Prediction of latent heat of vaporization of multicomponent mixtures

131

Fluid Phase Equilibria, 8 ( 1982) 13 I - 147 Elsevier Scientific Publishing Company, Amsterdam-Printed

in The Netherlands

PREDICIION OF LATENT HEAT OF VAPORIZATION MULTICOMPONENT MIXTURES

ABRAHAM

TAMIR

Departmenr (Recieved

OF

of Chemical Engineering, July ZOth, 1981; accepted

Ben Gurion University of the Negev, Beer Sheva (Israel) in revised form November

4th, 1981)

ABSTRACT Tamir, A., 1982. Prediction of latent heat of vaporization Phase Equilibria, 8: 13 1- 147.

of multicomponent

mixtures.

Fluid

A very simple method has been developed for predicting the differential latent heat of vaporization involved in vapor-liquid equilibria of multicomponent mixtures. The technique uses the UNIFAC method for predicting activity coefficients. In order to establish this method, 88 binary systems and 13 ternary systems, both nonazeotropic and azeotropic, were tested successfully. On the basis of the IO1 systems investigated, the mean overall deviation between the observed and predicted values was found to be 4.6%. Despite the fact that the majority of the systems tested were azeotropic, a consequence of the small amount of data available for the differential heats of nonazeotropic systems, the method proposed is equally applicable to nonaxeotropic systems. For azeotropic mixtures, it is possible to predict the latent heat (integral or differential) by means of an analytical equation which involves only the parameters of Antoine’s equation, with a mean overall deviation of 6.1%. From the differential heats obtained by the proposed method, it is possible to calculate integral heats by applying equations derived here which relate these quantities.

INTRODUCTION

The objective of the present work was to apply the UNIFAC method (Fredenslund et al., 1977), so far used only for calculations of vapor-liquid equilibria and the design of distillation columns, for predicting differential latent heats of vaporization of mixtures. Mathematical relations have also been derived between the integral and differential heats which make it possible to calculate integral heats from the predicted differential heats obtained by the proposed method. The author (Tamir et al., 1983) recently gathered information from Chemical Abstracts indicating that - 97% of the data available for latent 0378-3812/82/000&0000/%02.75

0 1982 Elsevier Scientific

Publishing

Company

132 heats of vaporization corresponds to pure substances and - 3% to binary mixtures and systems with more components. In addition, most of the data corresponding to the 3% are integral heats and the rest, needed in the present work, are differential heats. The experience accumulated in our laboratory in measuring latent heats of vaporization for single components and for mixtures (either from calorimetric or total-pressure measurements) indicates that this is not an easy task and that the amount of work required to cover satisfactorily the entire concentration ranges of a multicomponent mixture is substantial. The major conclusion drawn from the above facts is that the development of a means for predicting the latent heat of vaporization of a mixture from data for the pure components of the mixture, including factors which take into account the nonideality of the liquid mixture, is of the utmost importance. Attempts to predict heats of phase change for multicomponent mixtures were made by Tao ( 1968, 1969), Lee and Edmister (I 969), Manley and Swift (1972) and Edmister (1973). The first three investigations correspond to integral heats and the last to differential heats of phase change. The major drawback of these methods of prediction of integral heats is that they are restricted to isobaric conditions. On the other hand, the method suggested in the present paper is applicable for both isothermal and isobaric conditions. The starting point of the derivations is usually the Gibbs-Duhem equation. The application of the final equation-which is valid over the total temperature and pressure ranges-requires an equation of state and the vapor-liquid equilibria data, namely T-X-Y. The latter are not usually available for all compounds of practical use. On the other hand, the advantage of the UNIFAC method is the utilization of data for a restricted number of groups to obtain activity coefficients for systems for which no experimental data are available. The range of application of the UNIFAC method, and hence of the method proposed here, is for system pressures up to IO-15 atm. and for temperatures between 275 and 400 K. A prediction method by group contributions to vapor pressures and hence enthalpies of vaporization was recently suggested by Macknick and Prausnitz (1979). However, the method, applicable for heavy liquid hydrocarbons, is restricted to pure components. The application of the UNIFAC method for mixtures proposed in the present work requires the following statement to be made (to avoid criticism of its use for predicting differential latent heats): the latent heat comes from the temperature dependence of vapor pressure, which is in turn a function of the temperature dependence of the pure-component vapor pressure and of an activity coefficient. The purecomponent vapor pressure is often well known, but the latter term is not. The built-in temperature dependence of UNIFAC is only fair, because the parameters used in the UNIFAC system are arrived at by a method which

