918
JOSEPHA. CARUSOAND ALEXANDER I. POPOV
A Potentiometric Study of Acid-Base Equilibria in 1,1,3,3=Tetramethylguanidine
by Joseph A. Caruso and Alexander I. Popov Department of Chemistry, Michigan State University, East Lansing, Michigan 48883 (Received August 88, 1967)
Acid dissociation constants of four 5-substituted tetrazoles, perchloric acid, m-chlorobenzoic acid, and phenol were determined in l11,3,3-tetramethylguanidineby potentiometric techniques. A hydrogen indicator electrode and a mercury-mercury(I1) chloride reference electrode were used. Perchloric acid is the strongest acid with pK, = 3.11 and phenol is the weakest with pK, = 7.54. The pK. values obtained by the potentiometric method are in good agreement with the values obtained from electrical conductance measurements.
Introduction The usefulness of nonaqueous solvents in the study of acid-base equilibria (particularly in the Br@nstedLowry sense) is clearly illustrated by the large number of analytical techniques that utilize either pure nonaqueous solvents or their mixtures for a wide variety of titrations of substances that, for on ereason or another, cannot be analyzed in aqueous solutions. With few exceptions, the development of the theory of acid-base equilibria in nonaqueous solvents, however, has not kept pace with the practical applications. Acidic solvents, such as acetic acid and sulfuric acid, have been studied very intensively and the nature of acid-base equilibria in these solvents has been elucidated particularly by the classical investigations of Kolthoff and Bruckenstein in acetic acid solutions’ and by Gillespie and his coworkers2 in sulfuric acid. On the other hand, acid-base equilibria in basic solvents seem to have been studied less completely, although of course, there are significant publications on such solvents as p y r i d i ~ i e , ~ - ~ and ammonia, 1 3 -I5 Recently, we reported an electrical conductance study on 5-substituted tetrazoles in a strongly basic solvent, 1,l13,3-tetramethylguanidine (hereafter abbreviated as TMG).l6 I n order to establish a useful electrode SYStem in TMG, as well as to verify the results of the electrical-conductance study, a potentiometric study of acid-base equilibria in TMG was initiated. Since tetramethylguanidine has a relatively low dielectric constant of 11.0Ol16 it is to be expected that ionic equilibria in this solvent would be substantially influenced by ion pairing. It has been shown by Kolthoff and Bruckensteinl that in such cases the over-all dissociation of a weak acid H X will proceed in two steps HX H+X- a H + + X-, resulting in the over-all dissociation constant, KHx, which is given by the expression The Journal of Physical Chemistru
KHX=
aH tax aHX a H +x-
+
where the terms have their usual meanings. balance relationship may be written as
( C H X )= ~ [H+l
(1) The mass
+ [H+X-l + [HX]
(2)
where (CHX)~ is the total analytical concentration of the acid H X and the terms in brackets represent the equilibrium concentrations of the respective species. If we assume that the activity coefficients of uncharged species equal unity, that a H t = ax-, and that aHt = [H+], it then follows that (1) I. M .Kolthoff and S. Bruckenstein in I. M. Kolthoff and P. J. Elving, “Acid-Base Equilibria in Nonaqueous Solvents. Treatise on Analytical Chemistry,” Part I, Vol. I, The Interscience Encyclopedia Company, Inc., New York, N. Y . , 1959, Chapter XIII, and references cited therein. (2) R. J. Gillespie and E. A. Robinson in “Non-Aqueous Solvent Systems,” T . C. Waddington, Ed., Academic Press, Inc., New York, N. Y . , 1965,Chapter 4. (3) P. Walden, L. F. Audrieth, and E. J. Birr, 2. Physik. Chem.. Al60, 337 (1932). (4) W. A. Luder and C. A. Kraus, J . Am. Chem. SOC., 69, 2481 (1947). (5) D. S. Burgess and C. A. Kraus, ibid., 70,706 (1948). (6) R. Gopal and hl. M. Hussain, J . Indian Chem. SOC., 40, 981 (1963). (7) M. L. Moss, J. S. Elliot, and R. T . Hall, Anal. Chem., 20, 784 (1948). (8) M. Kat5 and P. A. Glenn, ibid., 24, 1157 (1952). (9) A. J. Martin, ibid., 29, 79 (1957). (10) B. B. Hibbard and F. C. Schmidt, J . Am, Chem. SOC.,77, 225 (1955). (11) J. Peacock, F. C. Schmidt, R. E. Davis, and W. B. Schaap, ibid., 77, 5829 (1955). (12) L . hl. Mukherjee and S. Bruckenstein, J . Phys. Chem., 66, 2228 (1962). (13) V. A. Pleskov and A. Monosson, 2. Physik. Chem., 156, 176 (1931). (14) G. W.Watt, J. L. Hall, and G. R.Choppin, J. Phys. C h e w 57,567 (1953). (16) J. L. Hawes and R. L. Kay, ibid., 69, 2420 (1965). (16) J. A. Caruso, P. G. Sears, and A. I. Popov, ibid., 71, 1756 (1967).
