4202
A. S. KERTESAND G. MARKOVITS
Acknowledgment. We wish to express our thanks to the U. S. Public Health Service (Grant GM-08347,
National Institute of General Medical Sciences) for financial support.
Activity Coefficients, Aggregation, and Thermodynamics of Tridodecylammonium Salts in Nonpolar Solvents by A. S. Kertesl and G. Markovits Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel (Received May 31,1968)
Vapor pressure lowering measurements on benzene, carbon tetrachloride, and cyclohexane solutions of trilaurylamine chloride, bromide, nitrate, perchlorate, and bisulfate have been carried out a t 25, 37, and 50”. The data analyzed via the Gibbs-Duhem relation reveal that the activity coefficients of the salts decrease abruptly with increasing concentration up to about 0.1 m and tend to level off a t higher concentrations. Interpreting the osmometric data in terms of molecular association of the solutes via the Bjerrum relationship, dimers and higher oligomers have been shown to exist in solution even a t the lowest measurable concentration. The formation constant of dimers in benzene increases in the order chloride < bromide < perchlorate < bisulfate. The thermodynamic functions evaluated from the change of the formation constants suggest that the bond energy is not greatly affected by the change in the solvent. The average AH” per dipole bond in a linear oligomer is about 3.3 kcal/mol, while in a cyclic oligomer it is around 4.1 kcal/mol.
The current interest in long-chain aliphatic amine salts in solvent-extraction processes has led us to undertake a thermodynamic study designed t o give information concerning ionic and molecular interactions in solutions of such salts in nonpolar, water-immiscible organic solvents. As a part of that project, we report here the results of osmometric, vapor pressure lowering measurements of several trilaurylammonium salts in benzene, cyclohexane, and carbon tetrachloride at 25, 37, and 50”. Allrylammonium salts, when dissolved in low dielectric constant organic solvents, usually exist in the form of ion pairs.2 Depending upon the nature of the amine salt and its concentration and the nature of the organic solvent employed, the ion pairs may either dissociate or associate into higher aggregates. In nonpolar solvents the ionic association constants for various alkylammonium salts has been shown t o be of the order of lO6-lO’, indicating that the dissociation of the ion pairs is negligible in salt concentrations practical for solvent-extraction processes (>0.01 M ) . 3 On the other hand, electrostatic molecular association of the ion pairs into dimers and higher oligomers in nonpolar solvents is a common phenomenon and is known t o affect metal extraction greatlye2v3 Consequently, for a mass action law treatment of the experimental data, activity coefficients are needed to correct The Journal of Physical Chemistry
for both the nonspecific nonideality of the solutes and for the specific nonideality caused by the aggregation of monomers. The considerable amount of both qualitative and quantitative work on the extent (number) and degree (size, both of aggregated units) of association of various long-chain aliphatic amine salts has recently been re~ i e w e d . ~Diluent ?~ vapor pressure lowering, determined by direct vapor pressure measurements or by isopiestic balancing, has been used by Coleman and Roddy4-6 for investigating departures from ideality in behavior of trioctylammonium sulfate and bisulfate in benzene. Bucher and Diamond,’ Muller and Dia(1) Chemistry Division, Argonne National Laboratory, Argonne, 111. 60439. (2) Y. Marcus and A. 9. Kertes, “Ion-Exchange and Solvent Extraction of Metal Complexes,” Interscience Division, John Wiley & Sons, Inc., London, 1968, Chapter 10. (3) A. S. Kertes in “Recent Advances in Liquid-Liquid Extraction,” C. Hanson, Ed., Pergamon Press Ltd., London, 1968, Chapter 1. (4) Chemical Technology Division Annual Progress Reports, Oak Ridge National Laboratory, Oak Ridge, Tenn., ORNL-3452, 1963; ORNL-3627, 1964, p 206; ORNL-3945, 1966, p 186. (5) C. F. Coleman and J. W. Roddy in “Solvent Extraction Chemistry,’’ D. Dyrssen, J. 0. Liljenzin, and J. Rydberg, Ed., NorthHolland Publishing Co., Amsterdam, The Netherlands, 1967, p 362. (6) C. F. Coleman, 1967, private communication. (7) J. J. Bucher and R. M. Diamond, J . Phys. Chem., 69, 1565 (1965).
