Activity Coefficients of Aromatic Solutes in Dilute Aqueous Solutions Constantine Tsonopoulos*l and John M. Prausnitz Department of Chemical Engineering, University of California, Berkeley, Calif. 94720
Activity coefficients of 147 aromatic solutes in dilute aqueous solutions have been calculated from solidliquid, liquid-iiquid, and vapor-liquid equilibrium data. Consideration is given to the effects of dissociation and hydrate formation. The calculation of activity coefficients from mutual solubility data is critically examined, especially through a comparison with vapor-liquid equilibrium data. The activity coefficients are correlated wiith the number of carbon atoms and the types of groups present in the aromatic compound; the group coritributions were found to b e generally additive. The resuits given in this work may b e useful for design of processes for water pollution abatement.
T h e thermodynamic .properties of dilute aqueous solutions are of interest in the design of processes for water pollution abatement. This work is concerned with the solubilities and activity coefficients of aromatic organic solutes in water in the temperature range 0-50°C. A rough correlation of solubilities, based on the number of atoms, structure, etc., of the solute, has been presented (Irmann, 1965). It is preferable, however, to correlate activity coefficients rather than solubilities, since the former depend only weakly on temperature and vary significantly less with solute structure and configuration. Further, the use of activity coefficients enables us to include in our correlat'ion experimental results determined from vapor-liquid aiid from liquid-liquid data. Finally, activity coefficients, rather than solubilities, are used in the design of separation processes such as extraction and adsorption. We first give the necessary equations for the calculation of activity coefficients from solid-liquid data in the absence of hydrate formation. .We also discuss the effects of electrolytic dissociation aiid (of hydrate formit'ion on the activit'y coefficients. Nest, we consider reduction of liquid-liquid and vapor-liquid data. Finally, we correlate empirically the activity coefficients of aromatic compounds in dilute aqueous solutions with t'he solute's molecular structure.
Since the two components are assumed to be completely immiscible in the solid phase fzS
=
fpure
(2)
zs
I n the liquid solution fz" = yzxzf2Q
where y 2 is t'he activity coefficient and x2 is the mole fraction of the solute in the solution; fLo is the fugacity of the solute a t the standard state. We take this to be the pure (subcooled) liquid solute a t the system temperature and pressure. Equations 1-3, with the hypothet,ical liquid as t,he st,andard state, give for the activit,y of the solute (4)
Both f s and f L are a t the system temperature and pressure. Equation 4 can be transformed into a more useful form, valid a t lorn pressures (Weimer and Prausnitz, 1965)
Solid-liquid Equilibria
Consider a two-component solid-liquid equilibrium. We are only interested in the activity coefficient of the solute (component 2 ) , which vie assume to be completely immiscible with the solvent (component 1) in the solid state. The equilibrium we are concerned with is therefore between the pure solid solute and i1;s solution in liquid 1, as represented by segments B C and DF in Figure 1. (Aqueous solutions of aromatic compounds almost always exhibit partial immiscibility in the liquid phase, as represented by CED in Figure 1; this is considered in a later section.) At equilibrium, the fugacity of the solute in the solid phase is equal to it's fugacity in the liquid solution
Present address, Esso Research & Engineering Co., Florham Park, N. J. 07932.
A f refers to the property change upon fusion, and At, refers to the property change upon trailsition in the solid phase; h and c, are the ent,halpy and the heat, capacity a t constant pressure, respectively. Tt, is the triple-point temperature, which is essenhlly equal to the normal melt.ing point, Tf, and T,, is the transition temperature. A single solid-phase transit,ion has been assumed in the derivation of eq 5 , b u t the equation can be readily extended if there are several transitions. The factor mult,iplying Afc, is small for T close to T,,, since the two terms in the last bracket,s have opposite signs and nearly cancel each ot,her. O n the other hand, when ( T f T ) / T = 1, the contribution of the Aft, term to the value of y z can become large. This increases the uncert'ainty in yz since Afc, is not known well and, contrary to assumption, may depend on temperature. Ind. Eng. Chem. Fundam., Vol. 10,
No. 4, 1971
593
electrolytes (with dissociation constants of the order of 10-lo mole/l.) dissociate extensively. For a dilute solution of a weak electrolyte i t can be shown
that (41 yz _ -
F
+ 4cz/K
-3-
0
SOL ID-LIOU ID EOUl L I B R I UM LIQUID-LIQUID EQUILIBRIUM
x2
Figure 1. Temperature-mole fraction diagram for a system with complete immiscibility in the solid and partial miscibility in the liquid phase
(7)
4~2/K
YO2
-
- 1)'
where YZ is the corrected activity coefficient and yoz is the activity coefficient neglecting dissociation; c2 is the molar concentration of the solute and K is the dissociation constant of the (1 : 1) electrolyte. (Equation 7 does not take account of dissociation of the solvent to give a common ion. For aqueous solutions of acids the common ion is H+, b u t water contributes only lo-' g of H+/l., which can be neglected.) Equation 7 is plotted in Figure 2. There are two limiting cases
as cz/K +0, as cz/K --ic m ,
Y L / Y O ~+cz/K YZ/YOZ+1
}
(8)
There is essentially no dissociation (y2/yo2 = 1.00) for = lo3, y2/yo2 = 0.97.) If we then let cz = mole/]. (or 22 = 1.8 X be the practical limit of infinite dilution, we conclude that for all solutes with K 5 lo-* mole/l. we can use eq 6 to calculate Y ~ ~ I I , the activity coefficient "at the practical limit of infinite dilution," Le., xz = Kortiim's (1961) compilation of dissociation constants of organic acids indicates that only the acids and the polynitrophenols have dissociation constants of the order of mole/l. or larger; picric acid has the largest K (0.2-0.6). For these substances, where dissociation is appreciable even at saturation, we calculate only Y Z a t saturation. To show that activity coefficients are more amenable to correlation than solubilities, consider results for anthracene and phenanthrene-which differ only in the arrangement of their condensed rings. This difference makes their melting points and their solubilities in water appreciably different; however, their activity coefficients are essentially the same.
