DISSOCIATION CONSTANTS OF TARTARIC ACID WITH THE AID OF

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Kov., 1960

DISSOCIATION CONSTANTS OF TARTARIC ACIDWITH THE AID OF POLARIMETRY 1739

DISSOCIATION CONSTANTS OF TARTARIC ACID WITH THE AID OF POLARIMETRY BY LEONARD I. KATZINAND ELSIEGULYAS Chemistry Division, Argonne National Laboratory, Argonne, Illinois Received M a y 26, 1960

With the aid of optical rotation determinations at 5461 d.,the dissociation constants of tartaric acid (0.2M ) are shown to be KI = 1.8 X 10-8 and KZ = 1.03 X respectively, with systems containing 0.4 N Na+. The specific rotations [a], based on the weight of tartrate ion, T--,for tartaric acid, bitartrate ion and tartrate ion are, respectively, 12.7,35.3and 48.1O a t 5461 A. The contribution of salting-out of the undissociated acid to the activity coefficients of the component ions is pointed out. Grounds are given for considering the possibility that the dissociation constant itself is a function of solution composition, particularly the cation composition.

In the course of other studies, it became necessary contribution of each species to the total rotation at to observe the effect of pH on the optical rotation of a given pH was the product of the corresponding tartrate over the pH range, 0 to 11. Inasmuch as specific rotation and the fraction of the total tarthe rotations of undissociated tartaric acid and of trate present in that form.The last was given by tartrate ion, a t the wave length investigated, dif- the equations fered by almost a factor of 4,and were determined (T')/C = K ~ K I / F (la) in general to better than 1% precision, it was real(HT-)/C = KI(H+)/F (lb) ized that it should be possible to extract from the (H2T)/C = (H+)'/F (IC) data both the rotation of the intermediate bitartrate ion and a verification of the dissociation constants where C is the sum of the concentrations of the unof tartaric acid. This work is being published be- dissociated acid, bitartrate and tartrate ions, and F = KlK2 f KI(H+) (H+)2 (2) cause on closer investigation of the data the procedure proved not only to be a sensitive way of de- These relations were derived algebraically from the termining these dissociation constants, but the usual expressions for the dissociation constants, and values found to fit our data, namely, K1 = 1.8 X the definition of C. In the calculations the dif10-3 and Kz = 1.03 X (0.4 N in Na+), differ ference between the hydrogen ion concentration considerably from values encountered in the used in the equations and the hydrogen ion activiliterature. The cation concentration is specified in ties as obtained from pH measurement is ignored. this way because it is well known that the optical The quantities [&']HIT and [ a ] were ~ deterrotation of tartrate is a marked function not only of mined by the necessity of matching the expericoncentration but of the cation accompanying it. mental rotations in the regions of complete associaI t is also possible, as will be discussed below, that tion and complete dissociation, respectively, and the same factors which affect the optical rotation were therefore approximately fixed by the data. may also affect the acid strength (dissociation con- Values for K1 and Kz were chosen, and the three stant). quantities of equations 1 computed. For those pH values for which (HT-)/C was equal to or greater Experimental .4 stock solution was made containing 0.2000 formula than 0.2, the difference between the experimental weight of chemically pure sodium tartrate per liter. Por- rotation and that ascribable to H2T T-, when tions of this were adjusted in pH by the addition of con- divided by (HT-)/C, gave a tentative value for centrated nitric acid (or NaOH, when required), and the The average was taken of the 25-30 such necessary corrections were made for the small volume change. [ a ] H T - . The pH of the solution was measured with the Beckman [CYIHT- values. From the three [a]values and the Model G pH meter to a precision estimated at f0.02 unit. fraction of total tartrate present as each species, For measurements in the acid range the pH meter was ad- the total expected rotation for each pH was comjusted with pH 4.00 buffer, and in the alkaline range with pH 7.00 buffer. The electrodes were repeatedly rinsed with puted, and compared with the experimental value. the sample solution until constant readings were obtained. The magnitude and direction of systematic deviaThe optical rotation a t 5461 A. was measured with the tions dictated the choice of dissociation constant Rudolph Photoelectric Spectropolarimeter, using a 10.0 cm. values for the next approximation, and these in jacketed polarimeter tube through which water a t 25 i turn gave the corresponding value of [a] HT -. Two 0.1' was circulated. Some 5-10 readings on each solution fairly sensitive criteria were available by which were averaged. The reproducibility of the rotation readings was about =!ZO.O02O for both experimental and blank goodness-of-fit could be judged: the absence of solutions, which amounts to about =!ZO.l" in the specific systematic deviations from the experimental rotarotations, [a], derived. tions, and the absence of systematic deviations in Results the series of [a]HT - values, which should be conThe results are shown in Fig. 1. For comparison stant within experimental error if the dissociation with the experimental values of [a], the curve gives constants were correctly chosen. With respect to the specific rotations calculated using K1 = 1.80 X the uncertainties in the values chosen for computing the curve in Fig. 1, it can be said that a K1of 1.8 X Kz = 1.03 x [cYIHzT = 12.7', [ a ] T = 48.1' and [CY]HT- = 35.3'. The specific rotagave a detectably better numerical match to tions mere calculated on the basis of the weight of the data than 1.7 X 10-3; that it was not clearly tartrate ion, T-, in the species indicated. The certain whether 1.00 X 10-4 gave a worse numerical fit than 1.03 X lop4for K z ; and that with these (1) Baaed on work performed under the auspices of the U. S. values of K1 and Kz, 17 out of 31 [a]HT- values fell Atomio Energy Commission.