TRIDODECYLAMMONIUM SALTSIN NONPOLAR SOLVENTS
4203
Table I : Values of the Coefficients A and B in the Density Equation Solvent
Benzene Cyclohexane
Carbon tetrachloride
t,
=c
25 37 25 37 50 25
A
0.8736 0.8608 0.7738 0.7622 0.7606 1.5844
TLA-HC1
0.0034
-0.400
mend,* and WilsonQstudied the distribution of several inorganic acids between their aqueous solutions and various organic solvents containing trioctyl- or tridodecylamine base and interpreted the results in terms of aggregation of the amine salts formed in the organic phase. The two-phase emf-titration method has been used in the studLy of the aggregation equilibria of longchain amine salts in various organic solvents. Osmometric data, preliminary in nature, on various dry binary systems consisting of some trilaurylammonium salts and an organic solvent have also been reported. 12-16 Experimental Section A!laterials. Tri-n-dodecylamine (trilaurylamine), a RhBne-Poulenc product, reagent grade BDH product of organic solvents, and Eastman Kodak White Label triphenylmethane, triphenylamine, benail, and tri-n-octylamine and BDH biphenyl were used as obtained. The procedures used in this laboratory for the preparation and purification of solid trilaurylamine (TLA) salts have been described e l ~ e w h e r e . ’ * ~All ’ ~ ~salts ~~ are white and crystalline, nonhygroscopic, anhydrous, and stable, at least up to their melting points. The melting points, uncorrected, were: TLA-HC1, 84-85’ ; TLA-HBr, 86-87’ ; TLA-HW03, 51-52’ ; TLA-HC104, 58-59’ ; and TLA-H2S04, 64-65’. They were checked for purity by elemental analysis and argentometric or acidimetric titrations of their alcoholic solutions. None of the salts contained either free acid or base. Densities. The densities of the solutions, prepared on a molar basis, were determined at least in duplicate with calibrated 63-ml pycnometers. For interconversion of molal and molar concentration scales, these densities were fitted to the binominal function d , = A BCM,with molar concentration of the amine salt, CM, as the independent variable. The values of the coefficientsA and B are given in Table I. Osmometry. The vapor pressure lowering of the organic solutions was determined by a Mechrolab osmometer, Model 301-A, at 25, 37, and 50’. As suggested by the manufacturer, a solute concentration of up to about 0.1 M was found to be the upper limit of achieving high accuracy and good reproducibility. The method consists essentially of determining the
+
TLA-HClOr
TLA-HBr
TLA-HNOa
0.031 0.031 0.096 0.096 0.096 -0.406
0.015
0.03
0.113
0.113 0.113 0.113 -0.431
-0.464
TLA-HzS04
0.03
-0.424
temperature difference of a solution and the pure solvent when brought into quasi-vapor equilibrium in a closed chamber. The theory and the practical limitations of the procedure have been previously reported. l8+0 The temperature difference is determined by matched thermistors and is expressed by the quantity Ar in the bridge, reading between the solvent on both thermistors and the solvent on one and the solution on the other. At equilibrium, the maximum Ar obtained for a given concentration m3is given by the equation d Ar dmk3
-=---
rlBR M I AH1 1000
(1)
where B is a temperature-dependent constant, rl is the greater resistance, 43 is the osmotic coefficient, AH1 is the heat of vaporization, and M I is the molecular weight of the pure solvent. We applied eq 1 and used triphenylmethane, tri(8) W. MDller and R. M. Diamond, J . Phys. Chem., 70, 3469 (1966). (9) A. S. Wilson in “Solvent Extraction Chemistry,” D. Dyrssen, J. 0. Liljenzin, and J. Rydberg, Ed., North-Holland Publishing Co., Amsterdam, The Netherlands, 1967, p 369. (10) E. Hogfeldt and F. Fredlund in “Solvent Extraction Chemistry,” D. Dyrssen, J. 0. Liljenzin, and J. Rydberg, Ed., NorthHolland Publishing Co., Amsterdam, The Netherlands, 1967, p 383, and references therein. (11) M. A. Lodhi and E. Hogfeldt in “Solvent Extraction Chemistry,” D. Dyrssen, J. 