cz/K 2 lo4. (When cs/K
VI 0: K
Subscript l 2
0.01
0.0I
0.I
c2/K
,
ACTIVITY COEFFICIENT M O L A R CONCENTRATION DISSOCIATION CONSTANT SUOt 4L0U~TSEO C 1 4 T E OSqLUT,E
1.0
I IO
Figure 2. Effect of dissocidtion on the activity coefficient of weak electrolytes (eq 7)
A good example of the cahtribution of the Arc, term to the value of y2 is provided by 4-chlorobenzoic acid. The normal melting point of 4-chlorobenzoic acid is 514°K and Afc,(Tf) is 26.9 cal/mole "K (Andrews, et al., 1926). This value is unreliable and most probably it is too high (Tsonopoulos, 1970). The value we have used for Arc, is 15 cal/mole "K. The three choices for Aft,, lead to the following results for log YZ a t 25°C Atc,(!!'f),
log
cal/mole "K
YZ(XZ)
at 25°C
0
15
26.9
2.71
3.29
3.79
Equation 5 gives the activity coefficient of the solute at 2 2 , its mole fraction a t saturation, which is usually of the order It is advantigeous, however, to correlate all of IO-* to activity coefficients a t some uniform composition, preferably at the limit of infinite dilution. to infinite Ordinarily, an extrapolation from xz dilution is a simple matter, as we can use the two-suffix Margules equation
where yz" is the activity cbefficient of the solute a t infinite dilution. Equation 6 gives the desired result if there is no dissociation. However, at sufficiently low concentrations even very weak 594
Ind. Eng. Chem. Fundom., Vol. 10, No. 4, 1971
ff,
Anthracene Phenanthrene
x z [at 25OC)
YZ(X21
7 . 5 8 X 10-9 1 31 X lo-'
1 814 X lo6 1 88 X lo6
O C
216 100
Phenanthrene is 20 times more soluble in water than anthracene, but the ratio of their activity coefficients is nearly unity. Similar conclusions are reached when we compare activity coefficients and solubilities in water of 3- and 4-chlorobenzoic acids. tr, 'C
3-Chlorobenzoic acid 4-Chlorobenzoic acid
55 141
xq (at
25'C)
4 . 5 8 X 10-6 8.35 X
7 2 (XPI
2.07 X lo3 1.97 X lo3
Because of their length, Tables I-VI will appear following these pages in the microfilm edition of this volume of the jobrnal. Single copies may be obtained from the Reprint Department, ACS Publications, 1155 Sixteenth St., N.W., Washington, D. C. 20036, by referring to author, title of article, volume, and page number. Remit check or money order for $7.00 for photocopy or $2.00 for microfiche. Table I gives melting temperatures and enthalpies of fusion for 181 aromatic compounds with t f >, 0°C. Table I1 gives transition temperatures and enthalpies of transition for the few cases where these have been measured. Table I11 gives available
data and estimates for Arc,; estimates are given only for those compounds with known tf, Afh, and solubility in water. The solubilities and activity coefficients of 81 solid aromatic compounds in dilute aqueous solutions are given in Table IV.
