NOTES
2272 tillation of 20 ml of TMG at atmospheric pressure in a nitrogen atmosphere, a large fraction of the carbon dioxide was lost by volatilization. The first fraction of 5 ml was 0.024 144 in carbon dioxide: the second and third fractions were 0.006 M. The product of TRIG used by us was 0.0017 M in carbon dioxide. It was distilled in a stream of nitrogen, the gas being passed through an Ascarite guard tube; the carbon dioxide content of the middle fraction was less than 0.001 M , being too small to be determined with any degree of accuracy. Experimental Techniques. To minimize uptake of atmospheric carbon dioxide, preparation and transfer TAIG solutions in AN was made in a nitrogen atmosphere, the nitrogen being passed through an Ascarite guard tube. The concentration of TMG was found by acidimetric titration of a l-ml aliquot after flooding with 20 ml of water. Brom cresol greenmethyl red was used as a mixed indicator. Potentiometricsand c onductometricgmeasurementswere carried out as described previously.
Acknowledgment. This work has been supported by Air Force AFOSR Grant 1223-67 and by a grant from the National Science Foundation. We are indebted to Professor J. F. Coetzee for constructive comments. (8) I. M. Kolthoff and M. K. Chantooni, Jr., J . Am. Chem. Soc., 87, 4428 (1965). (9) I. M. Kolthoff and M. K. Chantooni, Jr., ibid., 85, 426 (1963).
XIII. Another
Studies on Complexes.
Spectrophotometric Equilibrium Equation, a Simple, Versatile Apparatus Designed for
Its Use, and the Application to Some Charge-Transfer Interactions'
by P. R. Hammond Michelson Laboratories, Naoal Weapons Center, China Lake, California 08555 (Received Janilary 8 , 1908)
Results and Discussion The ionic mobility of the lyate ion, S-, was taken as 120,l while those of T1\IGH+ and (TAIG)zH+,75 and 40, respectively, were assumed to be the same as that taken for the corresponding DPG species-l Conductivity data of solutions of TAIG from 0.3 to 1.6 M are entered in Table I. Viscosity corrections were not made because of the low values of the conductance. The following paH values were found potentiometrically in solutions of 6.07 X 144 TAIGHPi containing various amounts of TRIG: 1.60 X M, 22.7; 4 3 0 X M , 23.1; 1.60 X lo-* M , 23.85; 116, 24.3; 0.19 M , 24.85; 0.374 A I , 25.3; 3.20 X 0.733 116, 26.7; 1.19 14,26.1; and 1.96 I d TAIG, 26.6, yielding values of pKdBHt and K * ~ , equal ~ + to 23.3 and 1.3, respectively. The value of 0.77 for the activity coefficient, calculated from the Debye-Huckel limiting law, was taken into account in treating the above potentiometric data. Neglecting BzH+ formation in solutions of T X G yields an average value of K d of~8.7 (Table I). Using Kfg,Ht = 1.3 in eq 1, we calculate an average value of p K d ~= S.9 and p K d ~ =~ 23.3. + A value of 32.2 is calculated for ~ K s Hwhich , is 3.7 units greater than the previously reported value.3 We believe that even the present value is too small, but of the right order of magnitude. The carbon dioxide content of a 11 1 1 solution of TAIG in AX probably was less than 2 x l O - 4 M . Even if this mere completely dissociated, the correction for this inipurity would be of the order of 300y0 of the specific conductance in the second column of Table I. With this large correction, p K d of ~ TAIG H the order of would be equal to 10, yielding ~ K S of 33.3. Because of the effect of traces of carbon dioxide, the true value may be larger. The Journal of Physical Chemistry
The equation proposed deals with the acceptordonor equilibrium of eq 1 A
+
D
=
(g - (: c)
K
C
(1)
c)
where a and d are the acceptor and donor concentrations put into solution and c is the equilibrium concentration of the complex determined by the constant K . The equation of Cilento and Sanioto2 may be simplified by introducing the dimensionless term n, the dilution, namely, the ratio of the volume of a diluted solution to its original volume. From the definition of K
K = n2c2-
and as a Q: c
[a
nzc (a - nc)(d - nc)
+ d + (n/K)]nc+ ad
(2) =
0
(3)
>d
[I - (1 -
[a
+ d + (n/K)]*
In the binomial expansion of the second bracket of eq 4, all terms in [ad/(a d)*I2 and higher are small, compared with earlier terms for all values of a and d , and
+
(1) Part S I I : P. It. Soc., 89, 8083 (1987).
Haminond and 11. H. Knipe, J . Amw. Chem.
(2) G. Cilento and D. L. Sanioto, 2. Phys. Chem. (Leipzig), 223, 333 (1963). The first reported use of a dilution method, although more complicated than those outlined here, would appear to be S. Skraup and L. Freundlich, Ann. Chem., 431, 243 (1923).
