AHMED A. TAHA AND SHERRIL D. CHRISTIAN
3430 of the structure of the several phases reported here and the ion-exchange behavior of the hydrated u n a -
changed forma of crZrP. We are in the process of obtaining this type of information.
Vapor Pressure Studies of Complex Formation in Solution. I. Trifluoroacetic Acid and Benzophenone in Diphenylmethane by Ahmed A. Taha and Sherril D. Christian Department of Chemistry, The University of Oklahoma, Norman, Oklahoma 73069 (Received February $0,1969)
A vapor pressure method described previously' has been used to investigate the self-association of trifluoroacetic acid (TFA) in the nonvolatile solvent diphenylmethane (DPM) and the interaction of TFA with benzophenone (Ph2CO)in the same solvent. Deviations from Henry's law in the condensed phase were attributed to formation of the TFA dimer, with a formation constant of 3.99 =k 0.17 l. mol-lat 30' and 2.64 f 0.28 l. mol-' at 40°, and the species TFAaPh2CO and (TFA)2*Ph&O,with formation constants of 40 -f 4 1. mol-' and 275 f 28 1.2 mol-2, respectively, at 30'.
Introduction
Experimental Section
Trifluoroacetic acid (TFA) is known to be a very potent proton donor in hydrogen-bonding reactions. The self-association of TFA in the vapor phase and in solution has been investigated by infrared spectral equilibrium and vapor density t e c h ~ i i q u e s . ~Although ~~ constants for the association of the acid are available for the vapor phase, very little information is available for such constants in solution.4 Infrared and microwave spectral data and vapor density measurements have been utilized to calculate formation constants and other thermodynamic parameters characteristic of vapor-phase complexes of TFA with aliphatic and fluorinated aliphatic acids,S,s ketones,6 and water.6 Little quantitative information is available about the stability of TFA complexes with proton acceptors in condensed phases, although infrared measurements have been reported for TFA in several solvents7** and for mixtures of TFA with HzO, diethyl ether, and methanol, respectively, in CCLg We thought it desirable to investigate the self-association of TFA and hydrogen-bonded complexes of TFA with various oxygen bases in organic media. To simplify the determination of association constants, we decided to use a vapor pressure method described previousIy.1 The present article presents thermodynamic results obtained for the dimerization of TFA and its interaction with the nonvolatile solute, benzophenone, in the nonvolatile solvent, diphenylmethane.
Materials. All the reagents used were either analytical reagents or CP grade reagents, except diphenylmethane which was a practical grade. The latter was purified by vacuum distillation. Trifluoroacetic acid was purified by double distillation through a 30-plate Oldershaw column a t a reflux ratio in excess of 10:l. Benzophenone was purified by double crystallization. After purification, all reagents were stored in vacuum desiccators containing a drying agent. The boiling point of the collected fraction of TFA was 72.3-72.5", corrected to 1 atm. Apparatus and Technique. The apparatus and technique have been described elsewhere.' In the self-
The Journal o/ Phyeical C h m b t r y
(1) A. A. Taha, R. D. Grigsby, J. R. Johnson, 8. D. Christian, and H. E. Affsprung, J. Chem. Ed., 43,432 (1966). (2) C. Ling, S. D. Christian, H. E. Affsprung, and R. W. Gray, J. Chem. SOC.,293 (1966). (3) R. E. Kagarise, Naval Research Laboratory Report 4956,Aug 8, 1958. (4) F. Thyrion and D. Decroocq, Compt. Rend., 260, 2797 (1966). (5) 8. D. Christian and R. 9. Hansen, unpublished work; 8. D. Christian, Ph.D. Dissertation, Iowa State College, 1956; C. C. Costain and G. P. Srivastava, J. C h m . Phya., 1, 1620 (1964). (6) C. Ling, 8.D. Christian, and H. E. Msprung, J. Chem. Soc., 2378 (1966). (7) L. W.Reeves, Can. J. Chem., 39,1711 (1961). (8) R. E.Kagarise, J. Chem. Phys., 27,619 (1967). (9) J. de Villepin, A. Lautie, and M. L. Josien, Ann. Chim. (Paris), 1141 1,365 (1966).
COMPLEX FORMATION IN CFaCOOH-(C6H&CO-(C6H6)zCHzSOLUTIONS association study, increments of about 0.1 ml of TFA were added successively to the diphenylmethane in the evacuated apparatus and the corresponding pressures were recorded. I n the heteroassociation study, increments of about 0.1 ml of TFA were added successively to a solution of known molarity of benzophenone (Ph2CO) in diphenylmethane in the evacuated apparatus. This was repeated for different concentrations of Ph2C0. The corresponding pressures were recorded for each increment of TFA. The entire run was repeated in each case to check reproducibility.
