Binary Systems of Electron Donors and Acceptors
449
Thermodynamic Properties of Systems with Specific Interactions Calculated from the Hard-Sphere Equation of State. II. Binary Systems of Electron Donors and Acceptors Aleksander Kreglewski’ and Randolph C. Wllholl Thermodynamics Research Center, Department of Chemistry, Texas A&M University, Co//egeStation, Texas 77843 (Received August 22, 7974) Publication costs assisted by Texas A&M University
An attempt has been made to separate the physical from the chemical part of intermolecular interactions for 32 binary systems of electron donors and acceptors. The calculations are based on the hard-sphere equation of state and the parameters of intermolecular energy established in part I (revised). The uncertainty of excess functions GDA and HDA, due to,the donor acceptor interactions, is estimated to be f 5 0 and f150 J mo1-l) respectively, a t the mole fraction x = 0.5. Comparisons with gas-liquid critical temperatures for four systems indicate that these interactions either vary with the temperature faster than with T-l, or are not conformal with London interactions, or both.
+
The thermodynamic excess functions, GE and HE, of many systems of two components are smaller than expected either on theoretical basis or by a comparison with the functions of the systems formed by each of the components with inert solvents such as alkanes. Spectroscopic measurements, made for a great number of such systems, invariably point to certain specific interactions between the two components, which we shall call electron donor acceptor interactions, or briefly DA interactions. For a given system, at constant temperature and composition, the observed functions can be separated into two contributions:
+
GE = G E o
+
GDA
HE = H E o+ HDA; etc.
(1) where GEo,HEo, etc., are the hypothetical excess functions in absence of DA interactions, and GDA, HDA,etc., are those due to DA interactions. For mixtures of inert solvents, GDA and HDA are always zero. For other systems, whose components are characterized by certain values qJk and qJJ/k(considered in part I), they are zero or negative. However, the strength of the DA interactions is not proportional to the values of qll/k and q J J / k .Systems with small 4)s may exhibit DA interactions stronger than expected. This problem, as well as the literature related to the chemical nature of DA interactions, is not considered in this paper. The purpose of this work is to estimate GEo,HEo,and the gas-liquid critical temperatures Tco (cp) of most of the systems for which data are available. If the size differences of the components are large, either GEo or HEo or both may become negative. However, if the sizes are similar (and such cases only are considered in this paper), GEo and HEo are always positive. The values of these functions depend roughly on three factors: (a) inequality of London energies eo that leads to small values of GEo, seldom exceeding 200 J mol-l for the equimolar mixture (x = 0.5); (b) inequality of the parameters q / k due to multipole interactions that may lead to large GEO and H E 0 and even a phase separation; (c) ordering effects associated with large values of qlk, but not proportional to them (part I),l that diminish HEo much more than GEo. Except rare cases of a compensation when clLO < eJJo but qar > v,~, the values of GEo and H E oare not small.
+
The values of GE0(2,3)and HE0(2,3)of a 2 3 system were usually equated to GE(1,2) and HE(1,2)of a 1 2 system, where “1”is an inert solvent so similar to “3” that the 1 3 system is practically ideal. Vera and Prausnitz2 found that GE of the 1-hexene benzene system at 303 K is about 140 J mol-l (x = 0.5) smaller than for the n-hexane benzene system. Since q / k of 1-hexene is negligibly small and eo values of hexane and hexene are very similar, the two must form nearly ideal mixtures and the difference between the two systems can be equated to GDA = -140 J mol-l for the 1-hexene benzene system. This result is most interesting in that both components are electron donors. Andersen, et ~ l . estimated , ~ HEo and GEo of the 1HC7F15 (CH&CO system by putting them equal to those of the n-C7F16 (CH&CO system in which DA interactions do not appear. The value of qlk of 1-HC7F15 is not known but it may be only slightly different from that of nC7F16 and the results are confirmed by a spectroscopic determination of HDA. Gaw and Swinton4 equated GEofor the C6F6 C & j System to GE O f the C6F6 C-CgH12 System. This system is discussed later. In most cases, it is difficult to find an inert solvent sufficiently alike to one of the components “2” or “3” and tg estimate directly GEo and HEoof the 2 3 system. Hence, attempts were made to estimate these functions by applying the theory of regular solutions and the solubility parameters of the pure components516or the interaction constants for mixtures.’ The present work is based on the hard-sphere equation of state and the relations given in part I. Results obtained for the internal energy of pure liquids and compressibility of gaseslss suggest that noncentral (London) energy cannot be ignored and we initially tried to include it in the relations for mixtures. Relations Including Noncentral Energy. Since this energy varies with T-l in the same manner as that due to multipole (specific) interactions, we may write for the pair interaction energy
+
+
+
+
+
+
+
+
+
+
where e* is the temperature independent part of London energy, q,/(kT) is the noncentral contribution to the LonThe Journal of Physical Chemistry, Vol. 79, No. 5, 1975
A.
