Variables in the Standardization of Ceric Solutions against Arsenious Oxide R. C. Schlitt and Keith Simpson Research and Deoelopment Center, Signal Chemical Co., P.O. 5206, Houston, Texas 77012 The standardization of ceric solutions against arsenious oxide primary standard has been investigated. The standardization of ceric sulfate is not direction dependent. Accurate standardizations are obtained when arsenious oxide is titrated with ceric sulfate solution and also in the reverse direction when ceric sulfate solution is titrated with standard arsenious oxide solution. The concentrations of osmium tetroxide catalyst and sulfuric acid do not affect the accuracy of the standardizations. However, the standardization of ceric ammonium nitrate solution is direction dependent. Accurate standardizations a re obtained when ceric ammonium nitrate solution is titrated with standard arsenious oxide solution. The concentrations of osmium tetroxide catalyst and sulfuric acid cause no noticeable effect upon the accuracy of the standardizations. The direct titration of arsenious oxide with ceric ammonium nitrate deviates from the anticipated smooth single-break potentiometric titration curve. The deviations and resulting inaccuracies were traced to a nitrate interference. In the direct titration with ceric ammonium nitrate the concentrations of osmium tetroxide catalyst and sulfuric acid were observed to be secondary contributions to the deviations. Several alternate procedures for the standardization of ceric solutions are described.
CERICSOLUTIONS have been prepared by dissolving a number of reagents, which include ceric sulfate, ceric ammonium sulfate, ceric ammonium nitrate, and ceric hydroxide, in 1N sulfuric acid. These solutions are usually standardized by the method of Gleu ( I ) , where arsenious oxide primary standard is directly titrated with the ceric solution. This time honored method has been firmly established as standard operating practice in many analytical laboratories and the results of the standardizations are unquestionably accepted as accurate, irrespective of the ceric reagent used in preparation. It is remarkable that so little attention has been given to different chemical behaviors of these solutions, which lead to incorrect standardizations. It was not until Smith and Fly (2),that the method was given any serious test as to its accuracy. More recently, Zielen (3) has published conditions for the standardization of ceric sulfate, and explained that the reaction between ceric sulfate and arsenious oxide is direction dependent, which is related to the incomplete reoxidation of the osmium tetroxide catalyst. Upon reviewing the latter publication, the workers in this laboratory noted that the observations of Zielen were not the same as our own. The purpose of this paper is to report our findings, and establish the conditions for accurate standardization of ceric solutions by the conventional direct titration method. This paper will also give an explanation for the directional dependence reported by Zielen. It will be shown that the uncertainty of the standardization and the directional dependence are related to the choice of reagents used to prepare the ceric solutions; namely, ceric sulfate and ceric ammonium (1) K. Gleu, Z . Anal. Chem., 95, 305 (1933). (2) G. F.Smith and W. H. Fly, ANAL.CHEM., 21, 1233 (1949). (3) A. J. Zielen, ibid., 40, 139 (1968). 1722
nitrate. Different potentiometric titration curves are obtained when titrating arsenious oxide in the conventional direction with each reagent. Contrary to that reported by Zielen, the reaction between ceric sulfate and arsenious oxide is not direction dependent, nor does the concentration of osmium tetroxide catalyst limit the accuracy of the determination. But the reaction between ceric ammonium nitrate and arsenious oxide was found to be direction dependent, due to a nitrate interference. EXPERIMENTAL
