-lot = 12
QD’12
l(l+exp-(g)+ 2P
.v - 1
2 ]=I
exp
-
[g
(1
- cos(+)]} (B9)
h comparison of Equations B7 and B8 shows the error introduced by considering the semi-infinite diffusion process to be finite is insignificant, about 1.7 x IOe4 per cent. .A curve showing the per cent variation of Equations B8 and B9 from Equation 137 for various values of P is presented in Figure 4. This curve s h o w that as the value of N is increased, the per cen’t error obtained from Equation B9 approaches that obtained from Equation B8. If there were no kinet’iccomplications, the error, resulting from assuming the semi-infinite diffusion process to be given by a finite number of S diffusion cells, can be taken directly from Figure 4 for a particular value of P .
However, when kinetic complications enter into the diffusion process, Equation B9 is not directly applicable because the boundary conditions are not the same. Nevertheless, it is useful in selecting the size of the coefficient matrix for a desired value of P . LITERATURE CITED
(1) Booman, G. L., Pence, D. T., Phillips
Petroleum Co., Idaho Falls, Idaho, unpublished data, 1965. (2) Brdicka, R., Hanus, V., Koutecky, J., “Progress in Polarography,” P. Zuman, ed., 5’01. 1, p. 175, Interscience, New York, 1962. (3) Carslaw, H. S., Jaeger, J. C., “Operational Methods in Applied Mathematics,” p. 44, Dover, Xew York, 1963. (4) Crank, J., “The Mathematics of Diffusion,” Chap. X, Oxford University Press, London, 1957. (5) DeLIars, R. D., Shain, I., J. Am. Chem. SOC.81, 2654 (1959). (6) Doug,l,as, J., Jr., “Advances in Computers, F. L. Alt, ed., Vol. 2, p. 18, Academic Press, New York, 1961. (7) Faddeeva, V. N., “Computational
Methods of Linear Algebra,” p. 65, Dover, New York, 1959. (8) Feldberg, S. W., Auerbach, C., AXAL. CHEM.36, 505 (1964). (9) Fisher, O., Dracka, O., Collection Czech. Chem. Commun. 24, 3046 (1959). (10) Forsythe, G. E., Wasow, W. R., “Finite-Difference Methods for Partial Differential Equations,” p. 102, Wiley, New York, 1964. (11) Harrar, J. E., Ph.D. thesis, University of Washington, 1958. (12) Jaeger, J. C., “The Laplace Transformation,” Chap. IV, Wiley, New York, 1959. (13) Kern, D. AI., Orlemann, E. F., J . Am. Chem. SOC.71, 2102 (1949). (14) Koryta, J., Koutecky, J., Collection Czech. Chem. Commun. 20, 423 (1955). (15) Koutecky, J., Koryta, J., Ibid., 19, 845 (1954). (16) Orlemann, E. F., Kern, D. U.,J. Am. Chem. Sac. 75, 3058 (1953). (17) Wagner, R. J., U. S. At. Energy Comm. IDO-16867 (1963). Received for review N a y 24, 1965. Accepted July 30, 1965. Work done under contract AT( 10-1)-205, Idaho Operations Office, U. S. Atomic Energy Commission.
Standardization of Thiosulfate Using Potassium Dichromate by Direct Titration V. P. R. RAO and B. V. S. SARMA Chemisfry Deparfmenf, Andhra Universify, Waltair, India The standardizcition of thiosulfate with dichromate by direct titration is described. Potassium dichromate i s potentiometrically titrated with sodium thiosulfate at pH 4.5, after adding 2 ml. of 0.2N copper sulfate to catalyze the dichromate-thiosulfate reaction. The method is compared to a newly developed modification of the Gaebler and Baty procedure. Thiosulfate is oxidized only to the tetrathionate state and the normalities obtained agree very closely with those obtained by the iodate, feivicyanide, or the older dichromate method.
T
HERE ARE several methods for the standardization of thiosulfate utilizing various oxidants (3-7, 9, IO), some of which are u e d as primary substances. Most of these methods involve the titration with thiosulfate of the iodine liberated from excess of iodide by the oxidant. Hahn ( 2 ) showed that if dichromate is reduced in presence of thiosulfate, the nascent chroniium(II1) generated forms a complex with thiosulfate which reacts sloivly with iodine, and thus higher titers are obtained. Although in strong acid solutions the rate of reaction between dichromate and iodide is fast, a high hydrogen ion concentration is undesirable as it facilitates air oxidation of iodide.