450
Kreglewski and R. C. Wilhoit
the values of qJJ. For example, the value for found from GE data with seven inert solvents is qJJ/k= 10 f 11 K, that is, the uncertainty is larger than the value itself and the value is virtually useless in further treatment of cornplex systems involving DA interactions. Hence, against all the evidence in favor of noncentral energy in pure fluids, In part I, the correction for size differences, [A~j/(kT)]l/~, the London energy was further assumed independent of and that due to ordering effects (such as, e.g., association), the temperature, consistently for mixtures and the pure [ ~ ~ j l ( k Twas ) ] ~formally , included in the expression for t. In components, i.e., 7, = 0; to = e*; x = q/(kT) (with respecfact, they do not affect e, but only the total Helmholtz entive subscripts ii, j j , and i j ) . ergy of the system. We thus include them in a separate Binary Systems with One Inert Component (Revised). term and write the van der Waals attraction function in a According to Sarolea’s theory, vlJ is proportional to qlJ different but equivalent form: ‘h(qrl q J J )and, therefore, in systems with an inert solvent i, it is proportional to v2qJJ. The proportionality constant appears to depend on the chemical nature of component j . For a system in which none of the components is an inert solvent don energy, and qI(kT) that of specific interactions. For an inert solvent, qlk = 0 and t = to = t*[l q,/(kT)]. Equation 2 can also be written
+
+
For reasons explained in part I, the coefficient 4.7 was replaced by 4.65. The proportionality constant q is such that for pure fluids q e = TC/(V*)1/3,where Tc is the observed critical temperature. Experimental data on critical constants indicate that in presence of weak or even moderate specific interactions (such as in perfluoroalkanes or acetone), the coefficient 4.65 remains the same and on this basis one may claim that q is the same. This allows the determination of e* from the relation
The combining rules, used in part I (and discussed earlier) are for the London energy
and for the specific interactions qij, in absence of D A interactions denoted by qijo
The combining rule for the noncentral qnij (London) interactions is not known. However, eij* probably follows the rule 1 1 -l Eij*
=
:,[
+
q]
and qnlJmay then be determined from the relation (9) q n i j / K = T [ ( E i j o / ~ i j *-) 11 vnll and vnJJwere evaluated from the acentric factors w by using the relation q,/k = 0.833wTC (see part I) where the observed TC was used instead of a hypothetical one due to London interactions only. In part I the values of q J J / kof compounds with specific interactions were established from GE and HE data for mixtures of such compounds with inert solvents ( q z z= qlJ = 0) assuming that to are independent of the temperature (an = 0 ) . In a renewed effort to establish these values in the same manner but including noncentral energy, i.e., from eq 2, calculations were made for random mixtures for which A,,/k and vlJ/k are zero. In such cases qJJk are small and for molecules with large noncentral energy qnJJ >> qnJJ. Consequently, relatively small errors in acentric factors and vnll of the inert solvents (i) caused a large scattering of The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
and