Reagents. Ceric ammonium nitrate, G. Frederick Smith Chemical Co., was prepared by dissolving 110 grams of Ce(NH4)2(N03)8 in 60 grams of 98% H2S04,then cautiously diluting to 2 liters with distilled water. This solution was filtered. Ceric sulfate, G. Frederick Smith Chemical Co., dissolved 104 grams of CeH4(S04)4in 60 grams of 98% HzS04, diluted to 2 liters, and filtered. Arsenious oxide, National Bureau of Standards, Sample 83C, was dried for 1 hour at 105 “C. Arsenious oxide solution was prepared by dissolving 4.98016 grams of As203in 65 ml of 2N NaOH. The solution was neutralized with 25 ml of 7.19N H2SO4, and then diluted to 1 liter with distilled water. Arsenic trioxide, “Baker Analyzed” Reagent, was dried for 1 hour at 105 “C. Hydroquinone, Eastman Distillation Products Industries, was dried for 1 hour at 105 “C and used without further purification. Potassium iodide, “Baker Analyzed Reagent, was dried for 1 hour at 105 “C. Electrolytic iron, G. Frederick Smith Chemical Co., was prepared by dissolving 1.40370 grams of Fe in enough 1:l HC1 to make 200 ml. Osmium tetroxide, “Baker Analyzed” Reagent, was prepared by dissolving 0.5 gram of Os04 in 200 ml of 0.1N HzSOa. Apparatus. The titrations were performed on Radiometer titration equipment, available from the London Co., Westlake, Ohio. The equipment consisted of an Auto-Burette ABU-1 equipped with a 25.00-ml Burette, pH Meter 26, Titrator TTT-11, and Titrigraph SBR-2. The titration vessel was a 100-ml electrolytic beaker which was fitted with a rubber stopper. The stopper held a platinum electrode, calomel electrode, buret delivery tube, and a small polypropylene tube opened to the atmosphere which served as a pressure vent. The titration vessel was magnetically stirred. Cleanliness of the platinum electrode was essential for accurate results, and this was accomplished by periodically dipping the electrode in chromic acid for 30 minutes followed by rinsing with distilled water. It has been suggested that perhaps the difference between Zielen’s observations and our own was due to differences in the sensitivity of the titration equipment. Zielen used weighing burets, digital pipet, and a potentiometer (but stated that a laboratory pH meter could serve as well) to produce the titration curves. This procedure, even though meticulously performed, at best gave a series of discontinuous
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
points which must be connected to produce a titration curve. Such a method to locate the end point in a potentiometric titration is most likely good to three significant figures and possibly to four figures, but it is doubtful if the method can be extended beyond four significant figures. The same type of plots can be drawn from data obtained by operating the Titrator TTT-11 in the manual mode along with the pH meter 26 and Auto-Burette ABU-1. However, it has been our experience that better results can be conveniently obtained by using the Titrigraph SRB-2, which incidentally is not a servo-recorder, in conjunction with the other pieces of equipment. The Titrigraph is made in such a way as to constantly establish equilibrium during the.course of a titration. The titration curve is drawn as a series of “stairstep” progressions which denote changes in both E M F and milliliters. These minute progressions are much smaller than can be achieved manually. The result is a titration curve that appears t o be continuous. With the aid of the Titrigraph and by choosing the proper amount of sample, it was possible to determine the number of milliliters to reach the end point for the following titrations to four significant figures. In addition to the visual titration curve, the titration equipment produces an audible signal. With a little practice the operator can follow a titration and locate the equivalence point by listening to the rhythmical signal of the micro-relay in the Auto-Burette ABU-1. When the micro-relay slows to its longest pause, the equivalence point has been reached, and the number of milliliters can be directly read from the digital counter of the Auto-Burette. Procedures. A. TITRATION OF ARSENIOUS OXIDE WITH CERICAMMONIUM NITRATE. A number of arsenious oxide solutions were titrated, wherein the concentrations of osmium tetroxide and sulfuric acid were varied. The solutions were prepared by dissolving 0.07 to 0.08 gram of NBS As203, weighed to the fifth decimal, in 1 ml of 2N NaOH, followed by neutralizing with 7.19N H2S04, which was varied from 2, 5 , 10, 15, 20, t o 25 ml, while the amount of catalyst was held at 1 drop. One drop of catalyst is about 0.074 mg of Os04. The volume of the solutions was adjusted to approximately 40 ml with water and titrated potentiometrically with ceric ammonium nitrate. The titrations