2273
NOTES
I
t
I
I
02
03
(16
OB
\\
LOO tl
Figure 1. Log A us. log n for systems of varying association constants K (1. mol-').
are neglected. Substituting the usual expression Ale for c, where A is the absorbance and E is the absorptivity a t the wavelength of measurement, then eq 5 , one of a family of equations, is derived. It is suitable for the
n nA Keacl 1
1
1
+ ea- + 2
(5)
condition a >> d or d >> a, where the terms l/ae or l/&,respectively, are neglected, or a = d. An experimental advantage of such a relation, namely, the preparation of one solution which is successively diluted, has already been notedSa From eq 5 , eq 6may Figure 2. Dilution cell for equilibrium stitdies.
be derived, and typical plots of log A against log n are shown in Figure 1. All equilibria produce curves of gradients contained within - 1, the slope for K = 03 , where the system obeys Beer's law, and -2, the slope for K = 0, where the absorbance decreases by the inverse square of the dilution. The equation can also be applied to gas-phase equilibria, where the total pressure of an acceptor-donor mixture may be reduced by equilibrating the sample with a known volume, and n relates t o this pressure ratio. For applying eq 5 , the apparatus of Figure 2 permits a quick and simple procedure. The original solution is put into the absorption cell uia the lower ball-shaped chamber, and measured volumes of solvent are added from the buret. Moisture-sensitive or otherwise reactive materials can be studied, for all taps and stop-
per seals are of Teflon. Wide necks of the cell and its connection facilitate liquid transfer. An alternative procedure is to introduce the lower concentration component from the buret t o the original acceptor-donor solution. In a manner similar t o the above, a family of equations represented by eq 7 applies,
1 1 A Keacl
+ E-1a + -E1d
(7)
where the Benesi-Hildebrand equation3 is one member of this family. Continuous variation plots for examining the stoichiometry of charge-transfer interactions are obtained by adding a solution of one component to an equal-concentration solution of the other. Another use (3) H. A. Benesi and J. H. Hildebrand, J . Amer. Cliem. Soc., 71, 2703 (1949).
Volume 72, Number 6
June 1968
2274
NOTES 1.0
0.8
,
\
1
\
-
NO2
N
O
z
NO2
W
-O
N
z
NO2 NO2
0.6
o'6 H H
0.4
\
H
\
\
N O z O N O z DICHLOROMETHANE
H
OICHLOROMETHPNE
I
3.0
400
mP
450
5SO
500
mP
mP
Figure 3. Observed spectra (as", 2-cm cell) for the mixtures shown. Concentrations ( M ) were (acceptor, donor): 0.50; (b) 0.005, 0.50; (c) 0.02, 0.20. Absorptions for the same concentration of acceptor are also shown, and (c) includes the small donor absorption.
(a) 0.029,
0 68 I O OICHLOROMETHANE 0.4
0,o
1
I
I
350
400
450
mP
'
0 350
0 400
1 450
_.-
350
400
460
500
mf-L
Figure 4. Observed spectra (26", 2-cm cells) for the mixtures shown. Concentrations (144) were (acceptor, donor): (a) 0.025, 0.312; (b) 0.36 X 10-2, 0.285; (e) 0.91 X 0.454. Also shown is the absorption for the same concentratioii of donor in (c).
for the apparatus would appear t o be in fluorescentquenching studies. Equilibria of systems producing the spectra of Figures 3 and 4 were studied (d >> a). Experimental Section Rlatheson Spectroquality solvents mere stored overnight over molecular sieve 4A, were decanted, and were distilled just prior to use. A sample of tetranitromethane, from the Trojan Powder Co., Allentown, Pa., having its melting point and infrared spectrum values in accord with literature values, was distilled once under reduced pressure. Tetramethyl-2-tetrazene had been prepared by the oxidation of 1,l-dimethylhydrazine, distilled from barium oxide, and was stored under dry nitrogen. Naphthalene, phenanthrene, p dinitrobenzene, and octafluoronaphthalene were crystallized from ethanol; hexanitrobiphenyl was crgstallized from glacial acetic acid containing 5% water; and tetracyanoethylene was crystallized from chlorobenzene. Benzene was Matheson Spectroquality grade dried with molecular sieve 4A as above, and tungsten hexafluoride, high purity, Alfa Inorganics, Inc., was used directly. Solutions of the hexafluoride were determined by gain in weight of the solvent in an all borosjlicate glass and Teflon apparatus. Details of the The Journal of Phusical Chemistry
latter procedure will be described in forthcoming p a,pers. Results and Discussion Colors of the systems of Figures 3 and 4 were produced immediately; the mixtures were prepared and were stable for at least 1 hr. Equation 5 was obeyed for all systems and Table I shows the experimental gradients, M , and intercepts, C, for least-squares estimates4 of the lines weighted by A4. Also shown are the n = 1.0 concentrations, the weighted standard deviations (SD) of the ordinate residuals, and the association constants ( K ) . Cell paths were 2 cm, room temperature was 26" throughout, and all estimates were performed on seven or eight points per run for n varying between 1.0 and 2.5. The values of K are all very small and, in most cases, the standard errors of the intercepts were comparable to C. Two criticisms that such small values indicate molecular complexing in solution are as follows. For weak associations, a "conspiracy" of experimental errors obscures the derived K and e values, so that little reliance can be placed upon themJ5and the scatter in results would seem t o justify this. Even for a system (4) P. R. Hammond, J . Chem. Soc., A , 145 (1968). (5) P. R. Hammond, ibid., 479 (1964).