133 gives some kind of average over a composition and temperature range for some mixtures or range of mixtures. However, the reasons for using the UNIFAC method are the following: (1) the agreement obtained between experimental and predicted results was very good; (2) the error introduced by using the temperature-averaged activity coefficients calculated by UNIFAC is very. small and is in the range of the experimental error: this conclusion can be drawn by considering eqn. (12) where the partial heat of mixing, p = - RT’ a In y, /aT, is smaller by two orders of magnitude than the heat of vaporization li of the pure component i; (3) it is common practice to neglect the temperature dependence of the activity coefficients in isobaric vapor-liquid equilibria calculations. RELATIONS

BETWEEN

INTEGRAL

AND DIFFERENTIAL

LATENT

HEATS

The UNIFAC method is based on data gathered mainly from vapor-liquid equilibria experiments. Consequently, the method proposed here, which is based on UNIFAC, will inherently predict differential latent heats. However, integral heats are usually needed for practical purposes, and hence in this section relations are developed between integral and differential heats. The word “differential” indicates that the latent heat is associated with infinitely small changes of conditions and transfer of matter between phases, as opposed to integral latent heat for which the change is finite, and usually associated with total evaporation of a liquid phase. Although in the case of mixtures it is possible to distinguish among several kinds of latent heats, as suggested by Strickland-Constable (1951), the relevant one for the case under consideration is that based on the following equations derived by Malesinski (1965, p. 70) for (1) isobaric and (2) isothermal vapor-liquid equilibria: (EP/aT),=

(U/aT),=

i r,[E(l+fl(X,)],Ti i=l

r=l

f: X,[@“(r,)-II,‘(X,)]/Ti i=l

i=l

y.(cv-

E”)

(1)

Xi@‘-

y’)

(2)

Equations (1) and (2) are the Clausius-Clapeyron equations for multicomponent mixtures, and hence the numerators may be identified as the differential latent heats I, = f: i=l

yi[~yv(yi)-iq’(X,)]

(3)

134

1

__;____ Ia

TZ TV

---_---

T -- ----:---T'

Fig. 1. T-X, Y, H-X,Y heats.

diagrams and demonstration

of characteristic temperatures and latent

and I,=

i x,[F(yi)-F’(X,)] i=l

(4)

where I, is the differential heat of vaporization needed to transfer to the vapor phase one mole of mixture of composition y from an infinite liquid mixture of composition Xi, and I, is the heat emitted when one mole of mixture of composition Xi is condensed from an infinite vapor mixture of composition q. For binary mixtures it is possible to demonstrate the differential heats I,, I, and the integral heat L, on an enthalpy-composition diagram as shown in Fig. 1. This can be obtained by considering eqns. (3) and (4) and some geometrical properties of the partial properties. A useful equation often used for computing I, from measurements of total pressure versus temperature at constant composition may be obtained as follows. Assume that the equation of state of the vapor mixture is given by PV=

ZRT

Recalling I, = -RZ[d

(5) that V= Xyic” and that usually In P/d( l/T)]

6’ z+ r’, eqn. (1) yields

x

Equations (3) and (4) are not immediately applicable and in the following section working formulae are derived in terms of pure-component and heat of mixing data. Isothermal phase changes The molar partial enthalpies

of component

i in a multicomponent

mixture

135 are computed as p&(Y)

Xi) = H&- + /,;( aH;,‘W),

6%

(7)

=H,:T + ~~(all:/ap),~,dP+PH;.,(~) x dP + AH&( Xi)