(11) c i j = 1/2(c,, + C j j ) Equations 10 and 11 are crude approximations for ordering effects in a mixture. The constants c are further called ordering constants. Formerly obtained values of the coupled parameters qJJ and v y can be converted to the pair qJJand cJJthrough the relation cjj = 2vlJlqJJ.The revised values given in Table I differ from those given in Table IV of part I for the following reasons. Former corrections for the effect of clustering in the vicinity of the critical solution temperature Tcs,AHc, and AGc, are probably too large and the theoretical constant DO should be replaced by a value, obtained by Fixman, matching observed heat capacities. The values adopted in the present calculations are Do = Bo = 38 J molT1 K-1/2 where Bo was tentatively set equal to Do as there is some evidence that the two are not very different. Further, the coefficient 4.7 in eq 4 was replaced by 4.65 and this caused a slight increase of all the values of qlk. The new values of qJJlk and cJJwere obtained, as before, by fitting to values of GE and HE of these compounds with the inert components i given in Table I1 and I11 in part I. In the present work, any of these compounds may be either component i or j and, therefore, qlk and c in Table I are written without subscripts. The values given in brackets for three compounds were obtained by fitting to GE at two or more temperatures and, as noted in part I in the case of methylamine, the resulting values of HE of these compounds with inert solvents vary too rapidly with the temperature. For example, for the Xe HC1 system the parameters used (qll = 0, qJJ/k = 85 K, cJJ = 1.62, Tcs= 155 K) match observed GE a t all three temperatures, however, HE/J mol-l varies from 1250 at 195.4 K to 560 a t 159.1 K. The reason is that a small part of t(r) of CH3NH2 or HCl varies with the distance r less rapidly than does London energy and mixtures of these compounds with inert solvents are not exactly conformal solutions. Binary Systems of Electron Donors and Acceptors. For all the systems considered in this paper, the correction for the effect of size differences All = 0. Table I1 shows the results obtained for two systems by fitting qlJ/k to match observed GE at one temperature. The values of q/k and c of the pure components were taken from Table I and clJ was evaluated from eq 11. The agreement with the experimental data for GE and HE (given in Table 111)is satisfactory a t
+
Binary Systems of Electron Donors and Acceptors
451
TABLE I: Average Valum of the Couplad Parameten q/k and c dk
Benzene Toluene o-Xylene
11 0.5 17
rn-Xylene p-Xylene Dimethyl ether Di-n-propyl ethe? Acetone 1.4-Dioxane Tetrafluoromethane PerfI uoroethane
14.5
0 0 0 0 0 (0) 0
17 25' 5.5 137 117 24 60'
Perfl uoropropane
94
Perfluoro-n-butane Perfluoro-n-pentane Perfluoro-mhexane Perfl uoro-n-heptane Perfluoromethylcyclohexane
n/k
C
104 147 169 169 140
C
82 16 5.5
Perfluorobenzene Dichloromethane Chloroform
1.44 1.665 1.10 1.2c
Carbon tetrachloride Ethyl bromide Carbon disulfide Methylamine Ethylamine n-Propylamined Diethylamine Trimethylamine
1.29
Triethylamine
1.23 1.20 1.175 1.24 1.26
Aniline Pyridine Acetonitrile Hydrogen chloride
1.67 0 0
0 0 0 :1.408) 1.83 2.20 0 0 0 1.83 2.52 11 2 0 ) 11.62)
1
11.5 -0 11921 96 61 15 5.5 1 95 42 (3221 1851
-
520 K . 'Estimated by a correlation with other perfluoron-alkanes 'Evaluated from F data determined by S. Glowka. Bull. Acad. Polon. Sci. Sei. Sei. Chim. 20. 163 119721. bEstirnated dEstimated F = 497 K. Nota: In all Tables. the temperatures q/k and Tare in kelvins. free energy and enthalpy in J mol.', and molar volume in crn3mo1.'