2275
XOFES
Table I : Dilution Plots and Equilibria for Some Charge-Transfer Interactions Kavelength, Systema
TK AI-NAPH
HIL’DP-PHEN
PDNB-TMT
THF-BZ
TCE-BZ
TCE-OFN
460 470 480 450 460 470 450 460 470 380 390 400 410 370 380 390 400 390 400 410 420
K, M
C
a
d
0.528 0.707 1.046 0.607 0.801 1.098 0.874 0.947 1.009 0.440 0.463 0.506 0.557 0.691 0.624 0.604 0.624 2.196 2.181 2.168 2.422
-0.014 -0.012 -0.057 -0.002 -0.005 -0.028 0.035 0.030 0.045 0.037 0.026 0.010 0.019 -0.001 0,021 0.033 0.022 0.188 0.150 0.188 0.063
0.029 0.029 0.029 0.005 0.005 0.005 0.020 0.020 0.020 0.040 0.040 0.040 0.040 0.005 0 005 0.005 0,005 0.009 0.009 0.009 0,009
0.500 0.500 0.500 0.500 0.500 0.500 0.400 0.400 0.400 0.500 0.500 0.500 0.500 0.400 0.400 0.400 0.400 0.454 0.454 0.454 0.454
I
1035~
3 3 3 5 5 6
5 4 5 2 2 2 3 3 2 1 1 8 7 9 9
1. mol-1
-0.05 -0.04 -0.11 -0.01 -0.01 -0.05 0.10 0.08 0.11 0.17 0.11 0.04 0.07 0.00 0.08 0.14 0.09 0.19 0.15 0.19 0.06
a System abbreviations are: TNM-KAPH, tetranitromethane-naphthalene; HYDP-PHEN, hexanitrobiphenyl-phenanthrene; PDNB-TiLIT, p-dinitrobenzene-tetramethyltetrazene; THF-BZ, tungsten hexafluoride-benzene; TCE, tetracyanoethyleae; and OFN, octafluoronaphthalene. Solvents were as shown in Figures 3 and 4.
described in later articles. Values of E also exhibit scatter and are not tabulated. They may be readily derived from the data of Table I and are typically in 0.8 the region lo3 cm-l mol-’ 1. Continuous variation plots of Figure 5 verify that interactions producing the 0.6 spectra are 1: 1. The experimental observations’ on the tungsten hexA afluoride-benzene system are thus confirmed, although 0.4 the conclusion that the absorption arises from a “complex” is disputable. The tetracyanoethylene-benzene 0.2 measurements are in moderate agreement with earlier studies,* when account is taken of the difference of the units and of the temperature of examination. The 0.0 00 02 04 0.6 0.8 1.0 spectrum of the octafluoronaphthalene system with FRACTION OF ACCEPTOR tetracyanoethylene is similar to the benzene and is Figure 5. Continuous variation curves for: (a) WF&e&, displaced a little to longer wavelengths. This suggests (b) dinitrobenzene-tetramethyltetrazene, (e) C ( N O ~ ) ~ - C I ~ H ~ , that other charge-transfer maxima with this donor of measurement (d) C6rj4-C&, (e) C & ~ - C I ~ F ~Wavelength . should be similarly displaced and that its ionization (mp), combined acceptor plus donor concentrations ( M ) , and potential is close to and perhaps a little lower than cell p t h lengths (em) are: (a) 370, 0.16, 2; (b) 450, 0.10, 2; that of benzene. (e) 430, 0.10, 2 ; ( d ) 420, 0.05, 2; (e) 400, 0.05, 5. that exhibits no energy of interaction, but can allow charge-transfer transitions between loose-contact partners, a small experimental K value (about 0.20 1. mol-l) may be possible.6 Thus from the equilibrium measurements alone, and for the solvents chosen, there is no certain evidence that complexing occurs in any of the above systems. Experiments to examine this will be
Acknowledgment. The author thanks Mr. R. R. Lake for help in the preliminary stages of this study. (6) J. E. Prue, J . Chem. Sac., 7534 (1965). (7) H. F. Priest and W. C. Schumb, J . Amer. Chem. SOC.,70, 2291 (1948). (8) R. E. Merrifield and W. D. Phillips, ibid., 80, 2778 (1958). Volume 72. Number 6 June 1968