(8)

In the present case, where UNIFAC is the basis for all predictions, the effect of pressure on enthalpy will be neglected. Hence, the above equations reduce to H&(Y)

=H;r

+zE;,,(E;)

R!,(XJ

=H,‘J- +aH’,,,(x,)

(9) (10)

Noting that lj, the molar heat of phase change of pure i, is given by the difference li=H;--H,’

(11)

substitution of eqns. (9) and (10) into (2) yields /VT= i Y[li,T-3.,(X,)] ,=I

(12)

+AHG(Y,)

The integral heat is generally defined as (13) or, similarly, replacing Xi by Yi. Substitution of eqns. (9) and (10) into (13)-noting that the partial enthalpy of the vapor in eqn. (9) is computed on the basis of the liquid composition X,-yields, for isothermal conditions, LVT= 5 Xi!,,,+AH;(Xi)-AH;(Xi)

(14)

i=l

A relation between the integral heat and the differential heat at constant temperature is obtained from eqns. (12)-( 14) as LVT~IvT.+

f: (Xi--

I=1

l$+&(~Xi)]

+AH;(Xj)

-AH;(Y)

(15)

Isobaric phase changes

The partial enthalpies are computed from the equations q.“,(Y)

= H;T + t?;(T-

R;,,(Xi)

= H& + c;,(T-q)

T.) +m;,T(q)

(16)

+ai,,(Xi)

(17)

136 where CYPi are mean values of cP, with respect to temperature, T is the boiling temperature of the multicomponent mixture at a total pressure P, and q is the boiling temperature of pure i at the same pressure P, as demonstrated in .Fig. 1 for binary mixtures. Substitution of eqns. (16) and (17) into (2) yields

(18)

+AH;(yi) The integral latent heat at constant partial enthalpies

pressure

is obtained

by means of the

~~T’(Xj)=~~~.TT’+~~(TY-Ti)+~~.T”(Xi)

(19)

R;‘,i( Xi) = H&I + c;,( T’ - 7;) -tm;,,~(

4)

(20)

where TV and T’ are shown in Fig. 1. Substitution of eqns. (19) and (20) into (13) yields L++Xi[Iiq,+~(T’-

q)-C;,(T’-

q)]

+AH;.(&)

-A&(q)

(21)

The relation between eqns. (18) and (21) as L,,=/,,+

i (&i=l

-Cb,T’]-

i

the integral

and differential

y)[li,T;-q(C;-C;)] r;[(~~-~~,)T-~i,=(X,)]

heats is obtained

from

+ i X&,T’ i= I

+AHT(&)

r=l

+H;(q)

-AH&(XJ

(22)

It should be emphasized that the equations developed previously can be considerably simplified by noting that the heat of mixing in the vapor phase, AH;(y), is usually small. It seldom amounts to 0.2% of the heat of phase change. In addition, the heat of mixing in the liquid phase, AHi( Xi), is two orders of magnitude smaller than the heat of phase change, and may also be ignored, as a first approximation. For azeotropic mixtures, Xi = q, TV= T’ = T and consequently, eqns. (15) and (22) give Jk, = L, and 4,

(23) = LJ

137 METHODS

FOR PREDICTION

OF LATENT

HEATS

Nonazeotropic and azeotropic mixtures The method suggested here is very simple and, as shown, gives results which are in good agreement with experimental observations. The basic information needed for the predictions is the following. (a) Activity coefficients of the components in the mixture; these are provided by the UNIFAC method (Fredenshmd et al., 1977). (b) Vapor pressures of the pure components as functions of temperature. Such information is easily available and is usually expressed by means of Antoine’s equation with an excellent goodness of fit to experimental data, usually of the order of 0.5%. Consequently, it seems that the dominant error in predicting I, by the proposed method stems from uncertainties in the UNIFAC method. The prediction of the latent heat of a mixture at a given temperature T and composition Xi is carried out as follows. By using subroutine UNIFA (Fredenslund et al., 1977, p. 231), it is possible to obtain the activity coefficients of each component in the mixture. The total pressure P above the mixture (assuming that fugacity can be replaced by pressure) is given by

i=l

where Pi0 is the vapor pressure equation

of pure i, which is given by the Antoine

log,oP,=A,-B,/(t+Ci)

