A. s.KERTES, 0. LEVY,AND G. MARKOVITS
3568 compounds exhibited photoelectric effects similar to the Chl-BLM. It should be mentioned that although our present investigation has been limited to the use of visible light in the electromagnetic spectrum, the BLM photoelectro-
metry can be easily extended to other regions as well with proper equipment. The use of readily available commercial instruments is anticipated. Acknowledgment. This work was supported by a National Institutes of Health grant (GM-14971).
Aggregation of Alkylarnmonium Tetrahaloferrates in Benzene by A. S. Kertes, 0. Levy, and G. Markovits Department of Inorganic Chemistry, The Hebrew University, Jerusalem, Israel
(Received December 17, 1969)
Osmometric, vapor pressure lowering measurements on 0.005-0.1 M benzene solutions of trilaurylammonium tetrahaloferrates, (C12H2&.NHFeC14 (TLAHFeClJ and ( C E H ~ E ) ~ N H F(TLAHFeBn), ~B~~ and tetraheptylammonium halides, (CTH&NCl (TeHpAC1) and (C7H15)4NBr (TeHpABr), and tetrahaloferrates, (C7H15)4' NFeCld(TeHpFeCl4) and (C7H1&NFeBr4 (TeHpAFeBrJ, indicate that the deviation of these solutions from an ideal behavior is due to a dipole-dipole-type molecular association leading to the formation of oligomers as high as the 24-mer. The deviation has also been interpreted in terms of changes in the activity coefficients of the solutes via the Gibbs-Duhem relationship. The theory of the osmometric technique has been modified and extended to show that a nonlinear relationship of osmometric calibration curves is an intrinsic property of the method.
Reporting recently on the nonideal behavior of solutions of tridodecylammonium salts in nonpolar solvents,l we have shown that both the extent (number) and the degree (size) of molecular association of these solutes is markedly affected by the anionic part of the ion pairs. Such an effect, observed in the past by Kraus and coworkers2in systems containing short-chain (five carbon atoms per chain, or less), lead to the generalization that for salts having a small and a large ion, the association number reaches very high values. Since this dipole-dipole aggregation is also affected by the amine class from which the salts are derived,a it occurred to us that an extension of the earlier work to include both large anions and different amine classes may be desirable before further generalizations on the behavior of these and similar electrolytes in nonpolar solvents could be justified. We have prepared4 salts of tetrachloro- and tetrabromooferric acid (having a radius of the anion about 2.65 Ab) of tridodecylamine (trilaurylamine, TLA) and tetraheptylammonium (TeHpA) hydroxide and measured the vapor pressure lowering of their benzenic solutions. For comparison, we have also studied the behavior of the corresponding simple alkylammonium halides, not investigated previously. I n this report, as in the previous one,l the osmometric data are analyzed in two ways: (i) in terms of nonspecific nonideality in the system expressed through the activity coefficients of the solutes via the GibbsThe Journal of Physical Chemistry, VoE. 74, No. 90,1970
Duhem relationship, and (ii) in terms of specific nonideality, assuming that the observed nonideality is entirely due to association of the solutes into molecular aggregates, oligomers, of different size in a mass action law equilibrium with each other.
Experimental Section Materials. The preparation and purification of trin-dodecylammonium and tetra-n-heptylammonium chlorides, bromides, and tetrahaloferrates has been described previously, along with some of their physical proper tie^.^ Benzene was an anhydrous AR purity Mallinckrodt product. Osmometry. The equipment and the procedure for measurements in the solute concentration range 0.0050.1 M were earlier reported.' Due to the properties of the matched thermistors, reproducibility of readings is frequently poor (> 1%) at concentrations below the lower limit, whereas the upper limit is dictated by one or both of the following factors. The rate of heat exchange through the vapor phase" becomes slow above (1) A. S. Kertes and G. Markovits, J . Phys. Chem., 72, 4202 (1968). (2) C . A. Kraus, ibid., 60, 129 (1956),and references therein. (3) Y . Marcus and A. 8. F t e s , "Ion Exchange and Solvent Extraction of Metal Complexes, Wiley-Interscience, New York, N. Y., 1969,Chapter 10. (4) 0. Levy and A. 8 . Kertes, J. Inorg. Nucl. Chem., 31, 888 (1969). (5) A. 5. Kertes, H. Gutmann, 0.Levy, and G. Markovits, Israel J . Chem., 6,421 (1968).