0. Liljenzin, and J. Rydberg, Ed., NorthHolland Publishing Co., Amsterdam, The Netherlands, 1967, p 421; .M. A. Lodhi, Ark. Kemi, 27, 309 (1967). (12) G. Scibona, S. Basal, P. R. Danesi, and F. Orlandini, J . Inorg. Nud. Chem., 28, 1441 (1966). (13) F. Orlandini, P. R. Danesi, S. Basal, and G. Scibona in “Solvent Extraction Chemistry,” D. Dyrssen, J. 0. Liljeniiin, and J. Rydberg, Ed., North-Holland Publishing Co., Amsterdam, The Netherlands, 1967, p 408. (14) G. Markovits and A. S. Kertes in “Solvent Extraction Chemistry,” D. Dyrssen, J. 0. Liljenzin, and J. Rydberg, Ed., NorthHolland Publishing Co., Amsterdam, The Netherlands, 1967, p 390. (15) A. S. Kertes and G. Markovits, Symposium on Thermodynamics of Nuclear Materials with Emphasis on Solution Systems, International Atomic Energy Agency, Vienna, Sept 1967. (16) I. Mayer, G. Markovits, and A. S. Kertes, J . Inorg. Nucl. Chem., 29, 1377 (1967). (17) A. S. Kertes, H. Gutmann, 0. Levy, and G. IMarkovits, Israel J. Chem., 6 , 421 (1968). (18) A. P. Brady, H. Huff, and J. W. McBain, J . Phys. CoZZoid Chem., 5 5 , 304 (1951). (19) R. H. Mnller and H. J. Stolten, And. Chem., 7, 1103 (1953). (20) W. I. Higuchi, M. A. Schwartz, E. G. Rippie, and T. Higuchi, J . Phys. Chem., 63, 996 (1959). VoZume 72, hlumber 18 h’ozernber 1968
A. S. KERTESAND G. MARKOVITS
4204 Table 11: Values of the Coefficients a, b, c, and d in eq 2"
Solvent
t, o c
B B CT B
B C C C CT
B C CT
B C C C CT
B CT
Conon range, mol/l.
b
a
Std dev
TLA-HCI 0.7916 1.1139 0.7262
-1.945 -10.138 -3.340
8.46 41.31 10.22
0.00059 0.00027 0.00030
TL A-HBr 0.9173 0.00035 0.9281 0.00043 0.5067 0.00107 0.5314 0.00145 0.5094 0.00027 0 7528
-6.839 -9.522 -4.368 -5.258 -3.349 -9.785
36.23 122.01 26 62 36.84 19.43 52.80
0.00038 0,00012 0,00014 0.00013 0.00015 0.00015
TLA-HNOa 0.00086 0.8478 0.00067 0.4602 0.00283 0.3916
-5.535 -3.472 0.626
31.26 17.30 -10.35
0.00010 0,00004 0.00020
TLA-HClOI 0 7438 0.00212 0.2275 0.00144 0.3026 0.00171 0.3170 0.00092 0,4334
-6.165 -1.562 -1.765 -2.179 -6.486
22,03 7.89 5.18 8.00 33.42
0 00014 0.00011 0.00008 0.00010 0.00007
TLA-H~OI 0.00004 0.5560 0.00171 0.2942
-3.418 -2.100
13.28 11.94
0.00002 0.00012
25 37 25
0.01-0.10 0.01-0.03 0.01-0.10
0.00205 - 0.00155 0.00055
25 37 25 37 50 25
0.007-0.10 0.005-0.03 0 004-0.067 0.007-0.07 0.007-0.07 0.005-0.08
- 0.00021
25 25 25
0.01-0 * 10 0.01-0.08 0.01-0.10
25 25 37 50 26
0.01-0.10 0.008-0.10 0.01-0.10 0.01-0.10 0.004-0.11
25 25
0.01-0.07 0.01-0.10
I
d
I
- 0.00010
I
I
I
' B is benzene; C is cyclohexane; and CT is carbon tetrachloride,
octylamine, trilaurylamine, benzil, and biphenyl as reference standards. All exhibit identical osmometric behavior in the concentration range investigated, as shown, for example, in Figure 1 for benzene solutions at 37". Independent freezing point measurements on triphenylmethane in benzenez1indicate ideal behavior of the solute in the concentration range studied in this work. More recent and precise vapor pressure measurements on benzene solutions of benzil and triphenylmethane at 2504t6indicate a slight deviation of osmotic coefficients from ideal behavior, especially at higher solute concentrations. When calculating the activity coefficients of trilaurylamine salts in benzene, these deviations have been taken into account (see below). For all osmometric measurements the anhydrous salts were dissolved in dry organic solvents. Triplicate osmometric measurements in the concentration range studied show agreement t o within 1%or better. The values for the osmometric concentrations, S , were calculated from Ar via the calibration curves, and the obtained S values were fitted into the polynome
S
= a
+ bB + cB2 + dBa
(2)
as a function of the analytical concentration B, of the solute. The constants of eq 2, calculated by a computer program, are compiled in Table 11,along with the The Journal of Physical Chemistry
st,andard deviations. They are strictly valid only in the concentration ranges indicated.
