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Figure 5. Absorption spectra of 3.0 X lO-5M bromine in 90 % acetic acid-lOz water containing a 6 : l ratio of hydrogen bromide to bromide
This problem can be avoided by adding sufficient hydrogen bromide to the bromine solution used so that any additional hydrogen bromide produced in the bromination reaction has a negligible effect on the absorbance. A plot of absorbance of bromine in acetic acid-water as a function of added hydrogen bromide shows a leveling off around a mole ratio of approximately six hydrogen bromide to one bromine (Figure 3). A brominating solution of this composition was found to be quite successful for the indirect determination of small amounts of unsaturated compounds. Linear Beer's law plots were obtained at several different wavelengths so that the
sensitivity of the method can be varied by changing the wavelength. Curves are shown in Figure 4 for determination of cyclohexene, a typical fast-reacting olefin, and for allyl ether, which was the slowest-reacting compound determined by the spectrometric method. The discontinuity in the curves is caused by removal of the cell to add the sample and mix. These curves are replotted from automatically recorded curves of absorbance us. time. The curves obtained may be extrapolated if necessary to correct for slow side reactions. Results for the quantitative determination of trace unsaturation are given in Table 111. Considering the small amounts of unsaturation determined, the results seem quite satisfactory. For most of the analyses, 2.60 ml of 1 x lO-4M bromine, 6 X 10-4M hydrogen bromide in 90% acetic acid10% water was employed, and the absorbance in a 1-cm cell was measured at 410 mp before and after addition of the sample. Smaller amounts of unsaturation (0.02 peq) were determined by using a more dilute bromine-bromide solution and by measuring the absorbance at a lower wavelength (270 mp) where the tribromide ion has a higher molar absorptivity (see Figure 5). Under these conditions the method is so sensitive that a correction for the sample solvent blank is required. In the spectrophotometric method for unsaturation, it is necessary to correct for the dilution of the bromine solution resulting from introduction of the sample solution. This is done by multiplying the final absorbance by the factor, (VBr V,)/VB~ where , V B is ~ the volume of the bromine-bromide solution initially added and V , is the volume of sample solution added.
+
RECEIVED for review July 25, 1967. Accepted October 26, 1967.
Precision Standardization of Ceric Sulfate Solutions A. J. Zielen Chemistry Division, Argonne National Laboratory, Argonne, Ill. 60439 Standardization procedures for ceric sulfate solution accurate to 0.01% were verified by agreement between the National Bureau of Standards redox reagents: arsenious oxide, sodium oxalate, and potassium dichromate. Particular attention was paid to the catalyst role of osmium tetroxide in the As(lll)-Ce(lV) reaction. Incomplete reoxidation of the osmium to the Vlll state was found to cause serious errors. Depending on the amount of osmium, titration direction, and potentiometric vs. indicator end point detection, these errors ranged as high as 0.3-0.4% for a 2-meq sample. The only error-free method was found to be the potentiometric titration of Ce(lV) by As(lll), which is the reverse of the customary procedure. The redox indicator ferroin can also be used if a blank correction is applied. A similar direction dependence was observed in the potentiometric standardization of Fe(ll) with dichromate. Here, dichromate as the titrating agent avoids a small error.
RECENTWORK in this laboratory required very exact standardization of ceric sulfate solutions. Of the existing methods, the procedure of Gleu ( I ) with primary standard arsenious oxide and osmium tetroxide catalyst appeared to be the (1)
K.G1eu.Z. A n d . Chern., 95,305 (1933).
simplest and best. Indeed at the onset there was every reason to believe that, using weight burets and sufficiently large samples, this well known and universally accepted procedure could yield an absolute accuracy of 0.01 %. Very reproducible results were in fact readily attained. However, it was also observed that procedural variations such as titration direction, the amount of catalyst added, and potentiometric or colorimetric end point detection produced small but significant differences. Establishing the conditions for the most accurate ceric standarization was the goal of this work. A final check was obtained by agreement better than 0.01% between completely independent methods using the three redox standards of reference of the National Bureau of Standards : arsenious oxide, sodium oxalate, and potassium dichromate. Also, it is a surprising fact that a paucity of information exists in the literature substantiating the accuracy of the Gleu procedure. Gleu himself made only a very perfunctory check ( I ) . Smith and Getz (2) used perchloric and nitric acid ceric solutions to compare sodium oxalate, ferrous sulfate stan(2) G. F. Smith and C. A. Getz, IND. ENG. CHEM.,ANAL.ED., 10, 304 (1938). VOL 40, NO. 1, JANUARY 1968
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dardized indirectly via ceric sulfate and sodium oxalate, and osmic acid-catalyzed sodium arsenite. The investigators considered the agreement satisfactory, but the results were not impressive. The arsenious oxide values averaged 0.14 and 0.16x higher, respectively, than the sodium oxalate and ferrous sulfate standardizations for their solutions 1 through 7. The eighth and final solution gave a gross difference of more than 1%. A far superior piece of work was done by Smith and Fly (3) in their very careful check of ammonium hexanitratocerate as a primary standard. Essentially agreement at the 0.01 level was found between sodium oxalate and osmium tetroxide-catalyzed arsenious acid in both perchloric and sulfuric acids. This is, in fact, the only precise verification of the Gleu procedure found in the literature. However, Smith and Fly made what appeared at the time to be an insignificant change in the standard procedure-namely, using As(II1) as the titrating agent. As will be shown shortly, this is the essential step in obtaining a correct result at the 0.01 % level. EXPERIMENTAL Reagents. The following National Bureau of Standards