TABLE I I : The Excess Functions of Two Systems Evaluated for R,, Fitting the Observed Values of GE (Equimolar Mixtures) CHC13
+
K H 3 ~ 2 C 0n,/k
= 86 2 K
T
GE
&
298 313 323
-640 1-580)'
343
-480
-1880 -1740 -1660 -1510
-550
C6F6+
# -1 -1 -1 -1
4 5
5 6
C6H6 q,,/k
-
48 7 K
T
GE
d
@
303 313 323 343
i-60)a -40 -30
-510 -460 -420 -340
-03 -03 -03
-10
-03
'Observed value s,Jk was adjusted to match calcuiated GE with this value
all temperatures. The excess heat capacity CPE = (aHE/ aT), is smaller than the calculated value. Since HE is sensitive to the value of cjj, eq 10 and 11appear to be acceptable approximations. In spite of this agreement, such calculations are in principle not allowed because they include the chemical part of c(r) that varies with intermolecular distance more rapidly than the physical (London multipole) interactions. That is , c"41 = q0[l qjjo/(kT) q j j D A / ( k T ) ]where , qijo is the part of qjj obtained from eq 7. The part qjjDA = qij - q;jo should be treated as a separate term, nonconformal with the physical terms. A t least two phenomena show that the term cijoqjjDA/(kT)should be treated separately. First, for qijlk = 48.7 K fitting GE of the C6F6 C6H6 system at x = 0.5, one obtains a nearly symmetrical curve, whereas the observed values are positive a t x1 < 0.35 (Figure 1). We miss the most interesting result found by Gaw and Swinton, that the system forms simultaneously a positive and a negative azeotrope. Secondly, the critical temperatures evaluated by using the same values of q;j/lz are too high, in both cases by about 7 K a t x = 0.5 (Figure 2, curves 2). The curves show that DA interactions persist in the critical state of the CHC13 (CH&CO system, however, weaker than expected, whereas they vanish in the C6F6 && system and the curve evaluated for qij = qijo (eq 7) approximately follows the experimental points. Figure 3 compares two different treatments. The full curves were calculated in the above manner putting qjj = qijo. Only the data for the C6F6 -k C6H5 CH3 system point to very weak DA interactions, but in limits of error of the predicted values one may rather state that in all three sys-
+
+
+
-
c
---v---
i
P
-1000
I
I
0
0.5
1.0 X1
Flgure 1. Excess Gibbs energies and excess enthalpies of the C6F6 4- C6Hs system at 313 K. Dashed curves are hand drawn through the experimental points: (0) d determined by Gaw and S ~ i n t o n ; ~ (0) determined by Andrews, et a / . (ref ai to Table 111). In all figures, x1 is the mole fraction of the first component of each pair.
+
+
+
550
x
r'
500
I 1.o
1
0
0.6
+
XI
Flgure 2. Critical temperature curves of two systems: (0) CHC13 (CH&CO determined by Swietoslawski and Kreglewski (Bull. Acad. Polon. Sci. Ser. Sci. Cbim., 2, 187 (1954)); (0)C6F6 C8H6 determined by Powell, Swinton, and Young, (J. Cbem. Tbermodyn., 2, 105 (1970)); curve 1, calculated for qu = q t (eq 7); curve 2, calculated for q f fitting @ data (see Table 11); curve 3, fitting the Tc data of the CHCI3 (CH3)&0 system, q f / k = 68.7 K.
+
+
The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
A. Kreglewski and R. C. Wilhoit
452 TABLE Ill: Values of the Exces Functions of Equimolar Mixtures Calculated, vii = 11;
q?.
k
CC14
+
(CH3IzCO
CC14 + In-C3H7)20 CCld
f
1.4-Dioxane
T
Observed values
GE
838
678 103.3b 115d, 12ge. 115.5'. 1168 126c 132.5b 126c
@
GDA
,+DA
-50
-250 -200 -170 -140 -140
130 120 110 100 100 90
320 300 290 270 270 2 50
31 8
840
1710
2.2
298
190
370
0.1
293 298 303 313
850 840 830 820
1240 1270 1300 1360
0.5 0.5 0.6 0.7
3 87
298
200
400
0.3
-4854
1 00
298
140
290
0.0
-61 1
-900
65
298 323
500 460
940 920
0.0 0.1
-1 18'
-1060
9.7
298 308 318
1110 1090 1070
1490 1590 1670
-0.7 -0.7 -0.7
883' 909' 940'
1172"
18.0
318
1190
960
-0.4
1188"
900"
76
298
20
60
0.1
27 5
298 313 323 343
640 620 600 570
1050 1110 1130 1170
11
2 35 10 7
0.2
0.2 0.2 0.3 0.3
1.4 1.5 1.9
CHC13 .t In C3H7I2O
55
298
220
530
0.2
CHCI3 t 1 4 Dioxane
25 4
323
530
820
04
CHCI3 + (C2Hg)-jN
HE
273 288 298 31 3 318 343 11 8
0.2
GE
82C 79h 75h 547j
0.04i 0.08C
260i
-2508 -0.33P
-120 -1450 -650
-660 -670 -640 -620
- 1520
-130 -0.32"
-230 -180
-320
130
-423'.