3569
AGGREGATION OF ALKYLAMMONIUM TETRAHALOFERRATES 0.1 M , due mainly to the formation of a liquid film a t the drop surface’ attributed to the surface-active properties of the solutes under consideration, and the possibility of some heat loss due t o the high temperature differences between the solution drop and its environment. If reproducibility of experimental readings is satisfactory, the accuracy of molecular weights and/or activities determination will depend primarily on the calibration curves obtained by the calibration standards. Theoretically, using benzene solutions of nonassociated calibration standards such as triphenylmethane, triphenylamine, benzil, and biphenyl, resistance change is a linear function of the mole fraction of the solutes. It has been pointed out, however, that a slight deviation from ideal behavior has been observed, especially at higher solute concentrations. While the deviation may still be due to a small but finite lack of ideality of the calibrating solutes, we have now analyzed the theory of the method which may explain the lack of an ideally linear dependence of resistance changes with solute concentration, except perhaps in the dilute region. I n a way similar to the van’t Hoff-Planck limiting law for freezing point depression,8 the temperature difference, AT, between the pure solvent and a given solution of molar concentration c, is given9 by the simplified expression
where p is a constant expressing the interaction (solutesolute or solute-solvent), M and cp the molecular weight and density of the solvent, respectively, and AH, its molar heat of vaporization. Over a temperature range of a few degrees and a small resistance range, the temperature dependence of the thermistor resistance, r, of a pair of matched thermistors can be approximatedlO as AT = -T2Ar/Bro
(2)
where B is the so-called thermistor material constant depending on the nature of the semiconductor, and its value is determined from the experimental polynome 1727/T, when ro = 6700 s2 for the log r = -2.015 Hewlett-Packard No. 4115 thermistor after more than a year inuse (for 36-38”, B is 3973°K). Combining now eq 1 and 2 results in
+
to show that a plot Ar us. c should not necessarily yield a perfectly straight line, but with increasing c a decreasing slope can be expected, the initial value of the slope being defined as t g a = BroRM/lOOOqAH,,
(4)
Following the known1‘ theoretical considerations and calculations concerning the heat balance, one can evaluate the maximum value of t g a in eq 4 which depends on a constant, termed the thermodynamic yield, q, and which at 37”, using the equipment with physical and thermal characteristics as given by the manufacturer and those of benzene as used by the authors,” has a value of 7 = 0,811, and the calculated value for qtga = 489 (on a molar basis), as compared to the observed qtga = 492 for the lowest concentration of the standards measured. It is thus apparent that the difference between the observed and calculated slope is not significant and that the change in slope with the solute concentration is an intrinsic property of the method. For all osmometric measurements the anhydrous salts were dissolved in dry benzene. Triplicate Ar readings at equilibrium (5-20 min, depending on the temperature) show agreement to within 1% or better. The LETAGROP ALGOL program for treatment of osmometric data developed by Sil16n12and translated to FORTRAN by Rilango,laused in this work (CDC6400 computer), requires a constant slope for the input. We have now modified the program to use as input the ~
Table I: Values of the Coefficients a, b, c, d in Eq 5 t,
Solute
OC
TLAHCla TLAHC~~ TLAHBrb TLAHBrb TLAHFeCl, TLAHFeC14 TLAHFeCl4 TLAHFeBr, TeHpACl TeH p AC1 TeHpABr TeHpABr TeHpAFeCll TeHp AFeBrc
a
a
25 0.00205 37 -0.0015 25 -0.0002 37 0.0003 25 0.806 37 0.840 50 0.740 37 0.525 37 0.505 50 0.412 37 0.448 50 0.418 50 0.381 50 1.060