/
E ,--\ \
1
\ \ \
I
\
Solid-Liquid Equilibrium with Hydrate Formation
An addition compound (hydrate) usually makes its existence known through its effect on the T-xz diagram. Figure 3 shows such a diagram for a system that exhibits partial miscibility in the liquid. Segments BC and D F G refer to the solubility of the addition compound, and only G H refers to the solubility of the unassociated solute. The addition compound is taken to be stable a t its melting point, the temperature corresponding to point F. The composition a t F is xz = Y Z / ( Y I YZ), where ~1 is the number of moles of the solvent and v 2 is the number of moles of the solute in the addition compound; e.g., for C6H6OH.1j2H20, the mole fraction a t F is xz = 2/8. (Point F can be a metastable point, under GH, for less stable addition compounds.) Prigogine and Defay (1954) have considered the low-pressure equilibrium between an addition compound and a solution assuming that there is complete immiscibility in the solid phase and that the enthalpy of dissociation of the addition compound is equal to its enthalpy of fusion, Arb,,,, c. They obtain the relation
+
SOLID-LIPUID EPUlLlBRlUM LIQUID-LIPUID EQUILIBRIUM
Figure 3. Temperature-mole fraction diagram for a system with addition compound formation and two partially miscible liquid phases
l-
Equation 9 can be integrated if the composition dependence of the activity coefficitnt is known. For this dependence we use the van Laar equation
I
0
I
I
CA LC U L ATlON DATA OF BLANKSMA
/ 0.03 0.0 I 0.02
0
Figure 4.
x2
Temperature-mole fraction diagram for C6HsNH(NHz)*1/2H20 HzO;calculation with eq 13
where A and B are dimensionless parameters equal to In ylm and In y ~ ” respectively; , ylm is the activity coefficient of i a t infinite dilution. We modify this to the “practical” limit of infinite dilution (XZ G in order to avoid the effects of electrolytic dissociation. Equations 9 and 10 can be combined to give
+
With the given assumptions, we can int’egrate eq 11 between (Tin,x2J and (?“fin, zzfin)with the result (1 - X 2 f J (1 - X Z i J
t
which can be integrated between any two points on the solubility curve of the hydrate if A , B , and Afh,,,, are known as functions of temperature. We have few data for the enthalpy of fusion of the hydrates (at their melting point). I n the absence of such data, we assume that Ahpure c
=
YlAfhpure I
+
YZAfhpure
z
(12)
where Afhpure and Afihpure are the enthalpies of fusion of water and the aromatic compound, respectively. We further assume that the enthalpies of fusion are independent of temperature; therefore, in eq 12 we can substitute Afhpure (Tn) and Aihpure2(Tf2);Tfr is the normal melting point of component i. The temperature dependence of A and B is unknown, and therefore we assume that they are temperature independent. Generally, activity coefficients can be considered temperature independent only over narrow temperature range.
An example of the application of eq 13 in the determination of activity coefficients is given in Figure 4, where we have plotted T-xz data for the phenylhydrazine half-hydrate. (The data and the fit for the phenol half-hydrate are very similar.) Hydrate formation enhances significantly the value of y z d l l (Tsonopoulos, 1970). It is important, therefore, to know which aromatic compounds form hydrates, as well as the number of water molecules in the hydrate and the hydrate’s solubility in water. (Some known cases are listed in Table V together with the data necessary for the estimation of activity coefficients.) Tsonopoulos (1970) gives some qualitative criteria for hydrate formation. Ind. Eng. Chem. Fundam., Vol. 10, No. 4, 1971
595
I03
100
t
00
60
I
I
90
PHENOL(21
, O C
20
40
+ WATER
(1)
801 "BEST" L I N E THROUGH VAPOR-L IQUID' DATA
/
,'
/
/'
0
40
FROM LIQUID-LIQUID DATA I V A N L A A R EQUATION1
30
\
2 02.5
2.7
2.9
3.1
3.3
3.5
2
( I / T ) x l o 3 , OK-I Figure 5. The limiting activity coefficient of phenol in aqueous solution calculated from liquid-liquid and vaporliquid equilibrium data
Liquid-liquid Equilibrium
Most aromatic compounds, when mixed with water, form two part.ially miscible phases. Such solutions become homogeneous by raising the temperature to the solution's critical temperature (point E in Figures 1 and 3). These upper critical solution temperatures are in every case higher than t8hemaximum temperature of interest here, viz., 50°C. ?he composition of the two liquid phases a t equilibrium is given by xz'v (t'he mole fract,ion of 2 in the "water-rich" phase) and zlA (the mole fraction of 1 in the "aromatic-rich" phase) ; these mole fractions are called the mutual solubilities. Using the same standard states in both phases, the equations of equilibrium are Y I ( Z I ~ ) Z I=~ YI(ZI")ZI*
(144
yz(sz\v)zz"f = yZ(z2.4)zz*
(14b)
When xz* is nearly 1, eq 14b becomes
If xp* is not known, i t does not follow that me can assume t h a t yZ(z24)z24= 1, although this is a good assumption a t least for all aromatic hydrocarbons and their halogenated derivatives. (The solubility of water in all hydrocarbons a t 25°C is well under zl.4 = 0.01.) The activity coefficient a t nearly infinite dilution, y z d l 1 , can be determined using the two-suffix Nargules equation (16) (All systems in this section have dissociation coiistaiits less than lo-* mole/l.) For many systems z ~ A is substantially smaller than 1, and hence eq 15 is inapplicable. T o solve eq 14 for y2"f we need to assume some composition dependence for y1 and y2. If this compositioii dependence can be adequately represented by some two-parameter equation, then that equation and eq 14 constitute a readily solvable system of two equations with two unknon lis. 596