-740ad
-15 -290
-890
3305
-58oaa.ab
30 -20
-0 335m
-276k 187" 171° 187O 203O
0.02c
0 -422w
-1845'. -1919Y -181OY -1740y -1690y
-0.095*
-1947k
-0.868m
- 1200
-0.20=
-1 830ad
-60 -480
O.14Zw
-2970 -2920 -2870 -2860 -2480
-1270
-2650
298
230
600
CHC13 f CgHgNH2
22 7
298
720
970
-0.7
CHC13 + CH3CN
42 6
313
900
360
-0.8
c6F6t C6H6
30 3
298 303 313 323 343
410 410 400 390 380
620 630 650 660 600
288 298 31 8
400 390 360
870 840 790
298 323
630 570
1360 1330
2.0 2.5
6508" 680'"
-710 -650
298 323 343
550 520 510
830 820 810
0.0 -0.1 -0.3
330an 3158" 305a"
-500
298
630
930
-0.7
308 318 343 392
620 610 590 530
950 960 970 930
-0.7 -0.8 -0.9 -1.4
298
280
230
-0.3
298
240
560
0.0
318
600
950
1.2
343
220
530
293 298 318
460 460 450
620
298 308 328
130 120 120
170 170 170
234
98.1
9.05 59.5
32.5
The Journal of Physical Chemistry, Vol. 79,No. 5, 1975
640 710
0.4
-4O7Ox
-1 988
192'
-0.21ef
1 3Zag -604
-4968h, -4568i -480ah, -4538i -4528h, -4338i
1.2 1.4
-294 -38i
-4278h, -413ai -351 ai 61am 498" 42'"
-0.6 -0.7
-0.2 0.1 0.2 0.3 -0.3 -0.3 -0.4
393' 412' 387' 53880 4508f'
-780 -770
1 .o 1.1 1.1
-0.5
-4670
719"
0 8018k
-470 -440 -420 -380
-500 -500 -0.24"
-240
-50 -80
-1430 -2230
1€0.
-210
-790
-180
43.94
-400 -400 -380
-32'' -198' 332"
7385 62a5
-210
-210 -220
-1674'
65" 590 750
-
-810 -790 -750
0.85am 0.81a"
-1197f
293i
-1100 -1100 -1090 1080 1030
0.031m
-670 -730 (1601
-50
-60
453
Binary Systems of Electron Donors and Accept06 TABLE 111, continued
-
Observed values
Calculated, qil q$ T
CgHg t IC~HFJ~N
CgH6 t CgHijN
3.32
21.5
-0
1-CgH12 t CgH6
G
E
I
#
P
0.2 0.3
298
320
750
333 353
270 240
690 670
298 313 333
210 200 190
380 380 370
283
303
440 400
960 900
0.2 0.2
323
370
850
0.1
0.4 -0.2 -0.2 -0.2
H'
GE
!F
330"
GDA
0.006@
-420
122@
-150 -130
llOw 340a', 127w
$A
ea","'8 2!jau 44au
-80
-0.200'U
-370
-3,60
-0,208'U -0.233w
-330
272'w
-170
23!jaW 226.6'w
-160 -140
'R.P. Rastogi.J. Nath, and J. Misra,J. Phvr Chm.71, 1277 (19671. bM.B. Ewing. K.N. Marsh, R.H. Stoker,and R.P. Toml1ns.J. Chm. Thmnodyn. 2.297 119701. %.E. Wood and J.P Brurie, J. Amer. Chm. S a . 66, 1891 (19431. dR.K. Niwm and 0,s. Mahl. J. Chem. Soc. Funday T ~ I, 1872. L 1508. 'G. Scatchard, L.B. Ticknor. J.R. Goater.md E.R. McCartmry. J. A m , Chm.Soc. 74,3721 (1952). 'R.H. Stoker, K.N. Marsh, and R.P. Tom1inr.J. Qmn. Thennodyn. 1,211 (1969). Murakamiand G.C. Bemn,J. Chm.Thmnodyn. 1,559 11969). hG Scatchard and L.0. Ticknor. J. Amer. Chm.S a . 74,3724 119521. 'D.J. Subach and C.L. K0ng.J. Chm.Enno. D m 18,403 119731. 11, Brown and F. Smith.Aun J. olm.10,417,423 (1957). 