C. C. THOMPSON, JR., AND P. A. D.
3096
since, if the hydroxyl groups of intermediate IV are equivalent, a path is available for oxygen exchange between substrate and solvent. The mechanism of hydrogen exchange are assumed to be the same as those presented for the dialkyl phosphonates.6-8 The acidcatalyzed exchange may be formulated as
DE
MAINE
VOl. 85
vent, step (3), and loses a proton from one of the hydroxyl groups, step (4). The hydroxide ion catalysis of exchange presumably proceeds by direct proton abstraction. There is no physical evidence for the tricovalent tautomer of phenylphosphonous acid. The 0
CiHr . .
\/
normal form
is probably stabilized by con-
P
/ \
H'
'OH
jugation of the phenyl and phosphoryl groups.20 The C E H ~,OH \ /
tautomer
P:
I
will lose this stabilizing energy,
OH
HO
/-\
D
HO
D
The first step (1) involves a fast pre-equilibrium protonation, followed by the rate-determining step (2), the fission of the P-H bond to give the tricovalent tautomer, which subsequently picks up deuterium from the sol-
[CONTRIBUTION FROM
THE
but a partial compensation may be expected due to the conjugation of the phenyl group and the lone pair of the phosphorus atom, such as JaffC21 has found in triphenylphosphine. (20) ?VI. I. Kabachnik, T. A. Mastryukova, and T. A. Melentiyeva, T e t r a hedron, 17, 239 (1962). (21) H. H. JaEC and L. D. Freedman, J . A m . Chem. Soc., 74, 1069 (1952).
DEPARTMENT OF CHEMISTRY, UNIVERSITY OF MISSISSIPPI, UNIVERSITY, MISS.]
Solvent Effects on Charge-Transfer Complexes. I. The s-Trinitrobenzene-Naphthalene Complex in Carbon Tetrachloride, n-Heptane, n-Hexane, Cyclohexane, Chloroform, or Carbon Disulfide1" BY C. C. THOMPSON, JR., AND P. A. D.
DE
MAINE'^
RECEIVEDMAY 13, 1963 Formation constants and absorptivities for the 1: 1 s-trinitrobenzene-naphthalene complex in six inert solvents (CCL, n-hexane, cyclohexane, n-heptane, CHCl,, or C S ) were calculated with spectrophotometric data collected a t fifteen wave lengths between 3300 and 4000 A. a t 20 and 45". All data were processed with an IBM 1620-60 K computer using programs with the self-judgment principle, fail-safe procedure, error-analysis, and instructions for correcting concentrations for density-volume-temperature changes incorporated. Absorptivities ( a c ) for the complex a t the absorption maxima (near 3600 b . )a t 20' vary from 1294 ( f 2 2 ) for n-heptane to 1540 ( f 1 3 ) for n-hexane. As the temperature is increased from 20 to 45", the absorptivities decrease by approximately 10% except in CHCl3 systems where those between 3650 and 4000 A. are unchanged. The formation constant ( K )is independent of wave length a t each temperature in all solvents except n-heptane where a t 20" K , in moles/l. units, is 9.58 (kO.17) for wave lengths between 3300 and 3700 A., and then gradual!y increases to 14.G1 (f.0.17) a t 4000 b. At 45O, K in n-heptane is G 12 (f.0.09) a t wave lengths up t o 3850 A . , then it increases to 8.27 ( f 0 . 0 9 ) a t 4000 A. Average values for K a t 20" vary from 1.82 (f.0.08) in CHCL to 9.58 ( f 0 . 1 7 ) in n-heptane. However, the heat of complex formation appears to be independent of the inert solvent with a median value near -3.0 kcal. per mole except for cyclohexane where the value is -4.16 (f.0.63) kcal. Recent developments in theories of complex formation are examined. Variations of K with wave length and of uc with temperature are attributed to simultaneous higher order reactions.