STUDY OF
(3) Solving eq 3 for UH+
UH+,
we get
:= (KHx[(CHx)t -
Ref electrodej/HX(CHx)t (TMG)IHz (1 atm), Pt The reference electrode consisted of a mercurymercury(I1) couple, which was composed of a mercury layer in contact with a saturated solution of mercury(I1) chloride in TMG. The emf generated by this cell is given by the equation
+ 0.0592 log
EHx
=
Eo“
UH+
(5)
Eo”
=
E o ~ + . t / ~Eli ~ 2 Emf
(6)
where
+ +
Substituting eq 4 into eq 5 yields
Eo”
+ 0.0296 log KHX+ 0.0296 log
[(CHX)O
- aH+] (7)
It is seen that a plot of EHXvs. log [(CHX)~ - aH+] should give a straight line with slope of 0.0296 and intercept of Eo” 0.0296 log KHX. If KHX of an acid is known from independent measurements, the value of EO” may be calculated (assuming that the liquid-junction potential remains constant). Essentially the same technique is then used in an iterative process to calculate KHx values for other substances. As the first approximation, we can write [ ( c H X ) t a H + ] = (CHX)t. The emf values are then plotted vs. log (CHX)t and ti value of KHXobtained. From this value of KHX a first value of U H + is calculated and EHX is plotted vs. log [(CHX)t - %+I, from which a new value of KHX is obtained. The process is repeated until the consecutive KHXvalues converge within an acceptable tolerance. This method usually requires four or five iterative steps and is easily handled by a digital computer. In a similar potentiometric study using ethylenediamine as solvent, Bruckenstein and MukherjeelZ have postulated the following conjugate ion equilibrium
+
X-
+ HX
HX2-
0.0592 representing equilibrium 8, shown above. At the point of intersection of the two linear segments they obtain the relationship KHX%=
(4)
aH+])”*
Potentiometric studies of acids in TMG were carried out by means of the galvanic cell
EHX =
919
ACID-BASEEQUILIBRIA I N 1,1,3,3-TETRAMETHYLGUANIDINE
(8)
where (9) In the cases where the conjugate ion equilibrium is present, a plot of EHXvs. log (CHX)t yields two linear portions, one of slope 0.0296 representing the two-step ionization and dissociation equilibria, and one of slope
1 (CHX)tt
___
(10)
where (CHx)t’ gives the concentration of the acid at the point of intersection.
Experimental Part Reagents. The solvent purification and the preparation and purification of the 5-substituted tetrazoles have been previously described.*e Perchloric acid and mercury (both Baker Analyzed reagent grade), as well as Fisher Certified Reagent mercury(I1) chloride were used without further purification. Matheson Co., Inc. prepurified hydrogen was passed through a flow meter to assure constant delivery to the hydrogen-electrode half cell. It was then passed through a column of Ascarite and a column of Drierite before use. Phenol, obtained from Eastman Chemical Co., was purified by vacuum distillation in a micro distillation apparatus; m-chlorobenzoic acid was purified by recrystallizing from a water-ethanol mixture. Apparatus. The emf readings were taken on a Beckman expanded-scale pH meter. The 0-200-mV full scale was extended by recalibrating against the output of a Biddle-Gray portable potentiometer Model 605014. Readings were good to 0.2 mV. The cell used in the emf measurements was similar to one previously described. l’ Procedures. Solutions of various acids in TMG were prepared by the usual volumetric technique, but the manipulations were carried out in a drybox under a dry nitrogen atmosphere. It was found that a mercury-mercury(I1) electrode had a steady and reproducible potential when used in conjunction with a hydrogen electrode. A saturated solution of mercury(I1) chloride was prepared by suspending 2.00 g of dry salt in 100 ml of solvent and stirring the mixture for 2 hr. The solutions appeared to be stable for at least 24 hr. After the solution had been aged for several days, however, a black deposit was formed on the bottom of the flask. In order to avoid a possible source of error, fresh saturated solutions of mercury(I1) chloride were prepared just prior to use. Attempts to prepare a calomel reference electrode in TMG were unsuccessful, since addition of calomel to ThIG instantly produced a black precipitate. The reference-electrode half cell was prepared with a 1-cm layer of mercury and a platinum contact inserted into the mercury. Saturated mercury(I1) chloride solution was then added to the reference-electrode compartment. (17) J . A. Caruso, G . Jones, and A. I. Popov, Anal. Chim. Acta, 40, 49 (1968).