'L.A bath and A.G. Williamson,J. Chm. Thrmrodyn. 1,51 (19691. mL.A. Bwth,S.P. ONeill,and A.G. Wllliamaon,J. Chem. Thermodyn. 1,293 119691 "A.K Adya, B.S Mahl. and P.P.Sin&. J. Chem. Thermodyn. 5.393 119731. '0.0 DeshpandeandS.L. 0swai.J. Chm. Soc. Femday Tram l.lB72.1059. pP.R. Naidu and V.R. Krishnan. T r n z F m d a y S a . 81, 1347 (1965) 9H.J Bittrich. C. Kupsch, R . Gotter. and G. Bock. Pra. lnt. Conf Calorlmw Thennodvn. fH 783 (19711. 'K.W. Morcom and D.N. Travers, Tnnr Faraday S a . 62,2083 11968). 'V Fried. D.R. Francstchetti and G.B. Schneier,J. Chem. Ens Dam 13.415 119681. 'D.D. Deahpsnde and M.V. Pendye. Tmr FamdavSoc. 83,2149,2346 119671. "0.0 Dwhpandeand M.V Pandya. T m r FwsdaySoc. 61, 1858 119651. "I Brown and F. Smith.AuJt. J. Chm. B. 180 (19561. %.P. Ranogi. J. Nath, and J. M1rra.J. Chm. Thennodyn. 3,307 119711. 'T. Matsui, L.G. Hepler,and D.V. Fenby.J. Phyr Chm.77.2397 11973); L.G. Hepler and D.V. Fenby,J. Chm. Thmnooyn. 6,471 (19731. yK.W. Morcom and D.N. Travarr, Tmnh F . r a k y S a . 61,230 11965). %K. Nigam. B.S. Mahl. and P.P. Singh.J. Chcm. Thrrmodyn. 4.41 119721. MJ.Zawidzki,Z. Phva Chm. Sloechlom. Vllwndrh.ftalrhn36.129 (19CQl. %IRock . and W. Schrodar,Z. Phyr. Chm. Frankfurt VnMSln 11,41 (1967). =L.A.K. Stave1ay.W.I. Tupman. and K.R. Hart. T m r F m d a v S a . 61.323 (19651. %4.L. McGlashanand R.P. Rastqi. Tnna F r n d r y S a . 64,496 11968). mP. Boule. C. R. Acd. Scl. Sur. CzdB. 5 (19691. "0,R. Sharmeand P.P. Singh. J. Chm. Thermo6yn. 5.361 (19731. WA. Krsglewki, Bull. Acrd. polon. Sci. SH. Scl. chim. 13,723 (1965). &D V. Fenby. LA. McLure, and R . L Scott,J. Phvr cham. 70.602 (19661; 71,4103 (19671. "A. Andnms, K.W. Morcom, W.A. Duncan, F.L. Swinton,and J.M. Pol1ock.J. Chm. Thrnnodyn. 2.95 (19701. 'ism Ref. 4. &W.A. Duncan, J.P. Sheridmend F.L. Swinton. T ~ M FsndySoe. 82.1090 (19881. amA.W. Andrews, D. Hall,and K.W. Morcom,J. Chm. Thrnnodyn. 3,627 11971). "0.A Armitage and K.W. Morcom. Trma Fwadw S a . 66.688 (19691. WS.M. Houelni end G. Schnslder.2. Phvr Chm. Frankfurram Main 36.137 119831. W G . Kortum and H.J. Freier, C h m . /nu, Tech. 26,670 (19%). wT Treuczanowicz and H. Kehiaian. Bull. Acdd. Polon. Scl. &r. Scl. chim. 21.97 (19731. "A.W. Andrews and K.W. Morcom,J. Chm. Thrnnodyn. 3,519 (19711. -T.M. Letcher and J.W. Bavles. J. Chem. Eng O m 18.266 119711. "Calcuiated by the authors from thevapor pressure dataof S.W. Prsntis, J. Amen Cnem. Soc. 61.2025 (19291. wP,R Garrett, J.M. Pollock. and K.W. Morcom.J. Chm. Thermodyn. 3.135 (19711: 5.569 (19731. wWyw.Wgycicki,J. Qmn. Thermodyn. 6.141 (1974). owsee Ref. 2.