(25)

By using subroutine UNIFA at several temperatures possible to obtain P versus T from eqn. (24). Four and four of AT = -0S’C were found sufficient to If it is assumed that the relation between P and Clausius-Clapeyron by

around the given T, it is intervals of AT= 0.5’C yield good results for I,. T is given according to

lnP=a+b/T

(26)

and recalling

that I, is given by eqn. (6), then the result is obtained

that

I, = -RZb

(27)

The parameters a and b are obtained by fitting the data to eqn. (26). Instead of fitting the P-T data to eqn. (26), it is possible to apply eqn. (6) as follows and eliminate the process of fitting: I, = -RZ

A In P/A(l/T)

It was found

that AT=

(28) *O.S’C

in the vicinity

of the desired

point

was

138 satisfactory. The choice between the above-mentioned procedures is a matter of convenience. Another we of predicting IV using UNIFAC is based on eqns. (12) or (.18). Since A@(Xi) is usually two orders of magnitude smaller than I,, AH;(y) and the sensible heat are also small in comparison to ii, so they can be ignored, and eqns. (12) and (18) read I, = i i=

xi;

(29)

I

Assuming that the latent heat Ii of pure component i is known or may be obtained from Antoine’s equation, I, is obtained for a mixture with given T and Xi by calculating yi by means of UNIFAC: hence q = yi xi Pi”/P

(30)

It should be noted that eqn. (29) gave results identical using the previous methods.

to those obtained

Azeotropic mixtures For such mixtures, from eqn. (24) it is possible to write d In P/dT=

i i=

[( Xiy,P,“/P)(d I

In P!/dT)]

+ i [( X,PF/P)(dy,/dT)] ,= I (31)

For an azeotropic mixture, y, PF/P = 1. Assuming that dv, /dT= 0 (which is strictly accurate for athermal solutions), it is possible to calculate I, from I, = ZRT’ d In P/dT as I, = ZRT’

i Xi(d In PF/dT) ;=,

Application I,=2.3026

(32)

of eqn. (25) .yields RT’Z

i

X,B,/(t+C,)’

(33)

i=l

The factor 2.3026 comes from Antoine’s equation, where the vapor pressure as a function of T is usually expressed as log,, Pf. In order to express I, in J kmol-’ the factor before T* (K) in eqn. (33) is equal to 0.019156. RESULTS

AND DISCUSSION

In order to explore the accuracy of the predicted latent heats of vaporization and to confirm the methods described above, a large number of binary

