermodynamics, 11: 1137 - 1144. Van Ness, H.C., C.A. Soczek, G.L. Peloquin and R.L. Machado, 1967. Thermodynamic excess properties of three alcohol-hydrocarbon systems. J. Chem. Eng. Data, 12: 217 - 224. Van Ness, H.C. and M.M. Abbott, 1978. A procedure for rapid degassing of liquids. I & EC Fundam., 17: 66 - 67. Van Ness, H.C. and M.M. Abbott, 1982. Classical Thermodynamics of Nonelectrolyte Solutions: With Applications to Phase Equilibria, McGraw-Hill, New York, pp. 290 - 293.