Activity Coefficients For a nonelectrolyte or nonionized molecule in any solvent, the osmotic coefficient is
(3) where m is the molality of solute, MI is the molecular weight of solvent, and al is its activity. The ratio R of the osmotic coefficient of any solute to that of a standard is given by
R
=
#$3/#$2
= mdm3
(4)
where the subscript 2 refers to the calibration substance and the subscript 3 to the solute under investigation. The basis for the analysis of the osmometric data in our binary systems in terms of activity coefficients is the Gibbs-Duhem equation, which requires that #$ and y, the activity coefficient, be interrelated by -d In y
=
-d#$
+ (1 - #$)dIn m
(5)
(21) N.E.White and M. Kilpatrick, J.Phys. Chem., 59, 1044 (1955).
TRIDODECYLAMMONIUM SALTSIN NONPOLAR SOLVENTS
4205 In y3 = In YZ
+ In R +
= In yz
+ In R -
( R - 1) d In (-yzmz) ml'
1- R d ~2mz
(6)
For the case under consideration, where the solute concentration in the nonpolar solvent varies in the range between 0.005 and 0.1 M , eq 6 becomes In y3" = In 72"
=a
Figure 1. Osmometric calibration plot in benzene a t 37": A, triphenylmethane; 0 , trilaurylamine; 0 , trioctylamine; 13,biphenyl.
+ In R"
-
where the single primes refer to the lowest concentration data. Since y2 and y2' are equal to unity (see Experimental Section), eq 7 simplifies to In
73''
= In
R" -
mz"
1-R
R'
dY2mz- In 7 (8) Y3
80-
60-
. El
p 4020-
I ob2
% I
O.b3
Ob4
Ob5
Ob6
El2
Figure 2. Plot of Gibbs-Duhem equation (in benzene at 25"): A, TLA-"03; 0, TLA-HBr; 0 , TLA-HC101; 0, TLA-HxS04.
By plotting (1 - R)/m2against m2)the area under the curve between the limits m2' and m2" (experimental points) gives the integral on the right-hand side. Such plots are shown in Figure 2 for some of the solute-solvent pairs investigated. The value of the integral mas determined by a computer program. I n some cases, the relatively long extrapolation to infinite dilution may be subject to a small constant error in the activity coefficients represented by the polynomial (for the concentration range investigated) log y3 = A 3. Bm3
+ Cm? -k DmS3
(9 1
The constants of eq 9, calculated by a computer pro-
-15
002
0.04
006
008
010
m3
Figure 3. Plot of eq 9 (TLA-HBr a t 2 5 " ) : A, C&s; 0, CeHlz; 0, Cc4.
With m2 as the independent variable and including the ratio R, the integral formz2of eq 5 becomes
Figure 4. Plot of eq 9 (TLA-HBr in cyclohexane): A, 25"; 0 , 37"; 0, 50".
(22) K. 8 . Pitzer and L. Brewer, "Thermodynamics," MoGrawHill Book Co., Inc., New York, N. Y . , 1961, p 321.