139 and ternary systems, both nonazeotropic and azeotropic, were tested. The majority of the systems tested were azeotropic, which is because only a small number of differential heats are available for nonazeotropic systems. However, despite this fact, the method proposed is equally applicable for nonazeotropic systems. The results are presented in Tables l-4. In all the computations, the compressibility factor’2 was taken as 1, namely, the vapor phase was assumed to behave as an ideal gas. The justification for this assumption is the very good agreement observed in Tables l-4 between the experimental results and the predictions based on Z = 1. An estimate of the error associated with this assumption can be made as follows. The critical pressures for the systems reported in this work vary between 35 and 75 atm. The UNIFAC method is applicable up to - 10 atm., and hence the reduced pressure varies between 0.01 and 0.03 at 1 atm. and between 0.1 and 0.3 at 10 atm. The reduced temperature for the various systems varies between 0.6 and 0.85. From compressibility charts it can be seen that at around atmospheric pressure Z = 1, and a value Z 1: 0.8 is reached at - 10 atm. Thus it may be concluded that for the systems considered here, the ideal-gas assumption is justified and the resulting error in predicting the latent heat is within experimental accuracy. At high pressures, the effect of Z might become appreciable, and it is recommended that Z is computed from Z = 1 + BP/RT; B is the second virial coefficient of the mixture, which can be estimated (Tsonopoulos, 1974) for a large number of compounds of practical importance. Table 5 shows typical changes of y, and P as functions of t( At = *0.5’C) in the vicinity of the point t = 76.85”C for the ternary system cyclohexane(l)-benzene(2)-isobutanol(3) with X, = 0.5 and X, = 0.42 which was explored by &vi~toslttwski and Zielenkiewicz (1958). The changes in y, are very small but the change of the total pressure P with T is sufficiently large to determine I, accurately. Table 1 corresponds to a homologous series of binary azeotropes: aromatic hydrocarbons-aliphatic alcohols and pyridine-n-paraffinic hydrocarbons. The data for the integral latent heats were obtained by means of a calorimeter. However, in this case, the integral heats are identical to the differential heats. Table2 corresponds to a random collection of binary azeotropic systems for which Tamir (1981) reported parameters for correlating data for total pressure and composition as functions of temperature. The correlating equation was In P = A, + B,T- ’ + C,T, and hence I, = - R( B, - C,T’), which was considered as the observed value and is denoted in Table 2 as I,,,,,. It should be noted that the goodness of fit of the P-T data by the above correlation is of the order of 0.5%. Table3 contains data obtained by Udovenko and Frid (1948a, b) for nonazeotropic systems. The observed latent heats were obtained via the Clausius-Clapeyron equation from isothermal measurements of P as a function of T. Table4

140 TABLE

1

between observed and calculated values of differential latent heats of vaporization of a homologous series of binary azeotropes (Swi@os&wski and Zielenkiewicz, 1958)

Comparison

System

I obmd. (J kmol-‘)

D% Eqn. (27) * Eqn. (33) * Ben-Yair (1980)

p-Xylene(l)-propanol(2) p-Xylene(l)-isobutanol(2) p-Xylene(l)-butanol(2) p-Xylene-(l)-hexanol(2) Toluene(l)-methanol(2) Toluene(l)-ethanol(2) Toluene(l)-isopropanol(2) Toluene(l)-propanol(2) Toluene(l)-isobutanol(2) Toluene(l)-butanol(2) Benzene(l)-methanol(2) Benzene(l)-ethanol(2) Benzene(l)-isopropanol(2) Benzene(l)-propanol(2) Benzene(l)-isobutanol(2) m-Xylene(l)-isobutanol(2) m-Xylene(l)isoamylalcohol(2) Pyridine(l)-heptane(2) Pyridine(l)-octane(2) Pyridine( I)-nonane(2)

0.08 0.17 0.32 0.87 0.25 0.32 0.48 0.495 0.55 0.68 0.609 0.676 0.666 0.83 1 0.907 0.145

368.98 380.18 389.2 411.49 335.92 349.6 354.6 365.08’ 372.64 378.2 330.62 340.3 344.42 349.4 352.35 380.9

44.3 46.5 48.6 42.0 34.6 37.2 44.7 37.4 39.9 34.2 33.6 34.3 33.5 31.9 30.1 46.8

3.1 4.8 11.9 7.6 -11.5 -5.0 10.7 -5.1 1.9 - 10.8 -3.0 -2.6 -7.2 -6.4 -9.2 5.0

1.8 20.9 10.7 4.4 -6.9 -5.4 12.0 6.3 15.7 - 12.9 -2.6 -2.5 -8.5 5.3 2.8 21.3

14.2 14.5

0.480 0.253 0.561 0.899

400.47 368.34 383.32 388.24

47.8 39.3 41.7 40.6

12.1 12.9 11.8 0.7

21.5 11.8 20.8 19.8

N.R. 17.2 15.9 12.2

D%=

7.2

10.8

9.6

18.7 7.1 N.R. ** 5.3 17.8 2.7 7.6 -6.2 N.R. 4.2 1.2 - 1.7 -5.9 N.R.