were repeated with the amount of catalyst held at 3 drops, and again with the catalyst held at 7 drops. B. TITRATION OF ARSENIOUS OXIDEWITH CERICSULFATE. The above titrations were repeated, except ceric sulfate was the titrating reagent. C. TITRATION OF ARSENICTRIOXIDE WITH CERICAMMONIUM NITRATE AND CERICSULFATE.The sample of arsenious oxide used in the above titrations has been open several years. There was concern whether the anomalies observed during the titration were in fact due to contamination of the primary standard. As a check against accidental contamination, freshly opened Baker’s arsenic trioxide was titrated with ceric ammonium nitrate and ceric sulfate. A comparison of the titration results showed the primary standards to be equivalent. D. TITRATION OF ARSENIOUS OXIDESOLUTION WITH CERIC AMMONIUM NITRATEAND THE REVERSETITRATION.Ceric ammonium nitrate was used to titrate 15.00-ml portions of arsenious oxide solution. The amount of 7.19N H z S 0 4was varied from 2, 5 , 10, 15, 20, to 25 ml, while the catalyst was held at 3 drops. The volume of solution was adjusted to approximately 40 ml when needed, and titrated potentiometrically. The titrations were repeated with the amount of catalyst held at 7 drops. Then the titrations were reversed where 15.00-ml portions of ceric ammonium nitrate solution were titrated with arsenious oxide. The concentrations of osmium tetroxide and sulfuric acid were varied as before. E. TITRATION OF ARSENIOUS OXIDESOLUTION WITH CERIC SULFATE AND THE REVERSETITRATION.The same experi-
Table I. Other Methods of Standardization Ceric Ammonium Nitrate Composition of HydroPotassium quinone iodide Iron HzS04 and OS04 in method method method titrated mixture 0.09146 0.09143 0.09146 2 nil 0.09143 0.09147 5 ml H2SO4 0.09147 0.09150 10 ml 0.09151 0.09151 15 ml HzS04 0.09141 0.09161 20 ml H2S04 ... 0.09173 25 ml H2SOa 0.09148 20 ml HZS04,3 dr Os04 0.09145 20 ml H2S04,7 dr Os04 Ceric sulfate 2 ml H2S04 5 ml HS04 10 ml HzSO~ 15 ml H2S04 20 ml H1S04 25 ml H2S04 20 ml H2S04,3 dr os04
0.09677 0.09669 0.09673 0.09670 0.09669
...
0.09669 0.09673 0,09682 0.09685 0.09700 0.09715
0.09677
0.09672
ments were repeated except ceric sulfate was the oxidizing agent. F. TITRATIONOF ARSENIOUS OXIDEPLUS NITRIC ACID WITH CERICSULFATE.The titrations were conducted where 0.07 to 0.08 gram of AS203 was dissolved in 1 ml of 2N NaOH and neutralized with 25 ml of 7.19N H2S04. Portions of 0.2, 0.4, and 0.6 ml concentrated H N 0 3 were added plus 3 drops of catalyst. The solutions were adjusted to 40 ml with water and titrated potentiometrically with ceric sulfate. The titrations were repeated with 7 drops of catalyst. G . ALTERNATIVE METHODSOF STANDARDIZATION. Both ceric ammonium nitrate and ceric sulfate can be standardized against hydroquinone by direct titration. Samples of 0.1 gram of hydroquinone, weighed to the fifth decimal, were dissolved in varying amounts of 7.19N H2S04. The solution was adjusted to 40 ml with water and titrated potentiometrically with ceric solutions. Some titrations were performed with osmium tetroxide added to the solution. The presence of osmium tetroxide has no effect on the standardizations. This method is easily performed, requires no catalyst, is unaffected by acid concentration, and the reagent if needed can be easily purified by sublimation. The method does have the disadvantage that hydroquinone is slightly hydroscopic. Potassium iodide was used to standardize both ceric ammonium nitrate and ceric sulfate. The procedure was the same as that used for hydroquinone except 0.27 gram of KI was used. The potassium iodide method for standardizing ceric sulfate and ceric ammonium nitrate gives satisfactory results at low concentrations of sulfuric acid. At high concentrations of acid the method gives unsatisfactory results because of oxidative side reactions. The ceric solutions were standardized by titrating 10.00-ml aliquots of Fe solution, which were reduced with a 3-drop excess of 10% SnCI2, followed by 10 ml of saturated HgCL This method is more cumbersome than the hydroquinone method (Table I). RESULTS AND DISCUSSION
The experiments show that ceric sulfate solutions can be accurately standardized with arsenious oxide by the conventional direct titration method, and also by the reverse method where ceric sulfate solution is titrated with arsenious oxide. The titrations demonstrate that the stoichiometric reaction 2Ce(IV) -k H3As03 .t HzO + 2Ce(III) H3As04 2H+ will go to completion by adding Ce(1V) to excess H3As03or