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LEONARD I. KATZINAND ELSIEGULYAS

1740

1

r48

- --

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7

--

I

j4I 40 I-

K,: 1 8

-

K*: I 03

121

L-_i. I

’ PH.

Fig. 1.-The

variation of the E ecific rotation of 0.2000 M sodium tartrate s o b o n with pH.

within f 0.4’ of the mean value, 35.3’. (With K Z = 1.00 X 15 out of 31 [a] HT- values were within A0.4’ of the mean.) Of some 50 points for which experimental and calculated rotations are compared in Fig. 1, some three-quarters agreed within i=0.1O (the reproducibility expected of the rotation readings) or within the i 0.02 unit reliability of the pH readings, which in the pH 3 region might mean f 0.3’. The remaining quarter, with gross deviations (equally negative and positive), dated from a period in the measurements, which had been accumulated over a considerable period of time, when the pH meter was behaving erratically. These points were not so obviously “off” that they could be discarded out of hand.

Discussion There is a considerable number of papers in the literature which contain values for one or another of the dissociation constants of tartaric acid. Reference to a number of them can be found in the papers of Jones and Soper12and Bates and Canham.3 Values closest to those fitting our data are given by Britton4 and Britton and Jackson,bwith K 1 = 1.2 X and Ka = 1.0 X Most other values for Kl are in the range 0.9-1.0 X lov3while the K z values scatter from 1to 10 X lo+. Many of the literature values are admittedly approximate. A number of the determinations differ from ours in being aimed to give dissociation constants a t infinite dilution, and therefore may be expected to yield different values. An important difference must be noted between the usual salt effects on strong electrolytes, which is assumed in these papers and the situation when a weak electrolyte is involved. If one has, say, an HC1 solution of pH 2.0, and adds to this NaCl to, say, 0.4 M , the pH will be (2) I. Jones and G . G. Soper, J . Ckem. SOC.,1836 (1934).

(3) R. G. Bates and R. G. Canham, J . Research Natl. Bur. Sfandards, 47, 343 (1951). (4) H. T. 5. Britton. J . Chem. Soc., 1896 (1925). (5) H. T. 8. Britton and P. Jackson, ibid., 998 (1934).

