Amperometric Titration of the Tetraphenylborate Ion Method for Potassium ARTHUR F. FlNDElS and THOMAS DE VRlES Department of Chemistry, Purdue University, W e s t Lafayette, Ind.
Potassium tetraphenylborate dissolved in acetonitrilewater mixtures can be titrated with an aqueous solution of silver nitrate w-ith a high degree of precision. The method utilizes a dropping mercury electrode as an indicator with a mercury pool as a nonpolarized reference electrode at a potential of -0.1 volt us. the pool. The procedure is suitable for between 1 and 20 mg. of potassium but could easily be extended to higher amounts. The precision and accuracy compare with other methods for potassium in this concentration range.
T
HE tetraphenylborate ion is unique in that it forms insoluble salts of potassium, rubidium, cesium, and ammonium ions in aqueous media (9-ff). A large number of organic bases also form insoluble precipitates with this ion ( 4 ) . Previously a polarographic method using potassium tetraphenylborate in dimethylformamide had been developed for the determination of potassium ( 2 ) . h titrimetric procedure for potassium was developed by Rudorf and Zanier (8) based on the easy solubility of potassium tetraphenylborate in acetone-11 ater mixtures and the insolubility of silver tetraphenylborate in both acetone and water. The equivalence point was detected by means of the adsorption indicator eosine. Recently Hahn ( 5 ) utilized potassium chromate as an indicator in a modified Mohr titration of the tetraphenylborate ion. Kemula and Kornacki (6) published an amperometric titration method for potassium, in which the excess of a standard solution of sodium tetraphenylborate was titrated in dilute acetic acid with thallous nitrate. A titration of potassium tetraphenylborate with perchloric acid in acetone and glacial acetic acid was utilized by Flaschka (3, for the determination of potassium, using crystal violet as the equivalence point indicator. As potassium tetraphenylborate is soluble in a number of organic solvents, this Fork was initiated in order to study the feasibility of an argentimetric titration with an amperometric equivalence point. Dimethylformamide, methyl Carbitol [2(2-methoxyethoxy)ethanol], and acetonitrile were utilized as solvents for the potassium tetraphenylborate. From the point of view of precision and accuracy, acetonitrile was found to he the better solvent for dissolution purposes. Because a large amount of water can be tolerated before potassium tetraphenylborate begins to precipitate from acetonitrile, the titrant silver nitrate was dissolved in nnter.
(Carbide and Carbon Chemicals Co.), were used as obtained from stock. The standard silver nitrate solutions were prepared from weighed amount of reagent grade silver nitrate dissolved in water and diluted to the desired volume. Sodium tetraphenylborate (J. T. Baker Chemical Co.) was used v,-ithout further purification. Potassium tetraphenylborate, after precipitation from a solution of potassium chloride acidified with dilute hydrochloric acid, was recrystallized twice from acetone, washed thoroughly with water, and dried at 110" C. PROCEDURE
Weighed amounts of potassium tetraphenylborate were dissolved in 15 ml. of acetonitrile and enough water was added (5 to 8 ml.) so that the solution a t the e uivalence point contained 50 to 60% of acetonitrile by volume. six milliliters of mercury was added to the 100-ml. beaker to serve as the nonpolarized anode and the titration was carried out a t -0.10 volt us. the mercury pool. During the addition of titrant the circuit to the galvanometer and cell was opened; otherwise the momentary excess oi silver ion produced a galvanometer deflection of large magnitude. After the solution was stirred and allowed to stand for 15 to 30 seconds, the galvanometer was switched into the circuit and the diffusion current recorded. The equivalence point was determined by extrapolation of the current values to zero current. The same procedure was followed for the titrations performed with dimethylformamide or methyl Carbitol in the solvent system. The titrations in dimethylformamide were carried out at -0.20 volt; those in methyl Carbitol at -0.10 volt. DISCUSSION
I n order to obtain information about the potential to apply during the titration, current-voltage curves were obtained for potassium tetraphenylborate in acetonitrile-water mixtures
1.50
i
-
1.25
I
I
1.00
07
58
0.75
L
0
I
E
-;0.50
APPARATUS
A Sargent Model I11 manual polarograph was used to obtain the current-voltage curves as well as for the amperometric titrations. Corning marine barometer tubing which gave a drop time of 4.81 seconds, open circuit, was used for the dropping mercury electrode. All titrations were performed in a 100-ml. beaker with the dropping mercury electrode 7 mm. from the surface of the mercury pool. A calibrated microburet was used to measure the standard silver nitrate solutions. No degassing was necessary, as the titrations were performed a t such a potential that dissolved oxygen did not interfere. No temperature control was necessary.