0.7916 1.114 0.917 0.928 -16.14 -15.62 -17.33 -17.91 -13.27 -14.85 -14.24 -11.19 -10.51 -13.10
C
d
-1.945 8.46 -10.14 41.31 -6.839 36.23 -9.522 122.01 168.09 - 630.80 158.57 -576.91 201.97 - 823.69 277.67 - 1485.77 154.56 -614.5 232.61 -1233.17 199.94 - 934.06 139.06 - 602.34 125.14 - 512.32 176.25 -812.49
+ + cB2 + d B 3 ) . ‘ From
According t o polynome (S = a bB ref 1 (S = a f bB cB2 dB8). Q
+
+
(6) P.P.Brady, H. Huff, and J. W. McBain, J . Phys. Colloid Chem., 55, 304 (1951). (7) W. I. Higuchi, M.A. Schwarts, E. G. Rippie, and T. Higuchi, J . Phys. Chem., 63, 996 (1959). (8) R. Haase, “Thermodynamic der Mischphasen,” Springer-Verlag, West Berlin and Heidelberg, 1956,p 364. (9) R. V. Bonnar, M. Dimbat, and F. H. Stross, “Number Average Molecular Weight,” Interscience, New York, N. Y.,1958,p 116. (10) J. A. Becker, C. B. Green, and G. L. Pearson, Elec. Eng. Trans., 65,713 (1946); R.H.Muller and H. J. Stolten, Anal. Chem., 25,1103 (1953). (11) C. T.Tomlinson, S. H. Chylewski, and W. Simon, Tetrahedron, 19, 949 (1963). (12) L. G.Sillh, Acta Chem. Scand., 18, 1085 (1964); N. Ingri and L. G . Sill&, Ark. Kemi, 23, 97 (1964). (13) L. Mango, Italian Report R T (FIMA) CNEN (67)1 (1967). The Journal of Physical Chemistry, Vol. 74, No. 80,1970
3570
-I - 5
A. S. KERTES, 0 .LEVY,AND G. MARKOVITS
I
I
I
2
4
I
6
I
I
8 IO m 3 x IO*
I
12
I
14
TeHpAFeCI,,
a' \
I J
16
Figure 1. Activity coefficients of trilaurylammonium salts in benzene at 37".
2
4
6
osmometric concentrations calculated for each sample by means of the calibration curve, having thus Ar/c = 1.
IO
8 m3
x
12
14
16
lo2
Figure 2. Activity coefficients of tetraheptylammonium salts in benzene at 50'.
Results The osmometric concentrations, 8,were calculated from the experimental readings of Ar via the calibration curves and the analytical solute concentrations, B , fitted into the polynome
X
=
aB
+ bB2 + cBa + dB4
(5)
The constants of eq 5 calculated by a nonlinear leastsquares computer program are compiled in Table I for benzene as the solvent. Activity Coeficients. Similarly to our previous treatment' of the experimental data via the GibbsDuhem equation (where the equations and their deductions are given in full), the activity coefficients of the solutes, (yJ, in benzene were evaluated by a computer program. Figures 1 and 2 represent the variation of the activity coefficientswith the molal solute concentration for the tertiary and quaternary ammonium salts, respectively. Figure 3 shows the effect of temperature upon the activity coefficient of trilaurylammonium tetrachloroferrate. Molecular Association. Using again the theoretical approach described in detail earlier' and assuming an activity coefficient of unity for the solute aggregates formed in benzenic solution, we have evaluated by a linear least-squares program the overall stability constant, p, of the aggregates. Over 100 models were tested, the choice having been dictated by (i) the lowest value of the error square sum, and (ii) the restriction that in the temperature range of 25-50' no change of the model is likely to take place, meaning that the same oligomers persist for a given solute regardless of the temperature changes. The aggregation models for the The Journal of Physical Chemistry, Vol. 74, N o . 10,1970
-1.5
2
4
6
8
1 0 1 2
m3 x lo2
Figure 3. Activity coefficients of trilaurylammonium tetrachloroferrate in benzene a t different temperatures.
solutes investigated and the appropriate p values are compiled in Table 11. Some thermodynamic functions were calculated' for systems where measurements were made at more than one temperature. Values for AH,' and AS,' are compiled in Table 111, and Table IV shows the standard free energy change in the TLAHFeC14benzene system, along with the p's evaluated independently by a nonlinear least-squares program. The values for log p a t all three temperatures shown in Tables I1 and IV, calculated by two different methods, are in good agreement.