Ind. Eng. Chem. Fundam., Vol. 10, No. 4, 1971
Typical two-parameter equations for the composition dependence of y that can be used are the well known Margules, van Laar, and Scatchard-Hamer equat,ions. The relations giving the parameters in terms of the mutual solubilities have been reported by Carlson and Colburii (1942). All three of the above-mentioned equations have been examined by Brian (1965), who concludes that "the van Laar equations are generally far superior to the Margules and ScatchardHamer equations for predicting activity coefficients from liquid phase solubility limits alone." Three-parameter equations can be also used if the third parameter is independently set. The N R T L equation (Reiion and Prausnitz, 1968) has been used to predict activity coefficients from mut'ual solubility data (Renon and Prausnitz, 1969). The Wilson equation can be similarly applied t o partially miscible systems by introduciiig a third parameter (Wilson, 1964). The calculations with both of these equations are more tedious t,han those based on the two-parameter equat.ioris already mentioned. The serious drawback of the three-parameter equat,ions, however, is that t'he third parameter must be accurately known. Since the value of the third paramet,er frequently depends stroiigly on the nature of the system, it can be coiicluded that iii the absence of additional data, realistically only t,wvo-parameter equations can he used in the solution of eq 14. The van Laar equations for t,he activity coefficients are eq 10 and
A
The relations giving A and B in terms of the mutual solubilities are given by Carlsoii and Colburn (1942). Table V1 (deposited with t,he hCS hlicrofilm Depository Service) gives activity coefficient,s a t nearl! infinite dilution for 7 5 aromatic solutes in water. Vapor-liquid Equilibrium Data
The extrapolation from xz\v to very high dilutioii is arbitrary, unless it is done with an equation that is kriowii to fit t,he activity coefficieiit data for the system of interest. We c.an test the applicability of a given equation for a particular solut'ioii if \\-e have vapor-liquid d a h for this system over a substantial concentration range. We have such data for aqueous solutions of phenol (15-1OO0C), o-cresol (lOO"C), and aniline (40°, 99°C) Ext'eiisive vapor-liquid dat'a for aqueous solutions of phenol over the temperature range 15-100°C (Bogart and Brunjes, 1948; Brusset and GaynBs, 1953; Kliment, et al., 1964; Rlarkuzin, 1961; Schreinemakers, 1900; Schulek, et al., 1958; Weller, el al., 1963) have been used to calculate activity coefficients at, nearly infinite dilution; these are plotted us. l / T in Figure 5 . I n view of the large scatter, the best line through the experimental data is questionable. While it mag not be straight, there is no apparent, reason for the corner a t 41°C indicated by the activity coefficients calculated with the vaii Laar equations from mutual solubility data. Results obtained from the liquid- liquid data and the vaii Laar equation are unsatisfactory for t > 41°C. There is no evident, explanat'ion for the existence of t,he corner. The peculiar phenomenon is interesting, however, because it is probably related to the properties of the aqueous solutions of phenol and other compound,s. (A similar corner vas obt'ained using the three-parameter TTilson equation.) I n the present case I
we are more interested in knowing where the corner is, when t'here is one, siiice our analysis of the liquid- liquid equilibrium data becomes progressively poorer a t temperatures above the corner. I n the case of the phenol-water system, the corner in log y z d i l us. 1 / T occurs a t 41°C. As the melting point of pure phenol is 40.9"C, i t is enticing to generalize this fact and suggest t h a t the corner occurs a t a temperature equal to the normal melting point of the solute. The normal melting point of o-cresol, however, is 31.OoC. For this system, there is no sharp corner in the line representing the temperature dependence of log y 2 d i l ; inst'ead, there is a gradual bransition in the t'emperat'ure range 60-70°C. Further, in the o-cresolwater system t,here is good agreement between the activity coefficient's from vapor-liquid and liquid-liquid equilibria. The single vapor- liquid study for the o-cresol-water system (Brusset and GaynBs, 1953) gives a t 100°C a log y 2 d i l value only 1.5% smaller than t h a t calculated from liquid-liquid data. We may therefore expect t'hat the vaii Laar equat,ions are satisfactory for methylated phenols. Vapor-liquid equilibria for the aniline-water system have been investigated a t 40°C (Rock and Sieg, 1955) and 99°C (Horyna, 1959). The activity coefficients are plotted ill Figure 6. Activity coefficient.s from liquid-liquid equilibria are in good agreement with those from vapor-liquid equilibria u p to 5OoC, b u t above that temperature there is a sharI) decrease iii y z d " :is calculated from mutual solubility data. The aniline-water system t'hus behaves like the phenolwater system, b u t the coriier in the former case is a t a temperature much higher than the melting point. of aniline (-6.0°C). There is 110 correlat'ioii with the critical solution temperature, which is 66°C for phenol-water and 168"C for aniline- water. For the phenol-water syst'em we use t'he yZdll from vaporliquid equilibria; in all ot,her cases we use the results determined from liquid-liquid equilibria (Table VI).
