Berichte der Bunm-Gcdlschel t 1070 M. Rogalski et al. : Method for Determination of Vapour-Liquid Equilibrium

Verteilung im System Fliissig/Gas eineni Mehrstoffgemisch die unterschiedlichen Empfindlich-

Von Kolb [6] wurde bereits das binare Gemisch aus Chloroform und Aceton untersucht und Aktivitatskoeffzien- ten sowie thermodynamische Mischungsfunktionen bestimmt. Der Vorteil der hier beschriebenen Dampfraumanalyse liegt in der direkten Kopplung mit der chromatographischen Trennung, wodurch auf einfache Weise Mehrkomponenten- gemische untersucht werden konnen. Zu diesem Zweck wurde das oben genannte binare Gemisch durch Zugabe von Methanol zum ternCren Gemisch erweitert und in gleicher Weise untersucht. Aus diesem ternaren Gemisch werden drei binare Gemische erhalten, deren Dampfdruck-Diagramme in Abb. 3 dargestellt sind und von denen ein Stoffpaar negative und zwei Stoffpaare positive Abweichungen vom Raoultschen Gesetz zeigen.

Solche Dampfdruck-Diagramme werden auf einfache Weise erhalten, wenn die resultierende Peakflache wieder als Ma13 fur die Konzentration eines Stoffes in der Gasphdse gegen die bekannte Konzentration in der Losung aufgetragen wird. Im Gegensatz aber zum vorhergehenden Beispiel miissen bei

X A Z 1

Abb. 4 Gesaintdruck bei 50'C iiber dein ternlren Geinisch aus Methanol, Aceton und Chloroform. Der Gesaintdruck ist angegeben als Suinine der korrigierten Peakflachen ( Z F ) anstelle der Suinine der Partialdriicke. xA = Molenbruch von Aceton; xy = Molenbruch

von Methanol; xc = Molenbruch von Chloroform.

keiteii verschiedener Stoffe im GC-Detektor in Form von Korrekturfaktoren berucksichtigt werden. Da die Konzen- trationen hier als Molenbriiche angegeben werden, wird dieser Korrekturfaktor als sog. molarer Response-Faktor durch die Analyse einer Eichmischung nach bekanntem Verfahren bestimmt. Die korrigierten Fkchenwerte sind dann als Ma13 fur die Konzentrationen der verschiedenen Stoffe in der Cas- phase direkt miteinander vergleichbar. Da die korrigierte Fllche fur jede Komponente ihrem Partialdruck proportional ist, ergibt sich durch Addition der entsprechenden Flachen ein Flachenwert, der ebenso ein MaB fur den Gesamtdruck des Systems darstellt. Der Verlauf des Gesamtdrucks fur das hier untersuchte ternare Gemisch ist in Abb. 4 in raumlicher Darstellung gezeigt. Auf die Moglichkeit, die Flachenwerte direkt in Druckeinheiten umzurechnen, wurde bereits hinge- wiesen.

Experimentelle Bedingungen Die Untersuchungen wurden init folgenden Geraten von Perkin-

Eliner durchgefiihrt : Gas-Chromatograph F22/WLD; Saulenvor- druck 1.5 bar; halbautoinatisches Zubehor zur Dampfraumanalyse; Datensystem PEP-2. In die Probenflaschen von 6 in1 Inhalt wurde jeweils 1 inl der zu untersuchenden Mischung gegeben. Insgesaint wurden 69 Geinische unterschiedlicher Zusaininensetzung fur die Darstellung in Abb. 4 untersucht. Die Peakfliichen konnten init einer relativen Standardabweichung von 1 YO reproduziert werden.

Literatur [I] A. T. James und A. J . P. Martin, Biochem. J . 50, 679 (1952). [2] L. Breitenhuber und H . Binder, Mh. Chem. 100, 861 (1969). [3] L. Rohrschneider, Analyt. Chem. 45, 1241 (1973). [4] H . Hachenberg und A. P. Schmidt, Verfahrenstechnik 8. 343

(1974). [5] H . Hachenberg und A. P. Schmidt, Gas Chromatographic

Headspace Analysis, Heyden & Son Ltd., London-New York- Rheine 1977.

[6] B. Kolb. J. Chromatogr. 112, 287 (1975). [7] D. C. Legget, J . Chromatogr. 133, 83 (1977). [8] D. H. Jentzsch. H. Kriiger, G. Lebrecht, G. Dencks und J . Gut,

[9] B. Kolb, J. Chromatogr. 122, 553 (1976). Z. analyt. Chem. 236, 96 (1968).