Gaebler and Baty ( I ) have shown that oxalate or tartrate catalyzes the reaction between dichromate and hydriodic acid by complexing the nascent chromium(II1) produced. They obtained accurate results by titrating a mixture with thiosulfate a t low acid concentrations in the presence of oxalate without waiting. Sully (8) has observed that copper sulfate greatly accelerates this reaction, even in acetic acid medium. We have found that a direct titration of dichromate with thiosulfate can be carried out potentiometrically using copper(I1) as a catalyst a t p H 4.5. It is further observed that the direct titration of thiosulfate with dichromate is facilitated in the presence of iodide and oxalate. EXPERIMENTAL
Reagents and Apparatus. All chemicals used were Proanalysi or -4nalaR samples. -4 combination of a Kaycee potentiometer with a Cambridge reflecting spot galvanometer was used for potentiometric titrations. Potentiometric Procedure for Standardization. An aliquot of standard dichromate solution is taken in a beaker and 30 ml. of 4.45 p H acetateacetic acid buffer and 2 ml. of 0.2N copper sulfate are a d d e d ; t h e solution
is diluted t o 50 ml. T h e dichromate is then titrated potentiometrically with sodium thiosulfate. T h e normality of thiosulfate obtained b y this procedure is compared with t h a t obtained b y earlier methods and t h e results are given in Table I. Procedure for Standardization Using Iodide and Oxalate. T o a 5.0t o 10.0-ml. sample of sodium thiosulfate solution, about 70 ml. of water, 10 ml. of 20% potassium iodide, 5 ml. of 1 N oxalic acid, and 1 ml. of 1% starch indicator solutions are added, followed by 2 ml. of 5N sulfuric acid. T h e overall acidity on dilution t o 100 ml. is 0.1N. This order of mixing should be followed carefully as the solution becomes turbid because of decomposition of thisoulfate if the acid is added before dilution, The color change a t the end point in the titration of this solution with standard dichromate is from pale violet to blue violet, and is sharp and reversible. The normalities obtained b y this procedure are compared with those obtained by potentiometric and other earlier methods, and are given in Table I. RESULTS AND DISCUSSION
Potentiometric Method. In t h e absence of copper sulfate, t h e reaction between dichromate and thiosulfate is very slow. However, during t h e VOL. 37, NO. 1 1 , OCTOBER 1965
1373
titration (using a bright platinum rod and a saturated calomel half cell as indicator and reference electrodes) in the presence of copper(II), the potentials are stabilized in about 30 seconds. Just before the end point, however, the potentials are fleeting even in the presence of copper(II), and generally when the potential becomes unsteady even after one minute, the end point is very close. The results are uneffected when the volume of 0.2147 copper sulfate is varied from 1 to 5 nil., and it is not necessary to apply a correction for the amount of copper sulfate added. Copper chloride gives similar results. The potentiometric titration curves obtained under various p H conditions, for the same volume (5.0ml.) of dichromate are given in Figure 1. The graph shows that the titers decrease with increase in acidity. This decrease may be due to oxidation of thiosulfate beyond the tetrathionate stage, although sulfate could not be detected a t any pH in experiments using copper chloride as a catalyst. Titers coinciding with the oxidation of thiosulfate to tetrathionate could be obtained only with a pH of about 4.5. Even when the p H is 4.0, 0.5 to 1% lower titers are obtained. When the p H is 5, the potentials take 3 to 4 minutes to reach equilibrium even from the beginning; further, the solution becomes turbid during the titration. I t is significant to note that the medium should be buffered, because as thiosulfate is added, the p H of the solution is increased, resulting in the formation of turbidity in the solution. Oxalate and Iodide Method. T h e catalytic action of oxalate is noticeable only when the concentration of iodide in the solution is a t least 1%. If the iodide ion concentration is less t h a n 1%, the reaction between iodide and dichromate is not instantaneous under the experimental conditions of acidity. One to 5% of iodide is found satisfactory. The violet color is due to the forma-
Table 1.
Soh. 2
Av. a
sa0
-
480
-
' 6
I
4
440
-
2 35 4 0 0 -
4
E
Y
9
d360-
320
-
290
-
140
-
!