8CJ
4o ~ ll0
6F
t 4CJ
I
2p
, O c
A N I L I N E ( 2 1 + WATER ( 1 )
20
r VAPOR-LIOUID
..*\!
/
DATA
LFROM LIOUID-LIOUID
4
DATA
EQUATION)
(VAN LAAR
i
601'
4 0 1 301 26
I
I 30 HITI
x lo3
,
38
3.4 OK-'
Figure 6. The limiting activity coefficient of aniline in aqueous solution calculated from liquid-liquid and vaporliquid equilibrium data
Correlation of Activity Coefficients at 25OC
-4 theoretically attractive correlation of solubilities, or activit'y coefficients, would make use of a model for the structure of water. Although many models have been proposed (Horne, 1968), no model has as yet explained a d e q u a t ~ l ythe behavior of eibhcr water. or aqueous solut'ions. Pierotti, et al. (1959)) have presented an extensive correlation of activity coefficients "at infinite dilution" v i t h molecular structure. Their equat'ions are particularly simple for homologous series in water. For the activity coefficients of normal alkylbeiizenes in water, a t 25OC, Pierotti gives
log yz"
=
3.554
+ 0.622(nc - 6) - 0.466/(nC- 4)
(18)
where yZ" is the activity coefficient of t.he alkylbeiizene in an infinitely dilute aqueous solut,ion, aiid n, is the total number of carbon atoms in t,he hydrocarbon. We propose equations similar to eq 18 for the various classes of aromatic hydrocarbons, while for their derivatives we propose correct'ioii fact,ors for each group present. The level of the act,ivity coefficients of aromatic compounds in "practically irifinit'ely dilute" aqueous solutions is generally very high (102-106). At such high levels, large per cent deviations in y2 are of litt,le practical significance (I'ierot,ti, et al., 1959). We are interested in large differences in 7 2 . The approximate nature of the group-coiit,ributioii scheme, therefore, is acceptable for our purposes. A. Hydrocarbons. Aromatic hydrocarboris are appreciably more soluble in water t h a n aliphat'ic hydrocarbons;
I 03
Figure 7. a t 25°C
a
IO 12 C A R B O N ATOMS
14
16
Activity coefficients of monocyclic hydrocarbons
for example, a t 25"C, t h e solubility of benzene is x2 = 4.02 X lop4,while t,he solubility of hexane is 5 2 = 3.8 X (Selson and de Ligny, 1968). This significant difference can be partly attributed to the smaller size of the benzene molecule, but it is primarily due to Iveak coniplex formation between water aiid benzene. 1. Monocyclic Hydrocarbons. The saturated alkyl chains produce an effect on y z d l l that can be correlated ivith t'he number of carbon atoms. The dat'a for benzene, toluene, et'hylbenzene, propylbenzene, and butylbenzene are accurately represented by log yidi'
=
3.3918
+ 0.58239(nc - 6 ) ;
0
R R
=
H or straight-chain paraffin
(19)
Equat.ion 19 and the corresponding experimental data are shown in Figure 7 . The average deviation in log yz for eq 19 is 0.026 and for eq 18 it' is 0.140. Ind. Eng. Chem. Fundarn., Vol. 10, No.