* Z=l. * * N.R. = not reported.

contains results for ternary azeotropic mixtures. Unfortunately, data for differential latent heats of nonazeotropic ternary mixtures were not available. The latent heats obtained by !&vi@oskwski and Zielenkiewicz (1961) correspond to the homologous series cyclohexane-benzene-aliphatic alcohol and were obtained by means of calorimetric measurements. The latent heats obtained by Licht and Denzler (1948) (Table4) were derived from parameters of P-T measurements whicli were fitted by an appropriate correlation. The data of Pawlak and Zielenkiewicz (1965) in this Table correspond to ternary saddle rue&ropes composed of pyridine, acetic acid and a successive

141

TABLE

2

Comparison between observed and calculated values of differential tion of binary azeotropic systems (Tamir, 1981)

latent heats of vaporiza-

System

D%

Iobad. (J kmol-‘)

XI

Eqn. (28) * Eqn. (33) * Tetrahydrofuran(

I)-water(a)

Water(l)-formic

acid(l)

Chloroform( I)-ethanol@) Acetone(l)-chloroform(2) 2,6-Dimethylpyridine(l)-phenol(l) 4-Methylpyridine(l)-phenol(2) Ethanol(l)-heptane(2) Hexane(l)-isopropanol(2) Isopropanol(l)-ethylacetate(2) Acetonitrile(l)-ethanol(2) Ethanol(l)1,4-dioxane(2) Water(I)- l+lioxane(l) Carbon tetracbloride(l)-propanol(2) Methyl ethyl ketone(l)-water(l)

Methanol(

I)-benzene(2)

Ethanol(l)-benzene(2) Water(l)-pyridine(2) Benzene(l)-isopropanol(2) Benzene(l)-propanol(2) Cyclohexane(l)-isopropanol(2) Ethanol(l)toluene(2) Water(l)-2-chloroethanol(2) 2,CDimethyl pentane(l)-benzen Ethanol( 1)-ethylacetate(2) Ethanol(l)-ethylacetate(2) ** Ethanol( I)-ethylacetate(2) ** Ethanol( l)-ethylacetate(2) ** Ethanol( I)-ethylacetate(2) **

*

Z=l.

** Licht and Denzler (1948).

le(2)

0.903 0.855 0.582 0.490 0.859 0.384 0.307 0.325 0.616 0.770 0.218 0.680 0.871 0.447 0.876 0.466 0.564 0.663 0.649 0.563 0.321 0.478 0.718 0.758 0.701 0.845 0.647 0.752 0.852 0.546 0.384 0.296 0.341 0.417 0.543

300 320 320 360 320 320 430 440 330 320 330 310 330 330 320 450 400 350 350 300 300 350 310 350 320 320 330 330 350 330 320 293.8 314.2 334 363.2

31.0 32. I 42.4 41.1 31.7 33.6 49.8 50.4 39.7 32.5 34.6 34.0 39.7 39.7 33.0 34.5 34.8 35.2 33.2 36.4 36.0 34.9 44.7 41.5 35.1 33.9 34.9 40.3 42.8 31.8 35.8 36.4 36.0 35.5 34.8

-7.0 -2.9 5.8 6.8 -3.7 5.3 6.2 6.2 3.8 -3.3 -4.4 -6.2 -3.0 -1.3 1.1 -0.7 - 1.5 -2.3 -4.0 -0.6 - 1.0 - 1.5 3.9 0.8 -5.3 -6.9 -1.6 0.1 0.9 -1.0 - 4.4 -4.2 -3.7 -3.9 -5.2

-8.1 - 3.7 5.0 7.3 -0.6 8.3 8.0 10.7 1.5 -5.5 -5.5 - 7.6 -2.5 1.8 - 1.8 - 2.0 -2.0 -2.6 -5.1 -0.3 -2.2 - 3.7 4.5 1.0 -4.3 -3.8 -3.7 0.1 1.2 - 1.9 -4.5 4.5 4.3 4.6 5.7

4%=

3.4

4.1

142

TABLE

3

Comparison between observed and calculated values of differential latent heats of vaporization of binary nonaseotropic mixtures (Udovenko and Frid, 1948a, b) System

x, (TKJ

Propanol(l)-isobutanol(2)