+
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
+
1723
Table 11. Titration of Arsenious Oxide and Arsenious Oxide Solution with Ceric Sulfate. Titration of Ceric Sulfate with Arsenious Oxide Solution Ceric sulfate yields one potentiometric break. The Calculated normalities agree with the hydroquinone value of 0.09672N Normality By direct By direct titration of Composition of titration of arsenious and o s 0 4 in arsenious oxide By reverse titrated mixture solution titration oxide 2 ml H2S04, 1 dr o s 0 4 0.09671 5 ml HzSO4, 1 dr o s 0 4 0.09673 10 ml HzSO~,1 dr OS04 0,09673 15 ml H2S04, 1 dr o s 0 4 0,09670 20 ml H2S04,1 dr Os04 0.09676 25 ml H2S04, 1 dr Os04 0.09671 2 ml HzSO4, 3 dr o s 0 4 0.09672 0,09671 0.09675 5 ml H2S04, 3 dr OS04 0.09674 0.09669 0.09671 10 ml HS.04, 3 dr Os04 0.09668 0.09674 0.09672 15 ml H z S O ~3, dr Os04 0.09670 0.09673 0.09674 20 ml H z S O ~3, dr OS04 0.09672 0.09670 0.09670 25 ml HzSO~,3 dr Os04 0,09675 0.09670 0.09673 2 ml H?S04,7 dr OS04 0.09669 0.09672 0.09671 5 ml H2S04,7 dr Os04 0.09669 0.09667 0.09669 10 ml H2S04, 7 dr Os04 0.09671 0.09673 0.09672 15 ml H2SOa,7 dr Os04 0.09669 0,09674 0.09672 20 ml H2SO4, 7 dr o s 0 4 0.09669 0.09671 0.09668 25 ml H2S04, 7 dr Os04 0.09670 0.09669 0.09669
N (0
y-i
i
Increasinm l Ce H4(S04)4
0
v
-
l
?
% -
h
ri
r
Increasing
ml As20g
d
m
?
*
i
d
I
c------. Increasing Ce H,(S0,)4
ml
Figure 1. Ceric sulfate titration curves C is direct tiration of arsenious oxide with ceric sulfate
by adding H8AsO3to excess Ce(1V). The data compiled in Table I1 show that the concentrations of osmium tetroxide catalyst and sulfuric acid, by themselves and within the limits of these experiments, do not affect the accuracy of the standardizations. It is the authors’ opinion that the concentrations of catalyst and acid used in these experiments constitute their practical limits. To achieve accurate results it must be remembered that the concentrations of catalyst and acid could be reduced to the point where the rate of reaction of Ce(1V) and H3As03 becomes very slow and under this condition the titration equipment would not indicate the true equivalence point. Markedly different results were obtained when nitric acid was added to arsenious oxide solution containing osmium tetroxide and sulfuric acid followed by titration with ceric sulfate. Two potentiometric inflections were observed instead of the former single-break (Figure 1). The general observations were that the first potentiometric break occurred before the true equivalence point (the standardizations of ceric solutions by the hydroquinone method are taken to be accurate and these values are used for comparative purposes), while the second break occurred after the true equivalence point. Only in the presence of nitrate did the concentrations of osmium tetroxide and sulfuric acid affect the accuracy of the standardization. The greater the concentration of osmium tetroxide or sulfuric acid for a given amount of nitrate, the greater the separation of the double potentiometric break and the greater the deviation from the true equivalence point. The same double inflection also occurred when arsenious oxide was titrated with ceric ammonium nitrate. The first break occurred before the equivalence point and the second break occurred after the equivalence point (Figure 2). Again, the osmium tetroxide and sulfuric acid were observed to be secondary contributors to the deviation from the equivalence point. But in the reverse titration, where ceric ammonium nitrate was titrated with arsenious oxide, only one potentio1724