4, 1971 597
-
MONOCYCLIC HYDROCARBONS WITH STRAIGHT
The effect of unsaturation should decrease as the side chains get longer or more branched. 2. Polycyclic Hydrocarbons. The condensed polycyclic hydrocarbons (e.g., naphthalene and anthracene) have activity coefficients in aqueous solution t h a t are much lower t h a n those of t h e normal alkylbenzenes. Lowering of the activity coefficients results from smaller sizes of the polycyclic molecules and from stronger interaction of the condensed polycyclic hydrocarbons with water. The activity coefficients of benzene, naphthalene, acenaphthene, anthracene, and phenanthrene are accurately represented by
I I
--
-
log
yzd" =
3.3950
+ 0.35794(nc - 6); condensed polycyclic
-301 6
12
10
8
14
16
C A R B O N ATOMS
Figure 8. a t 25°C
Activity coefficients of polycyclic hydrocarbons
Equation 19 does not hold for the polymethylbenzenes (xylenes, mesitylene, durene, and pentamethylbenzene-the latter two, as well as hexamethylbenzene, are the only monocyclic aromatic hydrocarbons that are solid at 25OC). ,411 these compounds are more soluble in water than the corresponding ones a i t h the straight side chains because first, they are smaller in size or more spherical, and second, they interact more with water due to their stronger Lewis basicity. As a result, their activity coefficients are smaller, as indicated in Figure 7. For polymethylbenzenes log
yidl'
=
3.8227
+ 0.33044(nc - 6); 8
5 nc 5
12 (polymethylbenzenes)
(20)
Equations 19 and 20 give the upper and the lower limits, respectively, for the activity coefficients of the monocyclic hydrocarbons with saturated side chains. There are few data for arenes with branched side chains, but the effect on y z d " is not negligible. Although tertiary groups apparently have a somewhat larger effect than secondary groups, the scarcity of data forces us to consider together all compounds with branched chains log
yZdll =
3.2589
+ 0.53267(nC- 6 ) ;
no L 9; O
R
;R
=
branched-chain paraffin (21)
Equation 21 is given by the dotted line in Figure 7. The effect of unsaturation in the side chain is similar to that of branching: yzd" is towered. The molecule becomes more compact, and hence dissolves more easily, but also i t has a somewhat larger polarizability. I n the case of phenylacetylene we have some weak interaction between the 7r electrons of the triple bond and water, resulting in a further decrease of y z d l l , relative to t h a t of ethylbenzene. On the basis of limited data, the corrections to log y 8 " per unsaturated bond are double bond (=) in side chain: -0.30 triple bond (E) in side chain: -0.46 These rough estimates suggest that the lowering in log yzdl' per triple bond is one and a half times that per double bond. 598
Ind. Eng. Chem. Fundam., Vol. 10, No. 4, 1971
(22)
Equation 22 is plotted in Figure 8. Biphenyl and its derivatives differ significantly from the condensed polycyclic hydrocarbons; the former molecules are bigger, while their interactions with water are expected to be weaker. Their activity coefficients are therefore higher than those predicted by eq 22. The data plotted in Figure 8, however, indicate otherwise. We accept the experimental y z d l l value for biphenyl, but we seriously question the values for diphenylmethane and bibenzyl (1,Zdiphenylethane). For the latter solute y Z d l l is almost certainly in error since i t is lower than the activity coefficients of trans-stilbene (lJ2-diphenylethylene) and 1,ldiphenylethylene. The presence of the double bond in the diphenylethylenes should make their activity coefficients lower. B. Derivatives of Hydrocarbons. Substitution of a hydrogen atom with some other atom (or group of atoms) can produce compounds with significantly different solution properties. We have already established the dependence of t h e activity coefficients of hydrocarbons on the number of carbon atoms and molecular structure; we now relate the activity coefficients of the hydrocarbon derivatives to those calculated with eq 19-22. These equations, together with the appropriate corrections per substituted group, enable us to estimate the activity coefficients of a large variety of aromatic compounds in aqueous solution. We define a correction factor, A A
E
log
y2dil
(hydrocarbon derivative)
-
log y z d " (hydrocarbon with same ncand structure)
(23)