**

0.1

I obsd. (J kmol- ‘)

DI

48. I 47.0 46.2 53.7 47.9 46.7 55.4 50.9 49.1 35.6 35.8 36.0 36.9 37.6 39.2 35.5 36.5 41.1 35.2 36.1 42.2 34.8 35.5 40.9 42.4 41.0 40.1 41.4 41.2 42.2 32.2 33.3 39.1

2.6 1.3 0.3 5.4 1.2 1.1 6.7 4.6 3.9 4.3 0.7 -1.5 4.4 0.6 -0.03 2.5 0.9 1.9 2.7 2.2 5.4 2.4 4.3 7.2 1.9 - 1.8 -3.9 -3.7 -5.2 -5.4 2.1 -0.02 1.3

DX=

2.8

333.15

0.5

Propanol(l)-isoamylalcohol(2)

**

Isobutanol(l)-isoamyloalcohol(2)

**

Methanol(l)-dichloroethane(2)

Ethanol(l)-dichloroethane(2)

Propanol(

Isobutanol(

I)-dichloroethane(2)

I)-dichloroethane(2)

Isoamylalcohol(

I)-dichloroethane(2)

Ethanol(l)-water(Z)

Propanol(l)-water(2)

Ethanol(l)-chloroform(2)

* Z=l. ** Udovenko (1948b).

and Frid (1948a):

data

0.9 0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.7 0.9 0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.5 0.9 0.1 0.5 0.9

323.15

333.15

327.96

339.09

318.15

for the remaining

systems

Eqn. (28) *

from Udovenko

and Frid

* a b ’

Z=l. &vi@osIawski and Zielenkiewicz (1961). Licht and Denzler (1948). Pawlak and Zielenkiewicz (1965).

0.588 0.540 0.500 0.480 0.539 0.579 0.472 0.102 0.128 0.246 0.336 0.396 0.424

331.73 346.41 349.97 350.46 337.56 342.3 339.0 340.0 368.92 389.16 400.17 407.12 410.56

azeotropic

- 5.4 -2.6 -1.1 -1.7 -2.7 -5.5 -9.6 - 2.7 - 5.6 1.1 7.2 10.2 6.5 4.8

iFW=

Eqn. (28) *

DZ

33.9 32.8 31.8 31.4 35.0 35.7 36.2 35.6 32.3 36.8 40.4 42.0 39.8

‘)

of several ternary

I ob_ui. (J kmol-

latent heats of vaporization

0.108 0.280 0.420 0.480 0.228 0.113 0.273 0.641 0.05 0.166 0.312 0.430 0.482

X,

values of differential

Cyclohexane(l)-benzene(2)-ethanol(3) ’ Cyclohexane(l)-benzene(2)-propanol(3) ’ Cyclohexane(l)-benzene(2)-isobutanol(3) a Cyclohexane(l)-benzene(2)-butanol(3) ’ Benzene(l)-ethanol(2)-water(3) b Ethylacetate(ethanol(2)-water(3) b Trichloroethylene(l)-ethanol(2)-water(3) b Propanol( I)-benzene(2)-water(3) b Pyridin41)-acetic acid(2)-heptane(3) c Pyridine( 1)-acetic acid(2)-octane(3) ’ Pyridin41)-acetic acid(2)-nonane(3) c Pyridin41)-acetic acid(2)-decane(3) ’ Pyridine(l)-acetic acid(2)-undecane(3) ’

and calculated XI

between observed

System

Comparison

TABLE 4

3.5

-8.6 -2.6 -0.9 -1.0 4.9 4.5 8.1 1.9 0.6 0.8 4.9 1.2 -6.0

Eqn. (33) *

systems

144 TABLE 5 Changes of the activity coefficients calculated by UNIFAC and the total pressure P for the ternary system cyclohexaae(l)-benzene(2)-isobutanol(3) (kwi@oslawskiand Zielenkiewin, 1958)at X, =0.5 and X, =0.42 with temperature around T=76.85’C YI