2
I
2001
1 . 0 4.99 pH buffer 2. H4.45 p H buffer 3. 0 4.05 pH buff& 4. I3 3.72 pH buffer
I
I
IO
I2
of dichromate with
5. A 2..32 p H 7. E3 0.1N 8.
tion of chromium(II1)-oxalate complex.
buffer
1.42 p H buffer
6.
x
His04
1 .ON H2S04
titration. The acidity most favorable for the titration is 0.1 +0.05hr with respect to either sulfuric or hydrochloric acid, when the overall oxalic acid concentration is 0.05iV. As a further check, it was determined that when the mineral acid concentration is 0.1N, the optimum concentration of oxalic acid is 0.05 f 0.02N. At lower
It is of importance to note that if the amount of thiosulfate is more than 0.5 milliequivalent (10.0 ml. of 0.05 N solution) per 100 ml. of titration mixture, turbidity developed either before or during the titration. Experiments were carried out to investigate the effect of acidity on the
Normality of Thiosulfate Found
I
8
I
Figure 1 . Effect of pH on titration thiosulfate
by Various Methods Pot,entiometrica
0,04918 0.04920 0.04922 0,04920 0.04922 0.04911 0.04918 0.04920 0.04919
0,04914 0.04918 0.04914 0,04918 0.04914 0.04918 0.04918 0.04918 0.04917
0.04922 0.04920 0.04922 0.04920 0.04918 0.04920 0.04922 0.04911 0,04919
Oxalatea a b 0,04920 0.04920 0.04920 0,04920 0.04920 0,04920 0.04915 0,04920 0.04919
0,02465 0.02465 0.02465 0,02465 0.02465 0.02463 0.02465 0.02465 0.02465
0.02465 0.02465 0.02465 0.02463 0.02464 0.02463 0.02464 0.02465 0.02464
0,02464 0.02463 0.02464 0.02465 0.02464 0.02465 0.02465 0.02465 0,02464
0.02465 0.02465 0.02465 0.02463 0.02465 0.02465 0.02465 0.02465 0.02465
0.02465 0,02465 0.02465 0,02465 0.02465 0.02465 0.02463 0.02465 0.02465
a
Ref. 6" b
a
a = solution volume of 10.00 ml.; b = solution volume of 5.00 ml.
1374
I
6 4 Vol. of thiowlfrtc (ml.)
2
0
b 0.04922 0.04920 0.04922 0,04911 0.04922 0.04920 0.04918 0.04920 0.04919 a
Av .
360-
Ref. 4"
Ref. Sa Soln. 1
600-
ANALYTICAL CHEMISTRY
b
a
b
oxalate concentration, iodine liberation by dichlomate is not instantaneous. Fui ther, the iodine-starch blue color appears when only 9570 of thiosulfateis oxidized, although the blue color gradually fades. Thus, returning and uncertain end points are obtained. nxenthe concentration of oxalate is greater, higher titlers are obtained, ProbablY because Of over-oxidation of thiosulfate I
LITERATURE CITED
(8) Sully, B. D., J . Chem. SOC. 1942,
0. H., Baty, AI., ISD. EXG.CHEV.ANAL.ED. 13, 442 (1941). ( 2 ) Hahn, F. L., J . Am. f3em. 57, 614 (1935). (3) Kolthoff, I. AI., Pharm. Weekblad 5 6 , 644 (1919). ( 4 ) Ibzd., 5 9 , 66 (1922). (5) Kolthoff, I. 11.) 2. AnaE. Chem. 59, 401 (1920). (6) Ibzd., p. 411. ( 7 ) Kolthoff, I. >I., van Berk, L. H., J . d m . Chem. SOC.48, 2799 (1926).
( 9 ) Treadwell, F. P., Hall, ITr. T., “An-
(1) Gaebler,
366.
alytical Chemistry,” 9th Ed., Tol. 11, p. 588, Wiley, New York, 1942. (10) Tan Dame, H. C., J . Assoc. Ofic. Agr. Chemists 30, 502 (1947). RECEIVED for review November 24, 1964. Accepted J ~ l y20, 1965. One of LIS (B.V.S.S.) has received an award of a research fellowship from the Council of Scientific and Industrial Research (India).