Vol. 64

expected to increase slightly. This is because activity coefficients tend to decrease with concentration for these salt systems, until concentrations became greater than 0.5 molal. We have found the pH of 0.2 ill tartaric acid to be 1.90; the inclusion of KaNOs or NaCl to 0.4 M lowers the pH to 1.74. This difference from the behavior of the HC1 solution cited is to be ascribed to the salting-out of the undissociated organic acid molecule, a well-known effect. The activity of the undissociated acid is raised, and therefore the value of the ion activity product in equilibrium with it is also increased. The decrease in pH is evidence of this effect. This behavior of tartaric acid with salt has been known for a long time (e.g., Britton and J a c k ~ o nKolthoff ,~ and Busch6)and in fact the corresponding explanation was givens in 1928. This explanation does not, however, face the question of a possible change in dissociation constant of the acid, a question which will be returned to later. As was pointed out in connection with the iodineiodide-triiodide equilibrium,’ whenever a neutral component is involved which is subject to saltingout, the activities and the activity coefficients of the ions in equilibrium with it are elevated somewhat in parallel. This can be such as to override normal ionic strength relations of activity coeEcients and t o invalidate calculations in which these “normal” relations are assumed. This may well be one of the factors in the discrepancies between different determinations of the second dissociation constant for tartaric acid, even when apparently done by the same sensitive techniques insofar as pH determination goes. In all instances, extrapolations to zero ionic strength are involved in which activity coefficient relations are assumed (e.g., Bates and C a n h ~ ~ r nSartori, ,~ Costa and CamusE). The details of the assumed activity coefficient relations may well determine the differences in extrapolation. The value for K1 calculated from the pH data given above for 0.2 M solution is 0.91 X in the absence of salt, and 1.82 X with 0.4 M sodium salt added. (K1 = (H+)2/(0.20 - (H+))). Bates and Canham3give a K1 value of 0.92 X Therefore the salt effect alone will account for the difference in the K 1value obtained by us and that of the Bureau of Standards determination for infinite dilution. Our value for K z differs from theirs by a factor of about 2.4. The difference in the K2 values may be due additionally to their extrapolations involving the tartrate ion activities. More direct comparisons with the earlier data3 are impossible since they do not contain determinations at two or more pH values for the same salt (cation) concentration. Such data would permit explicit evaluation of both dissociation constants for a fixed salt concentration by use of the equationg (6) I. M. Kolthoff and W. Busch. Rec. trou. chim., 47, 861 (1928). (7) L. I. Katzin and E. Gebert, J . Am. Chem. SOC.,77, 5814 (1955). ( 8 ) G. Sartori. G. Costa and A. Csmus, Ann. chim. (Rome), 42, 205 (1952).

(9) Activity coe5cient terms aside, Bates and Canham’s equations 2 as and 3, or 4 and 3, reduce to our relation above (the sign of it appears in their equation 3, is incorrect); Sartori, Costa and Camus’ also use an equivalent equation.

Nov., 1960

SOLUBILITIES OF CALCIUM SOAPSOF LINEARCARBOXYLIC ACIDS

1741

tion constant itself. Though these workers chose to attribute the whole effect to activity change, the second alternative cannot be ruled out. As is now well-known10-12optical rotation is related to the The symbols fo, f-, f- represent the activity co- existence of absorption peaks in the far ultraviolet. efficients of the undissociated acid, bitartrate and Alterations in rotation are to be related to changes tartrate ions respectively, f + that of the proton. in the wave length and relative intensity of these The symbol C is the sum of tartrate species as absorptions. Such changes infer alterations in the energy levels of the molecule, and therefore possibly before and in the binding of the acidic protons to the carboxB = ( H + ) + (HT-) + 2(HzT) = (HT-)initial 2(H~T)initia1 ylate oxygens in the case of tartrate. It is therefore possible that there may in fact be changes in the Such a set of determinations would be valuable in dissociation of the acid under the influence of salts, tracing the actual course of the activity coefficients and in a manner specific to the cations, as is true of of the several species with concentration and with the optical rotatory effects themselves. Extension salt cation. of this to other weak acids with electron-donor As pointed out by Kolthoff and Busch,6 the salt groups is obvious. effect on tartaric acid dissociation may be due to (10) E. U. Condon, Rev. M o d . Phys., 9 , 432 (1937). activity effects alone, but there also exists the (11) W. Kuhn and E. Braun. Z. physik. Chem., [B]8 , 445 (1930). possibility of some real alteration of the dissocia(12) W. Moffitt and A. Moscoaitr, J . Chem. Phys., SO, 648 (1959).