E 3710

Rapid and Accurate Method for Determination of Vapour-Liquid Equilibrium M. Rogalski, K. Rybakiewicz, and S. Malanowski

Institute of Physical Chemistry of the Polish Academy of Sciences, Warszawa, Poland

Apparate und Methoden Losunyen 1 Phasengleichgewichte 1 Thermodynamik

1. Introduction Experimental determinations of the vapour-liquid equilib-

rium data consist in measuring temperature (T) , pressure ( P ) and the composition of the liquid (x) and vapour (y) phases

in the state of equilibrium. For the n-component mixture, using mole fractions as concentration units, it gives 2n independent determinations for each state examined. Due to the Gibbs-Duhem equation only three arbitrary chosen, from

M. Rogalski et al. : Method for Determination of Vapour-Liquid Equilibrium 1071 FJd. 81, Nr. 10 1977

the four above mentioned, parameters would be measured and the fourth one can be computed. In the case when all four types of parameters have been measured the thermodynamic consistency of the results can be checked additionally.

On the basis of the available in literature vapour-liquid equilibrium data it can be stated that the highest measuring accuracy is obtained by means ofa static method, i. e. a method in which the liquid and vapour phases are in the state of equilibrium and the boiling phenomenon does not occur. A long time necessary for equilibration, and expensive and complicated equipment are the disadvantages of this method. The apparatus used for measurements by dynamic methods, i.e. working in the stationary state of boiling under the pressure of an inert gas are considerably simpler, but ease and promptness of obtaining results are usually paid for by smaller accuracy. A thorough characteristics and classification of all methods is given by Hala and coworkers [I].

Measurement of T, P, x and calculation of y is usually an optimum procedure for a static method. As Swietoslawski ebulliometer [2] allows a very accurate measurement of boiling temperature as a function of pressure attempts to determine the same parameters by means of i t have been made [3] on the assumption that the composition of the liquid phase in the steady boiling state is equal within the experimental error to that of the sample prepared by weighing and introduced to the ebulliometer. Such assumption can be justified only for mixtures formed by components of which partial vapour pressures at the temperature of measurement differ only shightly, in another case errors arise from systematic deviations of the liquid phase composition, and its fluctuations caused by the apparatus work. The aim of the present paper is to present the procedure and apparatus which allows prompt acquisition of measurements results.

2. Apparatus

The proposed apparatus beeing a modification of Swietoslawski ebulliometer is shown in Fig. 1. It is a circulating still with a contin- uous circulation of both - liquid as well as vapour - phases.

A steady state corresponding to the thermodynamic equilibrium is established on the outside walls of thermometer well (T) contin- uously heated by a liquid and vapour stream delivered by Cottrell pump (H). Expansion occurring in the equilibrium chamber (E) and disturbances caused by the impact against the thermometer well result in establishing the equilibrium temperature in the well. Apart from the hydrodynamic conditions the amount of heat supplied by the heater of the Cottrell pump H is most revelant for the proper work of the apparatus. The interval of the supplied amount of heat corresponding to the correct steady work of ebul- liometer is fairly large. When the sample investigated consist of a pure substance nothing but a change of the intensity of stream flowing through the equilibrium chamber and a change in the ratio of the amount of substance of vapour to the amount of sub- stance of liquid (f = V / L ) in this stream accompany changes of the amount of heat delivered to the ebulliometer. The temperature remains constant over the whole range of the proper work and its change denotes that the apparatus is working outside the steady state.

In the case when mixtures are examined a different equilibrium temperature corresponds to each value of the f ratio in the equilib- rium chamber (Fig. 2) and the temperature measured depends on the amount of heat delivered by the heater H.

0 2 4 5 c m u

Fig. 1 Ebulliometer for determining the liquid-vapour equilibrium.

A, B: mixing devices; E: equilibrium chamber; H : Cottrell pump; J : Vacuum jacket; K : drop counter; T: thermometer well

Fig. 2 Dependence of the equilibrium temperature in the ebulliometer, filled with the binary mixture, on the value of the vapour to liquid ratio ( f ) and on the amount of drops D of the condensate flowing

through the ebulliometer drop counter

The devices (A and B, Fig. 1) for uniform mixing of the liquid flowing down from the equilibrium chamber (E) with the vapour condensate stream flowing from the condenser have been additional- ly introduced. Given in Fig. 3 are the results of the boiling temper- ature of a constant composition sample measured in an ebulliometer equipped with mixing devices A, B and without them. It is visible that mixing diminishes considerably the temperature osciljations caused by not uniform composition of the stream delivered by

Berichtr dcr Riinren-Cirlcll.rch:lll 1072 M. Rogalski et al.: Method for Determination of Vapour-Liquid Equilibrium

Cottrell pump to the equilibrium chamber. A continuous tem- perature measurement provides the value of the variance for each particular temperature determined. This information is especially useful for mathematical treatment of data because for mixtures of components considerably differing in vapour pressures the oscil- lation amplitude depends on mixture composition.