Volume 72, Number 12 November 1968
A. S. KERTESAND G. MARKOVITS
4206
Table 111: Values of the Constants in Eq 9 for the Evaluation of Log 7 3 as a Function of m3 A
Benzene, at 25" -8.575 55.10 -8.755 57 83 - 13,211 94.77 - 19.590 213.67
-0.0857 0.0259 -0,2291 -0.4012
TLA-HBr TLA-HNOs TLA-HClOa TLA-H~SOI
- 0.0794
- 0.2205 - 0.4054
Benzene,a a t 25' -9.394 -9.310 -13.637 - 19.840
TLA-HBr TLA-HNOa TLA-HClOd
-0.3586 0.4290 - 0.4467
Cyclohexane, a t 25" -27.207 347,93 18.973 168.98 -23.370 195.09
TLA-HCl TLA-HBr TLA-"Os TLA-HClOI TLA-H8Oa
-0.1361 -0.1160 -0.1860 - 0.3971 - 0.5640
-
I
- 0,0261
-
64.52 62.14 98.98 216.12
-
Carbon Tetrachloride, -21.310 -36.002 32.303 -42.525 -23.641
-
a t 25' 320.47 564.25 540.05 546.15 177.62
Benzene, at 37" -23.734 810.48 - 15.303 327.42
0.0636 0.0144
TLA-HBr TLA-HC104
-0.5190
Cyclohexane, a t 37" -21.159 221.46 - 19.526 151.01
TLA-HBr TLA-HCIOI
-0.1597 - 0.5402
Cyclohexane, a t 50" -20.751 222.61 -12.709 53.82
- 0.2278
D
C
TLA-HBr TLA-HNOs TLA-HClO4 TLA-H~SOI
TLA-HCl TLA-HBr
a
B
Std dev
- 151.09 -156.90 -308.06 - 975.26
- 195.97 - 174.65 - 323.80 -987.41
- 1722.36
0.0049 0.0015 0.0057 0.0046 0.0049 0.0015 0.0060 0.0045
-615 -47 - 615.69
0.0140 0,0058 0.0163
-2094.54 3748.50 - 3575 89 - 2487.04 -464.29
0.0064 0.0023 0.0071 0.0355 0.0404
-
I
- 10482.5 - 3272.9
0.0001 0.0017
-941.63 -463.48
0.0063 0.0102
-961.83 -83.99
0.0061 0.0247
Calculated using Coleman's data6 (see the text).
::I
I
0.4
fi
1
0.2
t
0.8
002
004
006
008
010
0.12
E,
Figure 5. Variation of the activity coefficient ys with the concentration of the salt in benzene at 25": A, A, TLA-HNOa; V, V, TLA-H2S04; 0, U, TLA-HBr; 0, e, TLA-HC104. Filled symbols are based on values corrected using Coleman's data; open symbols are uncorrected (see the text). The Journal of Physical Chemistry
gram, are compiled in Table 111along with the standard deviation. The variation of log y3 with rn3 for some of the systems is shown in Figures 3 and 4. Using Coleman's data6 on the activity coefficients of benzil in benzene, the constants for polynomial 9 have been recalculated and are included in Table 111. The differences in the activity coefficients ys are slight, as can be seen from the curves in Figure 5.
Molecular Association Another interpretation of the observed deviation of the binary systems from an ideal behavior is based on the assumption of molecular association of the solutes. The highly polar (dipole moments 8-9 D23)monomeric ion pairs, RzYH+X-, in low dielectric constant and nonionizing solvents, are capable of electrostatic dipole interaction to yield quadrupoles or dimers, (F&NH+X-),. At higher concentrations of the solute, in the (23) G. Markovits, Ph.D. Thesis, The Hebrew University of Jerusalem, Jerusalem, Israel, 1968.
TRIDODECYLAMIMONIUM
SALTS IN NONPOLAR SOLVENTS
majority of cases, formation of trimers and higher oligomers also has tal be considered. If an activity coefficient of unity for the aggregates is assumed, the total concentration of the amine salt is given by
B = b
+ nb"Pn + pbPpP + @'Pa
b
+ b"@n + bPpP + bqPp
(11) and the average number of monomers in a series of multirners is given by the relationship =
B/X (12) If it is furthLerassumed that the dissociation of the monomeric ion pairs into its ions is negligible2and that the formation of dimers and higher aggregates follows the mass action law, the concentration of free monomers b may be calculated from the known values of B and the experimental values of S using the Bjerrum relationship . ~= i
b(dS/db)
In b
=
In bl
=
+
B
=
aS
1:
1 / d~ In S
(13) (14)
since in the most dilute solution measured the electrostatic association is negligible and the approximation bl S is likely to be valid. b can be evaluated from a graphical extrapolation of eq 14. The value of b is most important in the determination of extent and degree of association. It is often difficult to obtain reliable values of bo, especially when association occurs over the whole range of solute concentration studied. Equation 14 can be formulated as
-
rS
PS1
Introducing eq 19 into eq 10 and 11, one obtains n
bo1
+ Cn(bo"p.)I"
fi = bo1
+ C(bonPn)I"
B
=
(20)
2
n
(10)
where b is the concentration of the monomeric species, in moles per liter; n < p < q are the number of monomers in the aggregates formed; and the 0's are the overall stability constants of these aggregates. The concentration of species present in the system, as determined experimentally, can be given accordingly
S
4207
(21)
2
Equations of this type may readily be solved by a linear least-squares program, using a digital computer, for values of n and p, and their standard deviation. For some of the binary systems investigated, the equations are inconsistent on account of small experimental errors, and more than one oligomer combination can be assigned to fit the experimental data. I n such cases, the oligomer combination with the lowest value of the error-square sum
p =
C(B - B c a l o d ) '
+c(S-
Soalcd)2
(22)
has been adopted. Some of our preliminary data,14 obtained previously by the curve-fitting method, have now been recalculated. As can be seen from the values given in Table IV, the agreement is satisfactory. Table IV also shows a comparison with values obtained by others, using or osmometric technique. l3 either distrib~tion',~,",2~
Evaluation of Standard Free Energies Thermodynamic properties of systems investigated here can be calculated from the change of the equilibrium constant
Pn =
[(TLA-X),]/[TLA-X]"
(23)
of the reaction
nTLA-X J_ (TLA-X).