D is reverse titration E is direct titration of arsenious oxide and nitric acid Arrows mark equivalence points metric break was observed, which coincides with the true equivalence point. The reverse titration appears to be independent of the osmium tetroxide and sulfuric acid concentrations, but this statement needs to be qualified because it was noted that the audible rhythmical signal of the microswitch in the Auto-Burette was irregular a t the equivalence point during the reverse titration whenever nitrate was present. Although this nonrhythmical signal led to no detectable fluctuations in the potentiometric titration curve or in the calculations, conceivably some extreme ratio of nitrate to osmium tetroxide to sulfuric acid could cause inaccuracies in ceric standardization by the reverse titration method. The double potentiometric break occurred in the direct titration only when nitrate was introduced into the reaction mixture, but in the reverse titration only one potentiometric break occurred even though nitrate was introduced into the reaction mixture. Thus, ceric sulfate can be standardized in either direction without interference because no nitrate is introduced into the titration beaker. But whenever ceric ammonium nitrate was standardized by the direct method, six moles of nitrate were added to the titration beaker for every mole of ceric. Two potentiometric breaks were then observed and the standardization was subject to inaccuracies (Tables I11 and IV). This directional dependence is due to the reaction of nitrate with arsenious oxide. Although this reaction is not fully understood, it appears that nitrate in solution with osmium tetroxide, sulfuric acid, and excess arsenious oxide, is reduced to lower oxidation states while arsenious acid is oxidized to arsenic acid. When this mixture is titrated with ceric solution, the ceric ion reacts with the remaining arsenious acid; consequently, the first potentiometric break occurs before the equivalence point. The calculated normality from the first
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
Table 111. Titration of Arsenious Oxide with Ceric Ammonium Nitrate
1150
Weight of arsenious oxide was in the range of 0.07 to 0.08 g. Two inflections occur. Normality was calculated for each inflection. Normality determined by the hydroquinone method was 0.09146N Composition of Normality HzSOa and o s o 4 in Detd from Detd from 1st inflection 2nd inflection 0.09166 0.09166 0.09134 0.09158 0.09114 0.09155 0.09193 0.09088 0.09082 0,09218 0.09032 0.09240 0.09125 0.09201 0.09118 0.09264 0.09107 0.09294 0.09057 0.09381 0.09045 0,09484 0.09027 0.09693 0.09155 0.09233 0.09124 0.09316 0.09092 0.09414 0.09075 0.09473 0.09080 0.09851 0,09067 0.09607
1c50
450
850
750
650
550
u) N
Figure 2.
. .
d d r.rD
Increasing
-
ml ks2C3
n l Ce(SH4)2(r;C5)6
o? 4 I
3::: I
,
Increarins
Table IV. Direct Titration of Arsenious Oxide Solution with Ceric Ammonium Nitrate and the Reverse Titration
Ceric ammonium nitrate titration curves
A is reverse titration of ceric ammonium nitrate with arsenious oxide E is direct titration
inflection is too large, Thus, the method of Gleu is not satisfactory for standardizing ceric ammonium nitrate solutions, because the ferroin indicator changes color with the first potentiometric break. In the reverse titration, arsenious acid is added to a mixture of ceric ion, nitrate, osmium tetroxide, and sulfuric acid. In this situation the arsenious acid instantly reacts with the excess ceric ion and the slow reaction between arsenious acid and nitrate does not occur until after the ceric equivalence point. Thus, ceric ammonium nitrate in the reverse titration yields only one potentiometric break which corresponds with the equivalence point. Variations in the concentrations of osmium tetroxide and sulfuric acid have been shown to influence the rate of reaction between nitrate and arsenious acid, but the exact function of these reagents remains unknown. There is one observation that has not been explained and that is the second potentiometric break which occurs after the equivalence point. It is difficult to imagine that osmium tetroxide, sulfuric and nitric acid can act as reducing agents, so this must mean all the reducing capacity of the mixture is vested in the arsenious oxide. Yet, in the titration with ceric solution, when nitrate is present in the mixture, there is a definite potentiometric break which occurs after the point where all the arsenious oxide should have been consumed. This seeming violation of conservation of matter was also noted in some of the titration curves in Zielen’s publication (3). It has been suggested that sulfuric acid, plus osmium tetroxide catalyst, can act as a reducing agent similar to Kjeldahl digestion and thus would account for the reduced materials found after the theoretical arsenious oxide equivalence point. It needs to be emphasized that this suggestion has not been proven and is still being investigated.