Rapid Removal of Alkali Metals from Quaternary Ammonium Bases by Ion Exc ha nge EUGENE D. OLSEN and ROBERT L. POOLE, JR. Department o f Chemistry, University o f South Florida, Tampa, Fla. The contamination of quaternary ammonium bases with alkali metal ions i s difficult to avoid. A simple procedure for removing sodium ion and other alkali metals from tetramethylammonium hydroxide, tetraethylammonium hydroxiide, tetrapropylammonium hydroxide, and tetrabutylammonium hydroxide on Dowex 50 W-X16 cation exchange resin i s described. It has been demonstrated that a sodium ion content in the bases of even 0.05M or more can be rapidly decreased to less than 1 p.p.m., with breakthrough capacities of about 20% of the total exchanige capacity, and yields of all four bases greater than 80%. Conditions necessary for optimum efficiency and yields were studied in detail. Breakthrough capacity data given should be useful in estimating the amount of resin that should b e used in purifying a given amount of quaternary ammonium base of known alkali metal content. Resins can b e regenerated and reused.
Q
bases have numerous important applications in analytical chemistry. Sonaqueous solutions of these bases are excellent titrants for the deterrnination of acids in organic solvents. They are superior to the alkali metal hydroxides and alcoholates because they can be used with the gla53 electrode without introducing the “alkali erior” and because they form salts which are more soluble in nonaqueous solvents than are those of the alkali metals (10). Similarly, tetramethylammonium h;,-droxide (TILIAiH) is a very useful titrant in potentiometric stability constant determinations, especially when there’ is a possibility of the ligand forming complexes with alkali metal ions (17). And while a UATERNARY AUMONUU
number of ligands will complex with alkali metals in aqueous solutions (W), this tendency to complex is accentuated in partially nonaqueous solvents (15). Other important applications of the bases or their salts include their use upporting electrolytes in the polarographic determination of the alkali metals (la),and their use in ion exchange separations involving the alkali metals (4,1 4 ) . I n all of these applications it is highly deqirable or even imperative that the alkali metal content of the quaternary ammonium base be low. I n potentiometric titrations in aqueous solution with the glass electrode, the “alkali error” a t high p H is well known (1). I n nonaqueous solutions, the deleterious and unusual effects of sodium and potassium on the response of the glass electrode is especially serious (8). I n polarographic analysis for the alkali metals, and in ion exchange separations of trace amounts of alkali metals, the presence of alkali metal impurities in the quaternary ammonium bases is intolerable. Unfortunately, reagmt or analyzed grade quaternary ammonium bases are not commercially available a t present. Harlo\T summarizes three widely used methods for the preparation of quaternary ammonium baces, and points out that all three are subject to alkali ion contamination (8). I n the classical preparation of quaternary ammonium bases a solution of a quaternary ammonium halide is reacted with a suspension of silver oxide (19). This procedure is sometimes used commercially ( 7 ) , and involves treating silver nitrate with sodium hydroxide to form the silver oxide precipitate. The precipitated silver hydroxide is thoroughly washed with distilled water before reaction with the quaternary
ammonium halide, but sodium hydroxide tends to adhere to the silver hydroxide, and sodium ion contamination of the final base is difficult to avoid. Peracchio and Meloche found it necessary to wash the precipitated silver oxide 12 to 15 times in preparing tetramethylanimonium hydroxide for polarographic studies of the alkali metals (16). Cundiff and Narkunas recently reported a procedure involving washing silver oxide with boiling water and methanol that resulted in sodiumfree tetrabutylammonium hydroxide (TBAH) ( 5 ) . Purified silver oxide is commercially available and can be used to prepare alkali-free base ( 1 4 ) , but even with this shortcut the silver oxide method is laborious and time-consuming. The other two widely used methods of preparing quaternary ammonium bases are likewise subject to alkali metal contamination. The potassium hydroxide method of preparing nonaqueous quaternary ammonium titrants yields bases containing 100 to 200 p.p.m. potassium ion (10), and the anion exchange resin preparation of Harlow, Xoble, and Wyld may also result in potassium ion contamination (9). An electrolysis method of preparing pure T M X H for polarographic studies has been reported by Supin (18), but has not been tried for other quaternary ammonium bases. Because the thermal instability of the free bases precludes purification by ordinary distillation methods (12 ) , another means of removing alkali metals is needed. I n an earlier article it was shown to be feasible to selectively retain alkali metals on Dowex 50 W-X8 in the tetramethylammonium ion form, even when the solution contained a fairly high concentration of tetramethylammonium ion (14). A deVOL. 37, NO. l l , OCTOBER 1965
* 1375