Volume 78, Number S March 1968
920 Sixteen-gauge platinum wires 1 to 1.5 in. in length were sealed into soft glass tubes and coated with platinum black by electrolysis in a previously described solution16for 5 min at 10 mA. The electrodes were then charged with hydrogen by cathodizing in a dilute sulfuric acid solution. As the measurements were taken, electrodes were interchanged to compare their response. Fresh electrodes were used when readings became erratic or when readings did not agree to within k0.5 mV between fresh and previously used electrodes. Immediately before use, the platinum electrodes were washed with distilled water, rinsed in acetone, and air dried. A gas dispersion tube was inserted into the hydrogenelectrode half cell and the half cell purged with hydrogen for 5 min. The reference-electrode compartment was then filled with saturated mercury(I1) chloride solution. Finally, the hydrogen-electrode compartment was filled with the solution to be studied. The bridging compartment was also filled with the same solution to minimize errors due to diffusion. A current of hydrogen was allowed to stream through the solution for at least 20 min. The readings were taken when changes in potential were about 2 mV or less over a 20-30-min recording interval. This behavior may be due to the hydrogen electrode coming slowly into equilibrium with the solution. It was found that when the system was thermostated in a constant-temperature bath at 25", the accuracy of the measurements did not improve. Reproducible measurements could be obtained in a water thermostat only after 40-45 min. All reported measurements, therefore, were taken in an unthermostated cell at room temperature of ca. 24". The reported emf values are the mean value of the best four readings and have average deviations of SO.5f1.0 mV. The hydrogen partial-pressure correction to the observed emf was ignored, since it would be less than experimental error.
Results and Discussion Over-all dissociation constants of 5-methyltetrazole, 5-benzyltetrazole, 5-phenyltetrazole, 5-p-chlorobenzyltetrazole, perchloric, and m-chlorobenzoic acids, and phenol were determined potentiometrically by the procedure described above. Unfortunately, in a number of cases, limited solubilities of acids in TMG precluded their study. For example, attempts have been made to study the dissociation of acetic acid, hydrochloric acid, and hydrobromic acid in TMG, but the experiments could not be carried out due to the low solubility of these acids in TMG. The value for EO" was calculated from the K H Xvalue for 5-benzyltetrazole obtained from electrical conductance measurements.16 The emf data were fitted by the method of least squares to yield a straight line with slope of 0.0288 (*0.0012) and an intercept of -0.8021 ( ~ 0 . 0 0 1 5 V, ) where the numbers in parentheThe Journal of Physical Chemistry
JOSEPH A. CARUSO AND ALEXANDER I. POPOV ses represent the respective standard deviations. Recalling that the intercept = EO" 0.0296 log KHX, the value of Eo" was calculated to be -0.6657 V. This value for Eo" was used in conjunction with the emf data to calculate the over-all acidity constants for the other systems. The data were analyzed by the use of a FORTRAN computer program run on a Control Data Corp. Model-3600 computer and the results are given in Table I. It is seen that there is good agreement between the potentiometric and conductometric methods, and that the experimental slopes agree well with the theoretical slope of 0.0296. The behavior of all substances listed, except phenol, is characteristic of weakly acidic substances in the concentration range of ca. 0.002-0.03 M . The same behavior was found for the conductance measurements which were done at