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METAL COMPLEXING BY PHOSPHORUS COMPOUXDS. 11. SOLUBILITIES OF CALCIUM SOAPS OF LINEAR CARBOXYLIC ACIDS' BY R. R. IRAN AND C. F. CALLIS Mansanto Chemical Company, Research Department, Inorganic chemicals Division, St. Louis 66, Mo. Received

May $1, 1980

Solubility products of calcium soaps of linear carboxylic acids from Ceto CI8are reported from measurements of the competition for the calcium between the insoluble soap and the soluble calcium tripolyphosphate complex. Data are given for various temperatures and ionic strengths. For the saturated soaps, the negative logarithm of the thermodynamic solubility = -2.63 1.24 product at 25', p [ K B P-,] is related to the number of carbons in the soap chain by the equation p[K.,] (No. of Carbons). The unsaturated linear calcium soaps, oleate and linoleate, were significantly more soluble than calculated from the expression for the saturated soaps.

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Introduction One of the techniques for measuring complexity constants is to use a nephelometric end-point for determining the competition for the metal ion between complexing and precipitating anions. I n a previous paper12 this procedure was utilized to measure the complexity constants of calcium with linear polyphosphates, using measured values of the solubility product of calcium oxalate. In the present study, the reverse is done; linear carboxylate anions are made to compete with the tripolyphosphate anion in tying up calcium, in order to measure the solubility product of these calcium soaps. Experimental Chemicals.-Sodium tripolyphosphate hexahydrate was used as the source of tripolyphosphate anions. It was prepared by four repeated fractional crystallinations of commercial sodium tripolyphosphate from aqueous solutions of ethyl alrohol. The final sample analyzed to better than !)9.7% Na6PrOto. Tetramethylammonium tripolyphosphate was prepared by ion exchanging the sodium salt with the hydrogen form of 100-200 mesh Dowex 50W-X2 and neutralizing the resulting acid immediately with tetramethylammonium hydroxide, as previously described.8 The (1) Presented before the Division of Inorganic Chemistry, 138th Meeting of the American Chemical Society, New York, September 1060. (2) R. R. Irani and C. F. Callis, THISJOURNAL, 64, 1398 (1960). (3) J. R. Van Warer, E. J. Griffith and J. P. McCullouph, J . A m . Chem. S O L ,11, 287 (1955).

stock solution was maintained a t 25' and a pH of 12 to avoid hydrolytic degradation. The C.P. grade hexanoic, octanoic, decanoic, lauric, m-yristic, palmitic, stearic and oleic acids were obtained from Eastman Kodak. The C.P. grade heptanoic, undecylic and linolcic acids were purchased from Matheson, Coleman and Bell. The nonanoic acid was technical grade from Matheson, Coleman and Bell. The tridecylic acid wm obtained from the K and K Labs., Jamaica, New York. The acids were ronverted to tetramethylammonium derivatives by neutradaation with Eastman Kodak reagent grade tetramethylammonium hydroxide. Other chemicals were C.P.grade. Procedure.-The nephelometric titrations were carried out at a pH of 12 using the same procedure previously descTibed2 except for temperature control and precipitating anions. I n the prcsent experiments, temperature was controlled to 3: 0.1' using a heater in combination with a heat-sensing Thermotrol unit, manufactured by Hallikainen Instruments, Berkeley, California. The concentrations of the calcium-precipitating anions, the linear carboxylates, were chosen below the critical mirelle concentration, and such that the competition for calcium with tripolyphosphate was favorable. In addition, no PZOS was detected in the precipitates formed upon addition of a slight excess of Ca++ to the solution containing P3Ol0-s and linear carboxylate anions. The ionic stlengths were adjusted to the desired values using tetramethylammonium bromide.

Results and Discussion The raw data showing the number of cc. of a calcium solution that must be added to a solution containing tripolyphosphate and linear carboxylate