tion, the differences between T c and the pseudo-critical temperatures Tc, are very small for all the systems and the approximate relations for (Tc- T,") cannot be a source of error. As stated above, the theory of conformal mixtures allows us to evaluate GEo, HEo,etc., only. These quantities were evaluated for a few systems, collected in Table 111, by setting = 7ijo (eq 7) and the average values of the ordering constants cij (eq 11).The values of GDA and HDArepresent deviations in observed GE and H E , respectively, due to DA interactions (eq 1).Initial evaluation of GEo disclosed that two systems, in absence of DA interactions, would be not far from phase separation: cc14 CsH5"z (estimated critical solution temperature Tcsm 269 K) and C C 4 CH&N (TCs = 288 K). The values given for these systems include the corrections A G C and A H C for the effect of clustering. T o begin with, we note that in no case was a nonsense, positive value of GDAobtained. Exceptionally, HDAis small and positive for the C6H6 (CzH5)zNH system only. The uncertainty of the predicted values was previously1 estimated to be about f 5 0 for GEo and f 1 5 0 J mol-l for HEo (at x = 0.5) when one of the components is an inert solvent. In these limits, for the system just mentioned GDA = H D A = 0. Another system for which GDA = HDA= 0 is CC14 CHsCN. In the case of the systems CC4 C6H6, CeH5NH2 + C6H6, and C6H6 + C5H5N the value of HDAonly exceeds the uncertainty limits. Since solid-liquid equilibrium or spectroscopic data point to, at most, very weak DA interactions in these systems and our calculations reflect it, we believe that the uncertainties of the values of GEo and H E o are not larger than for binary systems involving an inert solvent. The. values of G E of the C G H ~ N H C6H6 ~ system are not consistent. Since always HDA< GDA, the values of GE determined a t 343 and 392 K seem to be preferable. The system for which we obtained a positive value of H D A ,
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Figure 3. Critical temperature data for the systems of C6F6 with (1) ,6 i& C (2) C6H5 CH3, and (3) PC&i4 (CH3)a determined by Powell, et a/. (ref in caption to Figure 2). The full curves were calculated for = 7 8 (eq 7) and the dashed curves correspond to a crude approximation (all the 7's set equal to zero).
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tems these interactions become vanishingly weak in the critical region. The dashed curves in Figure 3 correspond to the crude approximation that all the 77's are zero. By neglecting 7's one gains a false impression that there are positive deviations in these systems. The ordering effects in the gas-liquid critical region are nearly negligible. For example, by putting v i j = 0 for the CHCls (CH3)2CO system one obtains T", by 1.3 K lower than for vijlk evaluated from eq 10 and 11. At any composi-
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The Journal of Physical Chemistry, Vol. 79,No. 5 , 1975
J.4. Justice
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C6H6 (CzH&NH, is unusual in that the ratio of observed values H E / G E = 4.5, whereas for random mixtures it may reach a value of about 2.1 and for nonrandom mixtures it should decrease below this va1ue.l For a proper combination of the values of to, qlk, and vlk, the value of HEo/GEo may become even less than unity. The agreement obtained for such a system, CCl, CH&N, shows that specific interactions in pure CH&N consist of multipole interactions that are conformal with to(r) of an inert solvent. However, if the association in the pure liquid is due to strong hydrogen bridges, as in CH3NH2 or the alcohols, the above theory fails for mixtures of such liquids with inert solvents as well as with electron donors or acceptors. The systems given in Table I11 would in absence of DA interactions be at least approximately conformal. We believe that the present values of GEo and H E o are more realistic than any previously estimated values because the ordering effects (particularly on HEo)were in earlier works ignored. One may tentatively classify as weak the DA interactions that produce GDAranging from zero to about -500 J mol-l ( x = 0.5) near room temperature (0 > G D A / ( R T )2 -0.20). Among such systems, the most interesting are the C6F6 C6H6 system and the last seven systems of components that usually behave like electron donors. The function GEo for the C6F6 C6H6 system appears to be smaller than for C6F6 C-CgH12 and accordingly we obtain a less negative value of GDAthan did Gaw and Swinton by a direct comparison of the two systems. Their results are confirmed in that GEo and HEo are asymmetrical in a direction opposite to that of the observed G E and HE so that GDAand HDAare