Two inflections are observed in the direct titration. The first inflection occurs before the equivalence point. The second inflection occurs after the equivalence point. Only one inflection occurs in the reverse titration and the calculated normality agrees with the hydroquinone method of 0.09146N Normality Detd Detd from 2nd from 1st Detd by inflection, inflection, composition of reverse direct direct H2S04and Os04 in titration titration titration titrated mixture 0.09142 0.09233 0.09127 2 ml H2S04, 3 dr Os04 0.09146 0.09249 0,09115 5 ml HzS04, 3 dr Os04 0.09102 0.09145 0.09267 10 ml HzSO~,3 dr o s 0 4 0.09141 0,09091 0.09316 15 ml H2S04, 3 dr Os04 0.09066 0.09144 0.09387 20 ml HzSO~,3 dr os04 0.09147 0.09525 0.09031 25 ml H2S04, 3 dr o s 0 4 0.09143 0.09224 0.0915 1 2 ml HzSOa, 7 dr Os04 0.09148 0.09295 0.09120 5 ml HzS04,7 dr Os04 0.09144 0,09427 0,09083 10 ml HzSO4, 7 dr o s 0 4 0.09144 0,09047 0.09468 15 rnl HzSO~,7 dr OS04 0.09145 0.09035 0.09673 20 ml HzSO4, 7 dr o s 0 4 0.09147 0,09059 0,09741 25 ml HzSO~, 7 dr o s 0 4
These experiments point to the fact that all is not well with the Gleu ( I ) method for standardizing ceric solutions and in particular, more work needs to be done on the behavior of interfering ions. Apparently, the variance between Zielen’s work and our own is the ceric reagent used in the experiments. Zielen purchased his ceric solution which was labeled ceric sulfate. Therein is the variance because of the widespread and confusing practice of preparing so-called “ceric sulfate solutions” by dissolving whatever ceric salts are available in sulfuric acid. The chemical literature, textbooks, and industrial procedures are full of examples where “ceric sulfate” is prepared by dis-
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
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solving ammonium hexanitrato cerate in sulfuric acid. The fact is, ceric sulfate solution and ceric ammonium nitrate solution are not equivalent, when standardized against arsenious oxide. The evidence compiled in this laboratory clearly indicates that Zielen did not use ceric sulfate in his experiments. Most likely, Zielen used ceric ammonium nitrate in sulfuric acid. Because there was a mix-up in reagents Zielen correctly ob-
served directional dependence but incorrectly attributed the phenomena to ceric sulfate and osmium tetroxide. The authors agree with Zielen’s conclusion that it is better to standardize ceric solutions potentiometrically rather than use colored indicators. RECEIVED for review November 18, 1968. Accepted July 8, 1969.
A Rigorous Solution to the Problem of Interfering Dissociation Steps in the Titration of Polybasic Acids Daniel Litchinsky, Neil Purdie,’ Mason B. Tomson, and Wesley D. White Department of Chemistry, Oklahoma State Uniuersity, Stillwater, Okla. 74074 A general equation for determining thermodynamic proton dissociation constants is described. The treatment is applicable to the simplest case, that of a monobasic acid, and to polybasic acids where the successive dissociation steps may or may not interfere. Its versatility is most rewarding in the solution of the problem of overlapping dissociation steps by the analysis of potentiometric data collected from a straight-forward titration of polybasic acids with a strong monoacid base. The interpretation of the general solution is specifically illustrated for citric acid and adipic acid, and the results, when compared with published data, are, in both cases, satisfactory. A third example on another acid, whose dissociation constants are not in the literature, illustrates the brief modification required in dealing with an acid salt.