Y2

Y3 km Hg)

k) 74.85 75.35 75.85 76.35 76.85 77.35 77.85 78.35 78.85

1.1274 1.1272 1.1270 1.1268 1.1266 1.1264 1.1262 1.1260 1.1258

I.1 156 1.1154 1.1152 1.1150 1.1148 1.1146 I.1144 1.1141 1.1139

3.8588 3.8522 3.8457 3.8391 3.8326 3.8262 3.8197 3.8133 3.8069

695.8 707.8 719.1 730.5 742.1 753.8 765.7 777.7 789.9

aliphatic hydrocarbon from the series n-heptane to n-undecane. Measurements of the latent heats were carried out using a calorimeter. The observed latent heats and deviations with respect to the calculated values, D% = 1Y Ld. - 4,. )/Lsd. Yare reported in the Tables. Table 1 contains values of D for three methods of predicting I,: (1) the UNIFAC method; (2) computations based on eqn. (33), which iS applicable for azeotropic mixtures; and (3) using values calculated by Ben-Yair (1980). In the latter method, Pi0 is predicted from group contributions, and deviations from observed values may exceed 10%. In the method suggested here, Pi0 is computed from Antoine’s equation, which yields extremely accurate values of Pp. Additional information needed in the method of Ben-Yair (1980) consists of values of y, obtained from UNIFAC. This step is equivalent to the present approach. On the basis of the values of the mean overall deviation D in Table 1, it may be concluded that the method suggested here is superior to that of Ben-Yair (1980). The reason for this is the additional error introduced in the latter calculations due to the need to predict Pi0 from group contribution. The present author thinks that prediction of e? is unnecessary, because reliable values can be obtained from Antoine’s equation for almost every component which is of practical use. It may also be concluded that eqn. (33) has the same capability to predict I, as the method of Ben-Yair (1980) but is simpler. Inspection of the remainder of the present Tables, namely, data for a total of 88 binary systems and 13 ternary systems, leads to the general conclusion that the method suggested here predicts quite accurately the differential

145 latent heat of multicomponent mixtures. The Antoine equation parameters needed in eqn. (33) were taken in the present work from Hirata et al. (1975) and Gmehling and Onken (1977). ACKNOWLEDGMENTS

Thanks are due to Moshe Golden, Drora Shmilovich, Yehudit Reizner and Osnat Ben-Yair for help in the numerical computations. Thanks are also due to Claudia Dragoescu, whose Master Th&is helped greatly in establishing the various equations for the latent heats reported here. LIST OF SYMBOLS

a, b Ai, B,, Ci C

G 0%

parameters in eqn. (26) parameters in Antoine’s equation, eqn. (25) number of components in mixture mean specific heat with respect to temperature of pure component relative deviation in percent from observed value, defined bY

1W Lsd.

- ‘& )/‘&,Ll.

mean overall deviation,

defined by (100/m)

$ 1Dil i=l to mixture com-

partial molar enthalpies corresponding positions q, Xi molar enthalpy of pure component partial molar enthalpies of mixing corresponding to mixture compositions y, Xi heats of mixing corresponding to mixture compositions q, xi

I L m

P

Pp

R V

v q t T T’

differential latent heat integral latent heat number of observations total pressure vapor pressure of pure component i universal gas constant molar volume of mixture molar volume of pure component i partial molar volume of component i in mixture temperature ( "C) temperature (K) or boiling temperature of multicomponent mixture corresponding to total pressure P bubble-point temperature (Fig. 1)

146 T xj, y;: Z Y,

boiling temperature of pure component i mole fractions in liquid and vapor phase respectively compressibility, eqn. (5) activity coefficient of component i

Subscripts C

talc. i i,T i,q. i,T’ i,TV obsd. V

VP VT T T’

condensation calculated component component component component component observed vaporization vaporization vaporization temperature temperature

i i i i i

at at at at

temperature temperature temperature temperature

at constant at constant T T’

T T, T’ TV

pressure temperature

Superscripts 1 V

liquid phase vapor phase

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