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nearly symmetrical functions of x i (Figure 1).The excess functions of the last system in Table 111, l-C6HI2 CsH6, were evaluated assuming qii = qijo = 0 because qii of l-hexene is certainly very small. The excess volumes VE are in most cases wrong. When component i is an inert solvent and qjj is large, the calculated values of VE are too large (part I). When there are DA interactions and qij increases, VE decreases below the observed value (see, e.g., Table 11). This excessive effect of 7 on VE, and also on VLoof the pure components, is almost certainly due to neglecting the temperature dependence of collision diameters u in the hard-sphere term $(() of the equation of state. For certain assumed values of the function u(T)we have found that I$(() moderates the effect of q on Vio.However, we did not yet try to apply these concepts to mixtures of fluids.
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Acknowledgments. This study was partially supported by the American Petroleum Institute Research Project 44 and the Thermodynamics Research Center Data Project of the Thermodynamics Research Center. References and Notes (1) A. Kreglewski and R. C. Wilhoit, J. Phys. Chem., 78, 1961 (1974). (2) H. H. Vera and J. M. Prausnitz, J. Chem. Eng. Data, 16, 149 (1971). (3) D. L. Andersen, R. A. Smith, D. B. Myers, S. K. Alley, A. G. Williamson, and R. L. Scott, J. Phys. Chem., 86, 621 (1962). (4) W. J. Gaw and F. L. Swinton, Trans. Faraday SOC.,64, 2023 (1968). (5) H. G. Harris and J. M. Prausnitz, lnd. Eng. Chem., Fundam., 8, 180 (1969). (6) R. Philippe and P. Clechet, "Third International Conference on Chemical Thermodynamics," Vol. Ill, Baden, Austria, 1973, p 118. (7) A. Kreglewski, Bull. Acad. Polon. Sci. Ser. Sci. Chim., 13, 723 (1965). (8) A. Kreglewski, J. Phys. Chem., 78, 1241 (1974).
The Debye-Bjerrum Treatment of Dilute Ionic Solutions J.-C. Justice Laboratoire d'Electrochimie, Universite Paris Vl, 75230 Paris Cedex 05, France (Received November 20, 1973; Revised Manuscript Received February 75, 1974)
It is shown that the generalization of conductance equations based on the Debye-Huckel correlation functions to the Bjerrum concept, as originally proposed by Bjerrum for the Debye-Huckel activity coefficient law, does not constitute an alteration of the original hard-sphere model as assumed by Fuoss. The consequences of what we call the Debye-Bjerrum treatment are discussed in detail and the analysis of experimental data using this approach is shown to be more satisfactory than with other methods used previously.
I. Introduction In the preceding contribution1 to this journal a critical analysis of a method proposed by the author2 for processing experimental conductance data has been presented. The criticisms of Professor Fuoss concentrate on two points. First, the replacement of the parameter a by R, the Bjerrum critical distance, is theoretically interpreted as an improper change in the initial model. I t is claimed that the new treatment would describe the properties of a model where ions are represented by hard spheres of radius R/2. The Journal of Physical Chemistry, Vol. 79, No. 5, 7975
Secondly, it is concluded that the new equation is inadequate for analysis of experimental data because it does not lead in general to a unique evaluation of the adjusted parameters. An answer to these two criticisms is presented. It is shown that the substitution of a by a critical distance R is a direct consequence of the introduction of an association concept to correct for the failure of the Debye-Huckel treatment of electrolyte solutions in solvents of low dielectric constant or for electrolytes of high valency. Also the criticisms concerning the supposed adulteration of the orig-