IT IS COMMONLY KNOWN that the analysis of titration curves for proton dissociations from polybasic acids is complicated if +.he ratio of successive dissociation constants is less than 1000. With a few notable exceptions, all attempts to obtain thermodynamic constants from the experimental data have involved extrapolation to zero ionic strength from a series of results evaluated in known constant ionic strength media. One reason for this more popular pursuit is the intrinsic labor involved in the calculation of activity coefficients in correcting to the standard state of infinite dilution. For polybasic acids, however, such a n extrapolation procedure often leads to erroneous values for dissociation constants other than the first. Although the equations are readily derived which would permit a direct analysis of a titration curve ( I ) , they are generally of high order in hydrogen acid concentration and are only conveniently solved by making permissible approximations. To reduce the labor in calculating dissociation constants, and in which it is legitimate to use these approximations, it has been customary to make precise emf measurements in buffer solutions of known composition ( 2 ) , and the procedure is perhaps justifiably described as the conventional approach to the determination of dissociation constants for interfering equilibria (3). Speakman (4), on the other hand, derived a n equation, quadratic in hydrogen ion activity, which permitted a graphical 1
To whom communications should be directed.
Ricci, “Hydrogen Ion Concentration,” Princeton University Press, Princeton, N. J., 1952. (2) R. G. Bates, J. Amer. Chem. SOC.,70, 1579 (1948). (3) M. Eden and R. G. Bates, J . Res. Nutl. Bur. Std., 62, 161 (1959). (4) J. C. Speakman, J . Chem. SOC.,1940, 855. (1) J. E.
1726
solution for dibasic acids to be made from a typical titration curve. The method was further improved by Eden and Bates (3). The suggestion was made (4) that the method might have some utility in analyzing for the dissociation constants of higher polybasic acids, if successive dissociations could be considered as independent pairs. This, however, is not always applicable, as Bates and Pinching (5) have shown for citric acid, in which the ratios of successive dissociation constants, K,/K2and K2/K3,are both about 44 a t 25 “C. As an alternative to the restrictive graphical solution, we have extended Speakman’s procedure to cover the general case. The analysis replaces the need to prepare precise buffer mixtures and will yield n thermodynamic dissociation constants for the polybasic acid H,A, by the simultaneous solution of n equations constructed from n data points taken from the buffer region of the potentiometric titration curve. A minimum of modification is required to make it applicable to the case where the undissociated form of the acid is charged and a n illustrative example for phosphinidynetripropionic acid is included. To test the treatment citric acid has been titrated and the results are compared with literature values corrected to zero ionic strength ; the experimental measurements made by Speakman have been used for a comparison of adipic acid by both methods. Some future application is foreseen in the area of proton dissociation from polymeric acids where it has been established that the dissociation constant is a function of the degree of dissociation a , and it is customary to talk of a n apparent dissociation constant (6). The buffer capacity of these solutions is low and resembles very closely that of polybasic acids in which several partially neutralized acid species coexist at the same hydrogen ion activity. It should be possible, for example, to describe a polymeric monobasic acid in solution as a n equimolar mixture of n monobasic acids and, by a treatment somewhat analogous to the present case for citric acid, to determine the n individual K1 values which would fit a mathematical equation to the experimental curve. EXPERIMENTAL
Citric Acid. Solutions of Fisher reagent grade citric acid approximately 10-*M were titrated, under nitrogen, with standard potassium hydroxide in a cell with liquid junction of the type
(5) R. G. Bates and G. D. Pinching, J . Amer. Clrem. Soc., 71, 1274 (1949). (6) H. Morawetz, “High Polymers,” Vol. 21, Interscience Publishers, New York, N. Y . , 1965.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