0.25
0.00
to2 Figure 1.
MATERIALS
Acetonitrile (Eastern Chemical Corp.), dimethylformamide
(Du Pont), and methyl Carbitol, CH30CH2CH20CH2CH20H 1899
0.0 -0.2 -0.4 -0.6 -0.8 -1.0 EMF., Volts vs. Mercury Pool
-E
Polarograms for titration of tetraphenylborate ion with silver nitrate A.
Before titration
B. After addition of
excess silver nitrate
1900
ANALYTICAL CHEMISTRY
both before the titration and after the addition of an excess of silver nitrate. Figure 1 shows the polarograms obtained for a 0.1853-gram (5.172 X mole) sample of potassium tetraphenylborate dissolved in 15 ml. of acetonitrile and 5 ml. of water before addition of titrant (curve A ) and after addition of 5.320 ml. of 0.1M silver nitrate, an excess of 0.148 ml. of titrant (curve B ) . The increase of the diffusion current at -0.10 volt is due to the increase of the silver ion concentration. The wave at -0.8 volt for curve A is due to the reduction of oxygen, and the lowering of the wave height for curve B is probably due to the adsorption of the dissolved oxygen on the silver tetraphenylborate precipitate. This wave disappears when oxygen is removed from the solution. The shift in the half-wave potential can be explained by the fact that there is a change in potential at the mercury pool because tetraphenylborate ions have been replaced by nitrate ions. From these polarograms it can be seen that the titration may be carried out at any potential between +0.1 and -0.2 volt os. the mercury pool, at which the limiting current for the silver ion occurs, with no interference from the reduction of dissolved oxygen, which occurs at -0.5 volt. As a result, no degassing of the sample during the course of the titration was necessary. In this work the potential was set at -0.10 volt vs. the pool in order to be on the fully developed plateau of the silver ion.
with more silver ion. The precipitate of silver tetraphenylborate formed with acetonitrile in the solvent system was white and flocculent and did not darken even after standing in daylight for 5 days in the presence of the mercury pool and an excess of silver nitrate. The reducing action of dimethylformamide-water mixtures has been reported ( 7 ) in regard to reduction of cupric ion to the cuprous state and so it is not unexpected that the solvent mixture would also reduce silver ion. Methyl Carbitol, no doubt, contains reducing impurities which cause the darkening of the precipitate.
-
ml-,
,-I
ml. Reagent Table I. Titrations of Potassium Tetraphenylborate Samples in Acetonitrile-Water Mixtures
K
Taken, Mg.
AgN03 to Equivalence Point, M1. Theoretical Found
A. 5.162 5.205 5.287 5.443 5.564 5.650 12.58 12.61 12.85 13.25 13.50 19.12 19.41 19.49 19,74 19.97 20.18
Titrations 1.323 1.334 1.355 1.395 1.426 1.448 3,223 3.232 3,293 3.396 3.461 4.900 4.974 4.995 5.059 5.118 5.172
with 0.1M 1.326 1.329 1.364 1.398 1.430 1.448 3.240 3.251 3,278 3.409 3.475 4.882 4.954 4.942 5.001 5.119 5.138
AgNOg 5.174 5.185 5.322 5.454 5.579 5,650 12.64 12.68 12.79 13.30 13.56 19.05 19.33 19.28 19.51 19.97 20.05
Titrations with 0.0334 1.000 0.988 1,000 1,007 1,008 1.012 2.000 2,001 2.001 2,004 2.010 2.012
AgNOs
B. 1,170
2.341
K
Found, Mg.