Discussion Though the shape of the curves representing the con-
357 1
AGGREGATION OF ALKYLAMMONIUM TETRAHALOFERRATES Table I1 : Log p, for the Various Salts Salt
t, o c
TLAHFeCh TLAHFeC14 TLAHFeC14 TLAHFeBr4 TeHpAC1 TeHpAC1 TeHpABr TeHpABr TeHpAFeClr
25 37 50 37 37 50 37 50
Model a-b-c
Log
2.14 f 0.05 1.95 f 0.03 1.81 f 0.06 2.21 f 0.09 4.96 =!= 0.06 4.74 rt 0.08 5.25 i 0.19 4.99 f 0.18 5.73 i:0.05
2-8-22 2-8-22 2-8-22 2-8-10 3-18 3-18 3-18 3-18 3-24
50
Table I11 : The Thermodynamic Functions for TLAHFeC14, TeHpAC1, and TeHpABr
As,', System
TLAHFeCl, TeHpACl
n
AH,O, koal mol-1
2 8 22 3
-4.4 -27.7
-7.7 -50.6 -9.2 -90.6
18
TeHpABr
3 18
cal mol-% deg-1
-4.9 -23.1 -132.0 -1.9 $36.2 -5.6
-100.0
-80.0
Table IV : The Standard Free Energy Changes and Formation Constants as Recalculated from the Thermodynamic Functions for TLAHFeC14 --25O-n
2 8
22
AGO, koal
-2.92 -20.78 -60.70
log k
~---37~-log AGO, Pn kcal
2.13 -2.86 15.15 -20.50 44.25 -59.08
--50°----. AG", kcal
2.00 -2.79 14.37 -20.19 41.43 -57.36
log Pn
1.88 13.59 38.61
centration dependence of the activity coefficients does not indicate formation of micellar aggregates of constant activity, as it is usually assumed t o be the case,14 still this dependence suggests a more pronounced nonideality of the metal-bearing salts, as was expected from our earlier results.' In the same line, aggregation of the quaternary ammonium salts is stronger than that of the tertiary salts with the same anion and approximately the same weight, at any given concentration in the range investigated. Trilaurylammonium salts, regardless of the anion, associate invariably through the dimer, which is apv
PO
LOP Pb
Log Po
14.94 i 0.05 14.32 i 0.01 13.45 I 0.03 15.32 i: 0.27 43.34 i 0.16 41.91 1 0 . 1 8 46.15 i:0.06 43.60 f 0.29 63.14 f 0.21
44.55 f 0.06 42.06 =!= 0.06 39.39 f 0.10 20.04 =t0.04
parently the basic aggregated unit in solution in equilibrium with the monomer and higher oligomers. Dielectric constant measurements on such solution^'^ indeed suggest that these dimers have a considerable dipole moment p z = 7.8 D for TLAHCl and 10.7 D for TLAHFeC14, implying a bent structure or a possible parallel position of the monomeric units in the dimer, rather than an antiparallel configuration which should lead to: low or zero dipole moment of the dimer. For the dimers of the simple trilaurylammonium salts, the chloride and the bromide, the calculated' bond energy has a value of AHz' = 3.3 kcal/mol, as compared to the value of 4.4 kcal/mol in the case of the tetrachloroferrate. The process of aggregation of the quaternary ammonium salts is apparently more complicated as reflected by the drastic changes in the y3 values with increasing solute concentrations. As a consequence, the choice for a model is more difficult, and for the most aggregated system, TeHphFeBrrbenzene, no appropriate model to fit the experimental data could have been chosen. The basic unit is apparently the trimer for both simple halides and the tetrachloroferrate, with a bond energy in a linear trimer of 3.9-4.6 kcal/mol. Earlier's and more recentle evaluations of the dipole moments of these salts from dielectric constant measurements in benzene suggest that no dimers but indeed trimers are formed in solution, with a dipole moment of -13 D for the simple halides and -20 D for the tetrahaloferrates. (14) K. Shinoda in "Solvent Properties of Surfactant Solutions," K. Shinoda, Ed., Marcel Dekker, New York, N. Y., 1967, p 5. (15) A. 8. Kertes, 0. Levy, and G. Markovits in "Solvent Extrection Research," A. S. Kertes and Y. Marcus, Ed., Wiley-Interscience, New York, N. Y., 1969, p 177. (16) 0.Levy, Ph.D. Thesis, The Hebrew University, Jersusalem, 1969.
The Journal of Phg8ical Chemistry, Vol. 74, N o . 80,1970