I +7

116,570 - -~ -l-2-r-- 115'580 I A t -. 3... ,. -t*#*e..s 115,550 * S d - d ~ * - __ _ _ .... te

116,550

mi 3; r Fig. 3

Fluctuations of temperature T in the equilibrium chamber of the ebulliometer as a function of time. I: ebulliometer without mixing; 11: ebulliometer with mixing devices unifying the flow of the liquid

and of the vapour phase condensate

The value of temperature error obtained is a sum of errors of temperature measuring device and the errors of the ebulliometer work (heat losses, overheating, fluctuations in liquid composition, inaccuracy of the manostat used). Accurate measurements of the boiling temperature 01' water over the range of 6 - 100 kPa have been performed in order to determine the order of errors which do not result from the composition fluctuations. The results obtained were smoothed by means of the Antoine equation. The value of the standard pressure deviation was 2.7 Pa which corresponds, for the pressure under which measurements presented in Fig. 3 were performed. to the error of temperature determination of about 0,001 K. By comparing this value with confidence limits given in Fig. 3 it can be stated that the error resulting from fluctuations of the phase composition is about five times bigger that the sum of the remaining errors.

3. Method

The ebulliometer is filled with a known mass of substance A and put into operation. After the steady state has been established measurement of P and T is performed. This can be done under various pressures. Then, without interruption in boiling a known mass of component B is introduced and the values of P and T are determined after the steady state has been established, and so on. The methods of working with ebulliometers have been discussed in detail [4,5]. The time necessary to establish the steady state after the introduction of a new sample without the interruption of boiling does not exceed 10-15 minutes.

For one mole of the sample boiling in ebulliometer the Equation (1) is satisfied.

V + L = l (1)

where: V , L are amounts of substance of the vapour and liquid

For each component i of this sample the following equation is

phases, respectively.

satisfied:

qa = v .y i + L ' X i (2)

where: qi is the mole fraction of component i in the sample; y i , x i are mole fractions of component i in liquid and vapour phases, respectively.

Designating f = V / L we obtain from Equations (1) and (2):

( 3 )

Equation (3) allows, by means of an iterative method, starting from yi values calculated for x i = q, values, computation of the com- position of liquid phase boiling in the ebulliometer for which the ratio f is known. The value of f depends on the construction of ebulliometer, amount of heat supplied to the Cottrell pump, and heat losses.

It is convenient to adopt as a measure off' the number of vapour condensate d r o p (D) flowing through the drop counter K (Fig. 1) in a unit of time.

lt is necessary prior to measurements to determine the range of the proper work of ebulliometer in terms of D for all components of the mixture examined. The range in which for a pure substance the measured value of T is, within the limits of experimental error, independent from D is assumed to be the proper one. Further measurements for mixtures are performed at such constant value of D which is within the limit of D for all pure substances forming the mixture examined.

In order to determine the numerical value off ' two independent methods were proposed. The first one by performing measurements for a pure substance in an ebulliometer modified to a flow apparatus with separate collecting of liquid and condensed vapour streams leaving the apparatus [6]. Consequently the f ratio can be deter- mined. The method does not yield good results oving to the change of the hydrodynamic conditions in comparison to the normal ebulliometer. The second one makes use of an ebulliometer enabling sampiing the liquid and condensed vapour phases [S,S]. This gives proper results, but due to the lack of uniform mixing of sampled liquids rather scattered.

In view of these facts a comparative method is proposed. The x , P , 7 data are determined in the ebulliometer for a known from literature, thermodynamically consistent and well measured system. The literature x ,y ,T ,P data are reduced and the type of Gibbs Excess Energy equation and the number of adjustable parameters giving the best representation chosen. Then, by the use of the chosen equation own x , T , P data are reduced with the simultaneous adjusl.ment of the f value by trial and error method, so that the values of adjustable parameters are closest to those obtained for literature data. 1 t =65"C Chlorobenzene n-hexane

LOO i-

Fig. 4 The Ciibbs Excess Energy (GE) of the chlorobenzene-hexane system

at 65°C as a function of the liquid phase composition. 0 : Brown data [7]. Experimental ebulliometric data: 0: not corrected for the actual composition of liquid phase; 0: corrected (f = 0.1 1).