1.168 1.170 1.179 1,180 1,185 2.342 2.342 2.345 2.353 2.355
Difference .Mg.
$0 012 - 0 200
+O 033
+o
$0 0 $0 $0 -0
+o +O -0 -0 -0 -0 -0 -0
011 015 000 06 07 06 05 06 07 08 21 23 00 13
- 0 002 0 000 -to 009 +o 010 $0 015 +o 001 +o 001 +O 004 $0 012 + O 014
Titrations were also performed in dimethylformamide-water mixtures following the same type of procedure, but in both cases the precision and accuracy were not so good as titrations performed in the acetonitrile-water mixtures. In all titrations performed in these two solvent mixtures with water there was appreciable darkening of the precipitate due t o the reduction of the silver ion to metallic silver, even when the titrations were performed in almost total darkness. It is assumed that either the titrant was reduced before the reaction of the silver ion with the tetraphenylborate ion or the precipitate was reduced after formation, liberating the tetraphenylborate ion which would react
Figure 2. A.
Titration of tetraphenylborate ion with silver nitrate
0.1 M silver nitrate in acetonitrile-water
B . 0.03 M silver nitrate in acetonitrile-water C. 0.1 M silver nitrate in dimethylformamide-water
Moreover, the literature (1) reports numerous cases of silver compounds forming stable complexes with nitriles, which may account for the inactivity of light toward the silver tetraphenyl borate precipitate in acetonitrile-mater mixtures and also the lack of reaction of the silver ion viith the mercury pool. RESULTS
Data for titrations performed in acetonitrile-water mixtures are shown in Table I. The molarity of the solutions titrated was from 1 x l O - 3 M to 2 x 10-2.M. The results obtained in the laboratory indicated that the method would apply to higher concentrations. The greatest deviation observed was 1.370; however, most of the samples titrated gave results within 0.6y0. The concentration of the silver nitrate was varied from 0.03 to 0.1M with no significant d fference in the precision of the re-
Table 11. Titrations of Potassium Tetraphenylborate in Dimethylformamide-Water Mixtures with 0.1M Silver Nitrate AgNOj t o Difference, K Taken, Equivalence K Found, llg.
Point, bll.
Alg.
19.50 19.52 19.56 19.57 19.68 20.84 27.34 27,44 35.03 35.06 35.48 35.53
5.012 5.090 5.100 5.044 5.032 5.370 7.082 6.972 9.138 8.845 9,270 9.118
19.56 19.86 19.90 19.68 19.63 20.95 27.63 27.20 35.64 34.51 36.17 35.57
LIg. +0.06 +0.34 +0.34 $0.11 -0.05 f0.11 +0.29 -0.24 +O. 61 -0.55 +0.69 1-0.04
V O L U M E 28, NO. 12, D E C E M B E R 1 9 5 6 sults. The composition of the solvent may vary widely between 60 and 1 0 0 ~ acetonitrile, o so long as the potassium tetraphenylborate remains in solution. I n previous methods which have been reported using nonaqueous solvents, the composition of the solvent had to be critically controlled (8) or be completely anhydrous (3). Results for titrations in dimethylformamide-water mixtures at -0.20 volt are shown in Table 11. These are not so precise as resiilts obtained in acetonitrile-water mixtures. A large number of titrations were performed with 0.01M silver nitrate in dimethylformamide-water mixture, but the results were from 2 to 5y0 high. Methyl Carbitol in the solvent system yielded results for titrations with 0.1M silve nitrate from 1 to 3.57, high. These titrations were performed at -0.1 volt us. the pool. Typical titration graphs are shown in Figure 2 for titrations in the acetonitrile-water and dimethylformamide-water system. This method should also be applicable for the precise determination of equivalent weights of organic bases, in case they form tetraphenylborate precipitates soluble in acetonitrile.
1901 ACKNOWLEDGMENT
The authors are indebted to the Atomic Energy Commission for funds under Contract No. AT( 11-1)-163. LITERATURE CITED
Dutoit, P., Friderich, L., B u l l .
SOC.
chim. France (3) 19, 321
(1898).