Methods of Calculation A . Self-Association. The association of carboxylic acids in dilute solution is commonly assumed to be restricted to dimer formation. If only monomers and dimers of TFA are present in dilute solution in DPM and in the vapor phase, we may relate the total acid pressure, P T , and the total or formal concentration of acid in DPM, fA, by the expressions
PT
PA
+
PAI
=
3431
and fB
=
CB
f KI~'CACBf K~~'CA'CB
(5)
result, where f B and CBare the formal concentration and the monomer concentration of benzophenone, respectively, and KII' and K218 are respective formation constants for the reactions TFA
+ PhzCO = TFAaPhzCO
and BTFA
+ Ph&O
= (TFA)Z*Ph&O
Since PhzCO has a negligible vapor pressure, it is possible to calculate P A and hence CA corresponding to each measured value of the total pressure. T.4 doing this, it is again assumed that Henry's law is valid for each solute species, so that CA = Pa/KAH. To obtain Kl1and Kzl,eq 5 is first solved for CBand the expression for CBis substituted into eq 4 to give the relation
+
PA K ~ " P A ~ (1)
and fA
=
CA
+ 2CA2
= CA
+ ~K;CA'
or (2)
where PAand PA^ are the partial pressures of TFA monomer and dimer, respectively; CA and CA% are the concentrations of monomer and dimer in DPM; and KzVand K: are the dimerization constants for the reaction BTFA = (TFA)2 in the vapor phase and in DPM, respectively. It is assumed that the dimer and monomer individually obey the ideal gas law in the vapor phase and Henry's law in the condensed phase. By utilizing the Henry's law constant, KAH= PA/CA,it is possible to eliminate CA from eq 2 to obtain the relation
+
P A / K A ~ ~ K Z ' ( P A / K A ~ ) ~ (3) Values of KAHand K: were determined by solving eq fA
(7) where AfA is the measured difference between the formal concentration of TFA in DPM at a given total pressure of TFA in the presence of dissolved benzophenone and the formal concentration of TFA in DPRI a t the same pressure in the absence of Ph2CO. A nonlinear leastsquares method was employed to fit sets of data (A~A, CA)in the form of eq 7 and thereby compute Klls and K2P.
Results and Discussion
I n the case of the TFA-DPM system, monomerdimer equilibrium appears to predominate up to the concentration limit of the present studies (0.25 M ) , Using the manometric method described previously1 values of K29 at 30 and 40" were found to be 3.99 f 0.40 and 2.64 f 0.34 1. mol-' and the corresponding K A values ~ were 106.0 f 4.1 and 148.0 f 6.0 mm 1. mol-', respectively. The data for the ternary system can be correlated by postulating the presence of only the 1 : 1 and 2 : 1 complexes of TFA with Ph2C0. Little improvement in the fit of data is achieved if additional polymers are assumed to be present. Constants calculated by the analysis based on eq 7 are (at 30"): Kip = 40 f 4 1. mol-' and K2P = 275 f 28 l e 2mol-2. Figure 1 shows a plot of the vapor pressure of TFA us. the corresponding formal concentrations of added TFA in the presence of the different concentrations of Ph2CO. It is interest~KCCA' K~~'CACB ~ K Z ~ " C A ~(4) C B ing to note that Villepin, et U Z . , ~ also postulated the
2 and 3 simultaneously. 'Using the known value of K2" (0.22 mm-' at 30" and 0.11 mm-1 a t 40')' a value of PA was calculated from eq 1, corresponding to each of the measured values of PT. Both KAHand K t and the standard deviations of these constants were then computed by a linear least-squares fit of data in the form required by eq 3. B. Heteroassociation. Attempts were made to fit the vapor pressure data for the ternary system (TFA and Ph2C0 in DPM) by assuming various combinations of aggregates between the two solutes. It was found that in addition to the 1:1 complex between TFA and PhzCO, a t least one additional polymer involving more than one TFA molecule had to be assumed in order to fit the data satisfactorily. If only the complexes TFA.Ph2CO and (TFA)z.PhzCO are assumed present, the formal concentration expressions . f ~= CA
+
+
+
Volume 78, Number 10 October 1969
3432 I
presence of 1:1 and 2: 1 complexes of TFA with the proton acceptors water and methanol. These workers concluded that the 1:1 complex is formed by a bridge between the TFA hydrogen and the oxygen of water or methanol, and they suggested two possible structures for the 2 : 1 complex
-
54.0
48.0
-
42.0
-
E 30.0
-
I
I
I
I
I
I
I
I
I
I
11-
36.0 -
E
18.0 -
I
Lb 24.0
0
>C-CF, /O---H-O’
CF 3-
C”
\0-H---0
-
/R
12.0
-
I
H 6.0 -
I1
Both I and I1 are consistent with the observation that the frequency shifts for the water and methanol 0-H vibrations which result when the complex is formed are small compared to the shifts observed in cases where it is generally agreed that hydrogen bonding occurs through the proton of the 0-H group. We tend to favor a structure similar to I for (TFA)2*PhzCOin view of the fact that the formation constant for the TFAPh2CO complex is considerably larger than that for the TFA dimer. Thus, in spite of the fact that TFA probably forms a cyclic dimer, with two hydrogen bonds, the dimer is less stable than the 1:1 complex, which very probably involves only one hydrogen bond. I n structure 11, the cyclic TFA dimer has been opened, and only one of the acid protons attaches to the oxygen of the basic molecule. It is unlikely that such a species could have a formation constant greater than the product of Kz” and Kl? (-160 mol-2) and the constant would probably be considerably less than this value. If one assumes a structure analogous to I, with both TFA molecules attaching to the ketone oxygen, it is possible to derive the relation
K21’ = (Kllal2/4
The Journal of Physdcal Chemistry
(8)
0
0.04 0.08
0.12
0.16
0.20
0.24
f A (moles/ liter) Figure 1. Total vapor pressure against concentration of trifluoroacetic acid in diphenylrnethane containing 0.000 M (0),0.020 M (W), 0.100 M (A), and 0.200 M ( 0 )benzophenone. Points are experimental; curves are calculated by least squares.
provided that the two lone-pair sites are equivalent and that inductive and steric effects can be ignored.I0 The value calculated from eq 8, Kzle = 400 Is2 is somewhat larger than the observed value (275 La mol-2). The discrepancy is not unreasonable, considering that both the inductive effect and the steric effect of a molecule of TFA bonded to the ketone should act in a direction tending to reduce the effective basicity of the unbonded lone pair in TFA*Ph2CO. Acknowledgment. This work was supported in part by the Office of Saline Water (Grant No. GS-14-010001-1315). (10) C. Lin, Ph.D. Dissertation, University of Oklahoma, 1964.