H. Lentz: Ein Mischungskalorimeter fur hohe Driicke 1073 Bd. 81, Nr. 10 1977

Table Calculation of the ratio f = V / L for the ebulliometer

(chlorobenzene-hexane system, isotherm 65 "C)

Constants of the Redlich-Kister equation in. lo5 u . 10'

f (1) (2) (3) Eq. (4) Eq. ( 5 )

Ebulliometric 0.00 0.2457 -0.2071 -0.1618 620 970 0.11 0.5739 -0.0252 -0.0408 134 144

Brown 171 0.00 0.5768 -0.0275 -0.0250 258 357

An example of the results for the chlorobenzene-hexane system is given in Fig. 4 and in the table. The system was choosen oving to a very large difference (70 K) in boiling temperatures. The objective function was the difference between the calculated and experimental values of pressure. The mean deviation (m) and root mean deviation (u) ofpressure were calculated according to formulae:

(4)

The agreement of Excess Gibbs Energy against composition data determined by the proposed ebulliometric method and by Brown [7] is excellent. So are the values of Redlich-Kister equation con- stants calculated from both sets of data.

It is also visible from the m and u values in the table that the data obtained by the ebulliometric method are characterized by smaller scatter of results, that the Brown isothermal data used for adjustment of the value off. As follows from Fig. 4 f is independent from the mixture composition which proves the assumptions of the proposed method. As was stated previously f is dependent on temperature and it was proved experimentally on the basis of the isobaric hexane-chlorobenzene [7] data that it raises with tem- perature. The temperature coefficient is 0.OOljK.

Shown in Fig. 5 is the dependence of the value off on the number of drops D counted at the drop counter K in one minute determined by means of flow ebulliometer [6] for pure benzene. The obtained values o f f are considerably lower due to the above mentioned reasons. However, the linear dependence of the value of f ratio on the number of drops per minute at the drop counter K over the range corresponding t o the steady state work of ebulliometer can be clearly seen. This justifies the use of this parameter as a measure of the f value.

40 80 120 160 200 /E311715/ D

Fig. 5 Dependence of the ratio (f) - the number of moles of the vapour phase to that of the liquid phase as a function of the condensate flow ( D ) through the dropper of the ebulliometer (drops/min).

4. Conclusions Ebulliometer is a very convenient device for determining

the vapour-liquid equilibrium. As the assumption that the composition of the liquid phase is identical with the com- position of the whole sample introduced to the apparatus is acceptable only for close boiling mixtures, a procedure for determining the true liquid composition is established. In the case of mixtures of components differing considerably in boiling temperatures a correction for the vapour to liquid ratio f = 0.11 should be introduced for approximate meas- urements. In the case of accurate measurements it is necessary to use one of the described methods for determination of exact values of 1:

References

[ l ] E. Hala, J. Pick, V. Fried, and 0. Vilim, Vapour-Liquid Equi-

[2] W. Swietoslawski, Ebulliometric Measurements, Reinhold,

[3] H. W. Prengle and G. F. Palm, Ind. Engng. Chem. 49, 1769

[4] W. Swietoslawski, Azeotropy and Polyazeotropy, Pergamon

[5] S. Malanowski, Rownowaga ciecz-para, PWN, Warszawa 1974. [6] W. Swietoslawski, Roczniki Chem. 9, 266 (1929). [7] 1. Brown, Austral. J. sci. Res. A S , 530 (1952). [8] W. Swietoslawski, K. Zieborak, and W. Brzostowski, Bull. Acad.

librium, Pergamon Press, Oxford 1967.

New York 1945.

(1957).

Press, Warszawa 1964.

Polon. Sci. CI 111 5 , 305 (1957).

E 3117

Ein Mischungskalorimeter fur hohe Drucke H. Lentz

Institut fur Physikalische Chemie und Elektrochemie, Universitlt Karlsruhe, KaiserstraBe 12, 7500 Karlsruhe

Hohe Driicke I Kalorimetrie I Mischungswarmen 1 Thermodynamik 1 Wasser-Methanol In einem Autoklaven aus hochwarmfestem Stahl werden komprimierte, durch Quecksilber voneinander getrennte Flussigkerten gemischt und die Temperaturveranderung des Stahlblocks gegen einen Referenzwert registriert. Durch eine elektrische Widerstandsheizung im Innern des Autoklaven laDt sich eine Temperaturerhohung durch definierte Energiezufuhr erzeugen und so das Kalorimeter eichen. Die Messungen konnen bei konstantem Druck oder konstantem Volumen ausgefuhrt werden. Fur Mischungen aus Wasser-Methanol wurden bei 23 "C und Driicken von 500 und 1000 bar die Mischungswarmen bestimmt. Fur 15 Mol.% CH30H wurden die Messungen auf 2000 bar

ausgedehnt.