Findeis, A. F., De Vries, T., ANAL.CHEM.28, 209 (1956). Flaxhka, H., Chemist-Analyst 44, 60 (1945). Flaschka, H., Holasek, A.. Amin, A. A I . , Arzneirnittel-Forsch. 4, 38 (1954).
Hahn, F. L., Z . anal. Chem. 145, 97 (1955). Kemula. W.. Kornacki. J . . Roczniki Chem. 28. 635 (1954). Pflaum,'R.T., Popov,'h. S.,Goodspeed, S . ' C . , ANAL.CHEM. .
I
27, 253 (1955). Riidorf, W., Zanier, H. Z., 2. anal. Chem. 137, 1 (1952). Wittig, G., Angew. Chem. 62A,231 (1950). Wittig, G., Kucher, G., Ruckert, A . . Raff, P., Ann. 563,110, 126 (1949).
Wittig, G., Raff, P., Ibid., 573, 195 (1951). R E C E I V Efor D review November 17, 19%.
Accepted h u g u s t 15, 1956
Theory of Countercurrent Distribution in Solvent Systems near a Critical Point C. A. HOLLINGSWORTHand 1.1. TABER Department o f Chemistry, University of Pittsburgh, Pittsburgh, Pa.
B. F. DAUBERT Central Laboratories, General
foods Corp.,
Hoboken,
By the use of the theory of regular solutions, equations are obtained expressing the behavior of partition ratios near the critical temperatures of complete miscibility of two-component solvent systems and near the plait point of three-component, symmetric solvent systems. These results are used with a criterion of separation to predict the optimum conditions for separation by countercurrent distribution in these systems. The theory is then applied to experimentally determined partition ratios of some triglycerides to predict the amount of separation that can be obtained. The theory leads to the following conclusions: In systems to which the theory applies, the relative behavior of a pair of solutes can be characterized by a constant, y, which is independent of the temperature or the third solvent component. Nearly optimum conditions for separation exist over a fairly w-ide range of temperature or solvent composition and far enough from the critical point so that extreme dependence on temperature or composition is not encountered.
W
I T H countercurrent distribution technique developed by Craig (2)using any given number of transfers, n, and any given ratio, T , of the two phases, the amount of separation obtained for two solutes depends upon the partition ratios (distribution coefficients) of the two solutes. I t often happens that t a o solutes are difficult to separate because both the partition ratios (or their reciprocals) are very large, say, 50 or more. When possible in such cases automatic equipment is used, which makes hundreds, perhaps even thousands, of transfers practical (9). When such equipment is not available, the value of T may be adjusted, but large adjustments are usually not convenient. A withdrawal procedure may be used, but the possibilities
N. 1. here are limited. It may be possible to obtain the desired degree of separation by recycling, but when the equipment is not automatic this can be laborious and time-consuming. Sometimes the solvent system can be modified to improve the values of the partition ratios; there are various ways of doing this, and they depend upon the types of solutes and solvents that are involved. Only one type of system is investigated here-one in which the solutes and solvents are nonelectrolytes and the solvent system possesses a critical temperature or a plait point within operating range. Both partition ratios (or both reciprocals) are lowered as the system moves toward a critical point. As the critical point is approached, both partition ratios approach unity, and separation is again poor. There is, therefore, an optimum condition for separation. In a two-component solvent system there is an optimum temperature, and in a three-component solvent system with a plait point there is an optimum composition ( 6 ) , where optimum refers to that temperature, or composition, a t which the degree of separation is a maximum for a given n and r. If the optimum conditions are not so close to the critical point that there is extreme dependence upon temperature or composition, it may be practical to carry out the distribution under these conditions. It was the purpose of the work reported here to apply the theory of regular solutions to obtain theoretical expressions for these optimum conditions for separation and to apply them to experimentally determined partition ratios of some triglycerides in certain solvent systems. PARTITION RATIOS NEAR A CRITICAL POINT
Two-Component Solvent Systems near Critical Temperature Let x and y be the mole fractions of the two solvents, X and Y , and let w be the mole fraction of a solute, W . For a regular solution the Gibbs free energy of mixing is given by