The activity coefficient of the hydrocarbon is calculated with the appropriate equation. For bipheng! we use the experimental y z d l l . There is often a substantial difference between ring and side-chain (or a) substitution. Unless otherwise noted, the A values given are for ring substitution. The significant results of the analysis of the yzdl' data (Tsonopoulos, 1970) are listed in Table VII. The results for ethers, aldehydes, phenones and quinones (Tsonopoulos, 1970) are too few and too inconsistent to allow any generalization. The correction factors are to a satisfactory degree additive, as the examples in Table VI11 indicate. The calculated values in Table VI11 have been determined with eq 19 and the data in Table VII. The difference between ring and chain substitution in the carboxylic acids (Table VII) is surprisingly large, but it has a plausible explanation. il carboxyl group and a benzene ring some distance apart should act independently. We would expect the effects of the aromatic ring and the carboxyl group to be nearly additive. On the other hand,
when the carboxyl group is directly attached to the aromatic ring, there is interference and the compound is less soluble than we would predict from the independent presence of the aromatic ring and the carboxyl group. Appreciable dissociation of the Carboxylic acids a t saturation makes necessary, for reasons discussed in an earlier section, the use of activity coefficients a t saturation. (The solubility of aromatic carboxylic acids in water is of the order of mole/]. or less.) Dissociation is probably the cause for the breakdown of the additivity assumption for the polyfunctional acids (Tsonopoulos, 1970). The activity coefficients of carboxylic acid esters in aqueous solution are predicted well, if we relate them to the activity coefficients of the aromatic acids. ?he difference is due to the substitution of the carboxyl H with an alkyl group (R); it is given by log rzdi1(ArCOOR) - log rzdll(ArCOOH)G 0.7n,R
(24)
where n o R is the number of carbon atoms in R, Equation 24 is applicable for COOR either on the ring or in the side chain, which suggests that only C=O from the carboxylic group interferes with the aromatic ring. The three values given for the correction factor due to NO2 indicate interference between NO2 and N H z and, to a lesser extent, between NOz and OH. Further, when NO2 is ortho to OH or to NHz we have strong intramolecular hydrogen bonding. Hence these groups are unavailabIe for intermolecular hydrogen bonding with water. This makes the activity coefficients of the ortho compounds in water considerably larger than those of the para and meta isomers. Temperature Dependence of Activity Coefficients
There are insufficient data to establish reliably the temperature dependence of the activity coefficient of aromatic compounds in dilute aqueous solutions. The temperature range of this investigation (0-50°C) is narrow and there appears to be a small overall variation of y Z d l i with temperature. The solubilities of the solid compounds increase with temperature, but the activity coefficients tend to show a weak maximum. Certainly they vary a lot less between 0” and 50” C than do the corresponding solubilities. The solubilities of benzene and other alkylbenzenes in water go through a minimum a t about 18°C (Arnold, et al., 1958; Bohon and Claussen, 1951; Franks, et al., 1963). This minimum is characteristic of mononuclear aromatic compounds (Franks, et al., 1963). The maximum in the activity coefficients a t the same temperature makes the activity coefficients temperature-insensitive in the range 10-25°C. To a good approximation it is possible to use the activity coefficients a t 25°C between 0 and 35°C. Perhaps a better approximation is to use temperature-independent A’s together with the activity coefficient of benzene as a function of temperature. RIost of the data that could be used to determine the temperature dependence of the A’s for some groups (e.g., OH, NHZ) come from the analysis of mutual solubility data with the van Laar equation. As shown in a previous section, such activity coefficient data are frequently suspect, and therefore their temperature dependence is unreliable. Conclusions
Activity coefficients of aromatic compounds in dilute aqueous solut,ions were calculated from solid-liquid, liquid-
Table V I . Correction Factors for log * / p per Group A
Group
1. F
0.14 0.70 0.92 1.40
c1
Br
I 2. OH (alcohols) (phenols) 3. COOH (in side chain) (on ring) 4. NHz 5. NO2 (hydrocarbons) (m-,p-phenols) (m-,p-anilines)
-1.9 -1.7 -1.7 -0.7 -1.35 0.15 0.3 1.0
Table VIII. Activity Coefficients of Aromatic Compounds in Dilute Aqueous Solutions at 2 5 ° C Exptl
Dichlorobenzenes 1,4-Dibrornobenzene 1,4-Diiodobenzene Chlorophenols 4-Chloroaniline Dinitrobenzenes 2,4,6-Trinitrotoluene Picric acid (2,4,6-trinitrophenol) Chloronitrobenzenes
4.75-4.82 5.24 6.22 2.24-2.27 2.94 3.38-3.94 4.36
Calcda
4.79 5.23 6 19 2.40 0.10 2.80 f 0.10 3.70 0.10 4.43 f 0 . 1 5
* *
*
2.20 i 0 . 0 2 2 15 0 . 2 5 4.14-4.25 4 24 1 0 . 0 5 4-Chloro-1,3-dinitrobenzene (4.44)b (4.33 + 0 10) a With eq 19 and the data in Table VII. b Values in parentheses are a t 50°C. The experimental ydl’of benzene in water at 5OoC was used in place of eq 19.