(234
with the temperature, for which AG" = -RT In p,
(24)
Instead, we have chosen t o evaluate thermodynamic functions via the Gibbs-Helmholtz equation AG" = AH"
d + TAS" = AH" + T-AGO dT
(25)
and the van't Hoff equations (under constant-pressure conditions)
and In I
=
J -I/.L~ d In S SI
(17)
when In b = In bo
+ In I
(18)
making the single assumption that the heat of reaction, leading to the equilibrium constant p,, is independent of temperature in the interval 25-50' Then an integration of eq 26 gives a function which is linear between In 0, and 1/T I
or b =,boI (19) and I can be calculated for any experimentally determined B and S.
(24) E. Hogfeldt and M. de Jesus Tavares, Trans. Roy. I n s t . Technol., Stockholm, No. 228 (1964).
Volume 72, Number 12 November 1968
4208
A. S. KERTESAND G. MARKOVITS
Table I V : Log p, for Trilaurylamine Salts a t 25'
_-----____-----
Solvent
Benzene
bo 2 3 4 30
0.0055 1.34 2.53 2.76
bo 2
0.0035 2.38 14.00
Benzene
16
Cyclohexane
bo 2 6
0.0012 3.46 13.28"
bo 2 4 10
0.0012 2.91 7.95
Reference 14. This work. References 7 and 8. benzene. " Printing error in ref 14.
lnp,
+ constant
AH," RT
= -~
AH,"
RT
=
b
+ Cb' exp( n
(27)
R
-=+ -) AH,"
AX,"
R
0.0046 2.26
References I 1 and 24.
2.27 14.07
e
References 12 and 13.
o-Xylene rather than
Table V : Heat and Entropy of Reaction 23a AH,',
System
n
koa1 mol -1
(TLA-HC1)-benzene (TLA-HBr )-benzene
2 2 3 3 6
-3.35 -3.29 -11.98 -6.59 -25.18
(TLA-HBr )-cyclohexane
G b o ,
cal deg-1
-5.6 -4.9 -27.5 -0.44 -34.2
mol-'
(29)
the data given in Table VI1 for the TLA-HBr-cyclohexane system. In the other two systems, the aggreement between the experimental and calculated (eq 29 and 30) values is equally good.