Introduction In the new computer method2 preselected limits of experimental error are used in tests of data compatibility with a number of alternate equations or theories. The method yields precise information for each parameter, thereby completely removing ambiguities in reported results.
+
K
For the reaction, A B1 7 C, the Benesi-Hildebrand,3a Ketelaar,3b and Scott4 noniterative spectrophotometric methods can be used to calculate the equilibrium constant, K , and ac, the absorptivity for C, only if [A] >> [B], aA and a B are known, and aA, aB, and ac are independent of concentration. Recent computer work in our laboratories has shown that aA and a B are seldom completely independent of concentration and the use of constant values for aA and aB
can result in erroneous conclusions. In the iterative method used in this work (see Data Processing Method) the restrictions' on relative concentrations and the required concentration independence of aA and a B are removed. For three systems researchers5-' have reported that the values for K calculated for 1:1 complex formation vary with wave length. Such variations in K and nonlinear Benesi-Hildebrand or Ketelaar plots have been attributed to the neglect of unsuspected higher order reactions. Recentlys there have been devised mathematically exact iterative methods for calculating K1, K2, aA, aB, ac,, and ac, for the equation sets
+B (11) A + B
K1
(I) A
CI; Ct Kl
CI; 211
+A
Kn
+B
Kn
Cz CZ
(1) (a) Taken from the Ph.D thesis of C. C . T . , University of Mississippi, 1964. (b) Department of Chemistry, University of Illinois, Urbana, Ill.
In these methods there are no restrictions on concentra-
(2) P. A. D. de Maine and R. D. Seawright, "Digital Computer Programs for Physical Chemistry, Vol. I , The Macmillan Co., h7ew York, N. Y., 1963. (3) (a) H. A . Benesi and J. H. Hildebrand, J . A m . Chem. SOL.,71, 2703 (1949); (b) J. A. A. Ketelaar, C. van de Stolpe, A . Goudsmit, and W. Dzcubas, Rec. 1rau. chim., 71, 1104 (1952). (4) R. L. Scott, ibid., 76, 787 (1956).
( 5 ) P. A. D. de Maine, M. M. de Maine, and C. Froese, J. Mol. Spectry.. 8 , 373 (1962). (6) P.A. D.de Maine and P. Carapellucci, ibid., 7 , 83 (1961). (7) H.J. G. Hayman, J . Chem. Phys., 37, 2290 (1962). (8) P.A. D. de Maine, J . Mississippi Acad. Sci., in press.
Oct. 20, 1963
SOLVENT
EFFECTSI N CHARGE-TRANSFER COMPLEXES
tions or absorptivities. Jurinskig has solved these equation sets for K1, Kz, ac,, and ac, with noniterative methods by imposing the restrictions: [A] >> [B], a A and a B are known, and a A , a B , and ac are concentration independent. He has shown that both consecutive (equation set I) and simultaneous (equation set 11) higher order reactions can explain variations in K with wave length and that the method used by Hayman7 is unsound because of the neglect of second and higher degree terms in the binomial expansions used. For the two simultaneous isomeric charge-transfer re actions
Ki
A+B-
c, cz
KP
with restrictions: [A] >> [B], a A and a B known, and ac, concentration independent, the formation constant ( K Q ) and absorptivity (aQ) calculated with the assumption that only one complex is formed are related to K1, Kz, ac,, and acPthusx0
a A , a B , ac,,and
K Q = KI UQ
=
(KlaC,
+
+ Kz
K2UCz)/KQ
(1)
(2)
In systems of this type K Qwill be independent of wave length, and aQ may increase, decrease, or remain constant as the temperature is increased. In contact charge-transfer theories, 11-13 reviewed by McGlynn, l 4 eq. 1 and 2 are modified KI f Kz K Q = KI + K P K B . . . (3) UQ =
(Kiuc,
+ + + K Z U C+~K ~ u +c ~. . . ) / K Q
(4)
Here K 3