liquid, and in a few cases vapor-liquid equilibrium data. The effects of electrolytic dissociation and hydrate formation on y z d i l were determined qualitatively. The analysis of liquidliquid solubility data with the van Laar equations appears to be satisfactory but not highly accurate. Activity coefficients a t 25°C are given by eq 19-22 together with the appropriate correction factors (Table VII). The correction factors are additive, with two exceptions: substituted acids and compounds forming strong intramolecular hydrogen bonds. Variation of activity coefficients with temperature in the range 0-50°C is small and, to a first approximation, can be neglected. Acknowledgment
The authors are grateful to John Newman for his help with the problem of electrolytic dissociation and to the Kational Science Foundation and to the donors of the Petroleum Research Fund for financial support. literature Cited
Andrews. D. H.. Lvnn. G.. Johnston, J.. J. Amer. Chem. SOC.48, 1274 (1926). Arnold, D. S., Plank, C. A., Erikson, E. E., Picke, F. P., Chem. Eng. Data Ser. 3, 253 (1958). Bogart, M. J. P., Brunjes, A. S., Chem. Eng. Progr. 44,95 (1948). ,
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Bohon, R. L., Claussen, W. F., J . Amer. Chem. SOC.73, 1571 (1951). Brian, P. L. T., IND. ENG.CHEM.,FUNDAM. 4, 100 (1965). Brusset, H., Gaynhs, J., C. R. Acad. Sci., 236, 1563 (1953). Carlson, H. C., Colburn, A. P., Ind. Eng. Chem. 34, 581 (1942). Franks, F., Gent, M., Johnson, H. H., J . Chem. SOC.2716 (1963). Horne, R. A,, “The Structure of Water and Aqueous Solutions,” in LLSurvey of Progress in Chemistry,” A. F. Scott, Ed., Vol. 4, Academic Press, New York, N. Y., 1968. Horyna, J., Collect. Czech. Chem. Commun. 24, 3253 (1959). Trmann. 37. 789 (196.5). . , F.. _ _Chem.-Tno.-Tech. , _ ... -.. = Kliment, V., Fried, V., Pick, J.,’Coilect. Czech. Chem. Commun. 29,2008 (1964). Kortum, G., Vogel, W., Andrussow, K., “Dissociation Constants of Organic Acids in Aqueous Solution,” Butterworths, London, 1961. Markuzin, N. P., J . Appl. Chem. USSR 34, 1121 (1961). Nelson, H. D., de Ligny, C. L., Red. Trav. Chim. Pays-Bas 87, 528 (1968). Pierotti, G. J., Deal, C. H., Derr, E. L., Ind. Eng. Chem. 51, 95 (1959). ~~~
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Prigogine, I., Defay, R., “ChemicalThermodynamics,” translated by D. H. Everett, Chapter 23, Wiley, New York, N. Y., 1954. Renon, €Prausnitz, I., J. M., A.I.Ch.E. J . 14, 135 (1968). Renon, H., Prausnitz, J. M., Ind. Eng. Chem., Process Des. Develop. 8, 413 (1969). Rock, H., Sieg, L., 2. Phys. Chem. (Frankjurt am Main) 3, 355 (1955). Schreinemakers, F. A. H., Z. Phys. Chem. 35, 458 (1900). Schulek, E., Pungor, E., Trompler, J., Mikrochim. Acta 52 (1958). Tsonopoulos, C., Ph.D. Dissertation, University of California, Berkelev. 1970. .~ .~.~. Weimer, R.’F:, Prausnitz, J. M., J . Chem. Phys. 42, 3643 (1965). Weller, R., Schuberth, H., Leibnitz, E., J . Prukt. Chem. (4) 21, 234 (1963). Wilson, G. M., J . Amer. Chem. SOC.86, 127 (1964).
RECEIVED for review December 18, 1970 ACCEPTED June 7, 1971
Determination of the Thermodynamic Contribution to the Diffusion Coefficient Matrix of a Ternary Liquid System John P. Lenczyk and Harry T. Cullinan, Jr.” Department of Chemical Engineering, State University of New Yorlc at Buffalo,Bu$alo, N . Y . 14214
An experimental technique for the direct determination of the chemical potential composition derivatives of a ternary liquid system is described. The results of equilibrium sedimentation experiments conducted on an ultracentrifuge are reported for the system acetone-benzene-carbon tetrachloride. Equilibrium composition distributions, obtained from 1 3 separate initial ternary compositions, are used to determine the ternary interaction parameters of the four-suffix Scatchard equations. Consistency is confirmed by back-calculation of the individual distributions. The experimental values of the chemical potential composition derivatives are compared to the predictions of the Wilson equation which requires no ternary parameters. The resuits indicate that the values of the chemical potential composition derivatives obtained from the Wilson equation are in close agreement with those obtained from the Scatchard equation with the experimentally determined interaction parameters.
w h e n a homogeneous single-phase mixture is subjected to a field of force, a distribution of concentrations sets in by reason of the differences among the sedimenting forces acting on the various species. The concentration gradients, as they are established, cause purely diffusive flows, and the process of redistribution continues until a balance is attained between the sedimenting forces and the diffusion forces. This balance corresponds to a state of true thermodynamic equilibrium. The diffusive fluxes are generally coupled so t h a t the rate at which a given constituent approaches its equilibrium distribution depends on the instantaneous distribution of all species present. At equilibrium the distribution of the individual components is still coupled through the solution thermodynamics because the chemical potential of a given 600
Ind. Eng. Chem. Fundom., Vof. 10, No. 4, 1971
species depends on all of the component concentrations. The theory of sedimentation is well developed (Fujita, 1962). Recently it has been suggested (Cullinan, 1968) and demonstrated for a binary system (Cullinan and Lenceyk, 1969) that the composition derivatives of chemical potential of nonideal liquid systems can be determined from equilibrium sedimentation experiments. These quantities are of importance in the study of the multicomponent diffusion process, because the practical diffusion coefficient matrix is the product of a fundamental diffusion coefficient matrix and the matrix of chemical potential composition derivatives. I n this paper the previous equilibrium sedimentation work is extended to the study of a ternary liquid system in order to determine the thermodynamic contribution to the practical