(30)
Discussion
The last two equations have been solved by a nonlinear least-squares procedure, and the values obtained are shown in Table V. From these values the changes in the free energy have been calculated and compiled in Table VI. The values of log 0, at 25" in Tables IV and VI, calculated by two different methods, are in good agreement. The same is true for functions B and S and the average aggregation number W , as can be shown from The Journal of Physical Chemistry
1.49' 3.13
TLA-HBr 0,0012 2.92 7.86 21.70
+- R
n
S =b
1.72
TLA-H~SOI 0.0010 3.63 13.66
AX,"
+ Crib" exp
and
Osmometrye
1.17'
0.0085 1.60
TLA-HClO, 0.0036 2.41 14.00 29.78
Now, eq 20 and 21 of the auxiliary functions can be written in the form B
0.009 1.30
TLA-HBr 0.0055 1.34 2.76
where the constant of integration is identified wit'h ASO/R to give In@, = -~
Emfd
46.10
8
Benzene
-Log p Distribution'
TLA-"21 0.0080 1.27
bo 2
Benzene
Computerb
GraphioaP
n
There are essentially two effects which contribute to the deviation of the solutes investigated here from ideal behavior. One effect is the solute-solvent interaction, which, among other consequences, reduces the activity of the free solvent, and another is the association of ions beyond the formation of ion pairs, leading to the formation of various oligomers and possibly also micelles. I n the range investigated, the concentration dependence of the activity coefficients is similar for all of the solute-solvent pairs studied : they decrease with in-
4209
TRIDODECYLAMMONITJM SALTSIN NONPOLAR SOLVENTS Table VI: Standard Free Energy Changes and Formation Constants of Reaction 23a 25'
(TLA-HCl)-benzene (TLA-HBr )-benzene
2 2 3
(TLA-HBr )-cyclehexane
3 6
Log
-1.71 -1.83 -3.79 -6.45 -14.98
1.25 1.34 2.76 4.72 10.90
Table VI1 : Experimental and Calculated (Eq 29 and 30) Values of B , S, and ? inithe System Trilaurylamine-H,ydrobromide-Benzenea t 25, 37, and 50" r---S-----
Exptl
Calcd
0.0066 0.0086 0.0133 0.0199 0.0333 0.0466 0.0633 0.0666
O.OCl59 0.0076 0.0123 0.0193 0.0328 0.0456 0.0543 0.0664
25 " 0.0036 0.0045 0.0065 0.0091 0.0133 0.0169 0.0192 0,0223
0.0105 0.0140 0.0210 0.0280 0.0350 0.0420 0.0490 0.0560 0.0630 0.0700
0.0106 0.0144 0,0222 0.0290 0.0353 0.0421 0.0480 0.0562 0.0635 0.0703
0.0140 0.0210 0.0280 0.0360 0.0420 0.0490 0.0560 0.0630 0.0700
0.0144 0.0210 0.0277 0.0352 0.0424 0.0492 0.0556 0.0615 0.0700
? -,L.-
Calcd
-
Exptl
Calod
0.0037 0.0045 0.0063 0.0088 0.0129 0.0165 0.0188 0,0219
1.83 1.91 2.04 2.19 2.50 2.76 2.78 2.98
1.60 1.69 1.95 2.19 2.54 2.76 2.86 3.02
37 O 0.0061 0.0076 0.0104 0.0127 0.0147 0.0168 0.0186 0.0210 0.0231 0.0250
0.0061 0.0076 0.0106 0.0129 0.0149 0.0171 0.0189 0.0213 0.0234 0.0253
1.72 1.84 2.02 2.20 2.38 2.50 2.63 2.67 2.73 2.80
1.74 1.89 2.05 2.23 2.38 2.46 2.54 2.64 2.70 2.78
50" 0,0082 0.0108 0.0133 0.0160 0.0185 , 0.0208 0.0229 0.0248 0.0275
0.0082 0.0108 0.0134 0.0161 0.0186 0.0209 0.0229 0.0248 0.0275
1.72 1.94 2.10 2.19 2.27 2.35 2.44 2.54 2.54
1.76 1.94 2.07 2.19 2.28 2.35 2.43 2.48 2.54
Exptl
Bn
kcal -1.65 -1.77 -3.45 -6.45 -14.58
Log
Bn
1.19 1.24 2.42 4.52 10.22
kcal
-6.45 -14.13
Log
Pn
4.34 9.52
The principles and theories of the chemistry of surface-active colloidal electrolytes implicitly assume that the formation of micelles at the critical micelle concentration takes place by aggregation of monomers, without intermediate, lower aggregates being formed. Investigations in connection with solvent extraction equilibria revealed that the aggregation of amine salts in nonpolar organic solvents involves intermediate stages in the monomer-micelle equilibrium. This study has confirmed previous findings (for earlier data, see ref 2 and 3) that the stepwise formation of oligomers in amine salt-organic solvent systems (RZNH+X-)%--+
creasing solute concentration, owing to an increasing aggregation number. This is apparently in contrast t o the behaviolr of anionic surface-active agents of the dinonylnaphthalene sulfonate type in benzene, cyclohexane, and heptane, where the aggregation number is independent of solute c o n ~ e n t r a t i o n . ~ ~ ~ 2 ~ The positions of the activity coefficient curves reveal, in general, that at a given solute concentration 73 depends on the anion associated t o the trilaurylammonium cation. The lowering of log 73 is less drastic with smaller anions, which exhibit a lower tendency toward aggregati~n.~'
50°---
AGO,
AGO,
koa1
System
---_-_
370
7--
AGO,
(R3NH+X-)mioelle
satisfies the requirements of the mass action law. The equilibria in this dipole-dipole aggregation process2 depend on both the nature of the solute and that of the solvent. The effect of the amine class from which the salt is derived and that of the length of the aliphatic chain has been discussed previously.28 I n this article it is shown that the nature of the anion is an equally important factor in determining the extent and degree of aggregation. I n a given solvent the aggregation of trilaurylamine bisulfate and perchlorate is more pronounced than that of the corresponding chloride or bromide. The extent of dimerization, for example, of the salts increases in the order C1- < Br- < Clod- < HS04-, and the degree of their aggregation also increases roughly in the same order (Table IV). The nature of the organic solvent and its solvation power are equally major parameters affecting aggregation. This can be shown by comparing the n and the corresponding Pn values of trilaurylamine bromide in (25) S. Kaiifman and C. R. Singleterry, J . Colloid Sci., 12, 465 (1957). (26) R. C. ]&le and C. R. Singleterry, J. Phys. Chem., 68, 3453 (1964). (27) In this connection it should be noted that the explanation for ideal behavior of similar solutes in an anion-exchange equilibrium offered previously (G. Scibona, R. A. Nathan, A. S. Kertes, and J. W. Irvine, Jr., J . Phys. Chem., 70, 375 (1966)) becomes untenable in view of the results presented here. The reason for the quasi-
ideal behavior observed in the (TLA-HC1)-(TLA-HBr) and (TLAHClOd)-(TLA-HRe01) exchange equilibria is that there is a similar deviation from ideal behavior of both salts in the pairs, rather than a conformation to their ideal behavior. (28) A. S. Kertes, J . Inorg. Nucl. Chem., 27, 209 (1965).
Volume 72*Number 12 November 1968
4210
benzene and cyclohexane, for example. The difference can be explained by the higher solvation power of the aromatic^,^^^^ exhibited by a solute-solvent interaction leading t o a shielding of the high dipole moment of the R3NH+X- ion pair and its stabilization, increasing simultaneously the compatibility of the polar monomer with the solvent. As was predictable, at higher temperatures the extent of aggregation is lowered, but its degree is apparently unaffected in the temperature range studied. Unlike the case of the heats of association by hydrogen bonding, no information is available on energies of association by an essentially electrostatic dipole-dipole interaction. Such interaction energy depends mainly on the dipole moment of the ion pair and the angle of their orientation in the molecular aggregate. Using the postulate of additivity of energies of normal electrostatic attractions and assuming that the energies calculated here are the sum of the dipole interactions (of equal length of dipole bonds in an oligomer) between undissociated ion pairs rather than between individual charges of the ions forming the ion pair, we have attempted to interpret the thermodynamic values given in Table V. The thermodynamic quantities for the formation of TLA-HC1 and TLA-HBr dimers in benzene are sufficiently close t o justify the above assumptions. AHz' for both salts in benzene is close t o AH3"/2 obtained suggesting that the for (TLA-HBr)3 in bond energy is not greatly affected by the change in the
The Journal of Physical Chemistry
A. S. KERTESAND G. MARKOVITS solvent. These values suggest, furthermore, that the dimers in benzene and the trimer in cyclohexane are linear. On the other hand, the high value of AH3' of the bromide in benzene can be explained by assuming that (TLA-HBr)3 is predominantly cyclic. The same is apparently the case with (TLA-HBr)e in cyclohexane. The average AH" per dipole bond in a cyclic oligomer of (TLA-HBr), is around 4.1 kcal/mol, regardless of whether the solvent is benzene or cyclohexane. When assuming a linear oligomer rather than cyclic for the trimer in benzene and the hexamer in cyclohexane, the average AH' per bond would increase to above 5.0 kcal/mol, which, compared with the AH2' of 3.3 cal/mol in the linear dimer, seems t o be unreasonably high.
Acknowledgments. The authors itre grateful to Dr. C. F. Coleman, Oak Ridge National Laboratory, for making available his osmotic coefficient data prior to their publication. Preliminary computer calculations have been carried out during the stay of A. S. K. with Professors L. G. Sillen and E. Hogfeldt at the Royal Institute of Technology, Stockholm. The author expresses his sincere thanks to \hem for the invitation, and to the USAF, European Council of Aerospace Research, for financial support (Grant AF EOAR 65-22) of his stay. Computer time has been supported by the Swedish Government through Statskontoret. (29) A. 8. Kertes and Y. Haboueha, J . Inorg. Nucl. Chem., 25, 1531 (1963).