samples were used as primary standards: AS& sample 83c, assay 99.99%; NazCzOa,sample 40g, assay 99.95 %; KzCrz07, sample 136a, assay 99.99%. All were initially dried at 105-10° for 4 to 5 hours and stored in weighing bottles in a desiccator over calcium sulfate hemihydrate (Drierite) between use. All weighings of the primary standards were corrected to in vacuo conditions. The listed assay values were used along with 1961 atomic weights based on carbon-12. The weights and analytical balance were checked to assure 0.1-mg reliability against a special laboratory set of Class S weights recently certified by the National Bureau of Standards and used only for calibrating purposes. Wide mouth, 4-inch funnels facilitated the transfer of primary standard samples from weighing bottles into 500-ml volumetric flasks. p h i s simple transfer was initially a great source of difficulty with arsenious oxide. The first analyses were run using an old NBS sample, 83a. This material was so finely divided that it appeared amorphous, and physical transfer of the fluffy powder was virtually impossible without some airborne loss. The more crystalline nature of sample 83c immediately solved this problem, but transfer to an extra wide mouth receptacle is still strongly recommended.] Approximately 0.1N solutions of potassium dichromate and sodium oxalate and As(II1) were prepared by weight. A Sartorius Model 21 16 balance allowed rapid weighing of the roughly 500 grams of final solution with an accuracy of 10.02 gram. By filling the volumetric flasks to the mark, solution densities were also available when needed. The dichromate and oxalate solutions were prepared in water swept free of oxygen by nitrogen bubbling. The oxalate solutions were made 1N in sulfuric acid. A typical As(II1) solution in 1N sulfuric acid was prepared from 1.7 grams of As203. A very thorough rinse of the transfer funnel with oxygen-free water to remove any tenacious film of oxide was followed by 20 ml of 5M sodium hydroxide. After complete dissolution, 60 ml of 5M sulfuric acid was added, and the solution was diluted to the mark after cooling in a 25" C water bath. Solutions lll6Nin As(II1) were used because titration with 0.1N arsenious and ceric solutions was observed sometimes to produce a small amount of white precipitate, perhaps due to a trace impurity in the ceric sulfate. To test if the well established air oxidation of As(II1) in basic solution ( 4 ) could cause an appreciable error during
the rather slow dissolution of arsenious oxide, a second series of As(II1) solutions was prepared under an inert atmosphere. This was done by bubbling nitrogen continuously through an aqueous suspension of the oxide in a stoppered Erlenmeyer flask while oxygen-free sodium hydroxide and sulfuric acid solutions were added to turn under nitrogen pressure. After addition of the acid no further precautions against air oxidation were taken. The stability in acid solution even in the presence of osmium tetroxide was tested by allowing a pair of As(II1) solutions in 1N sulfuric acid to stand overnight in beakers covered only with watch glasses. The first contained fairly high osmium (4.4 X 10-5M), and the same amount of osmium tetroxide was added to the second the next morning. Ceric sulfate was then added to both until in slight excess and titrated as usual. These two "standardizations" gave, respectively, 0.091045 and 0.091051 while a conventional titration with the same As(II1) stock when freshly prepared gave 0.091040, all results as milliequivalents of Ce(1V) per gram of solution. Air oxidation of As(III), which would give a high Ce(1V) concentration, obviously did not occur to any great extent. Ceric sulfate solutions 0.1N in 1N sulfuric acid were obtained in 2-liter batches from the G. F. Smith Chemical Co. and used as received. The same source supplied 0.025M solutions \ the redox indicators 1,lo-phenanthroline ferrous sulfate (ferioin) and 5,6-dimethyl-1,lo-phenanthroline ferrous sulfate. The osmium catalyst was prepared by dissolving the reagent tetroxide in 0.1N sulfuric acid. This was a rather old solution originally made up for other work to be 0.01M. After 18 months of frequent use, analysis indicated the concentration was down to 1.6 X 10-3M. For experiments where the amount of osmium was a variable, the stock solution was analyzed at intervals and observed to weaken by another 18% over a 5-month period. Linear interpolation was used to calculate the proper stock concentration for each run. All of these analyses were done spectrophotometrically using the thiourea complex (5). The data of Ayres and Wells (6) in the 10- to 40-ppm osmium concentration range were used to calculate a molar absorptivity of 4150 at 480 mg. The loss of osmium from this solution was, of course, due to the volatility of the tetroxide; however, the stock solution was stable in the sense that no evidence was found of reduction to lower oxidation states of osmium. The water used for all solutions was triple distilled starting with alkaline permanganate. All other reagents were of the highest grade available. Apparatus and Procedure. Potentiometric titrations were used throughout including the runs with redox indicators. The titrating vessels were large weighing bottles of 100-ml capacity covered by a Teflon cap machined to supply the required standard taper fit. Holes drilled in the cap provided support for the electrodes, a gas entry tube to allow passage of nitrogen through or over the cell solution, and an entry port for a buret. Magnetic stirring provided constant agitation. The redox indicating electrode was a shiny platinum wire with a diameter of 0.05 inch. This was cleaned prior to every titration by heating in a gas-air flame to yellow heat. A Beckman 39177 GP probe type glass electrode served admirably as the reference electrode while eliminating any possible interference caused by leakage from the salt bridge of a conventional reference electrode. However, all cell potentials have been converted to an absolute scale by calibration of the glass electrode against a normal hydrogen electrode ("E). The particular glass electrode used has been kept wet constantly during 4 years of service, and Sauerbrunn and E. B. Sandell, J. Am. Chem. Soc., 75, 3554 (1953). ( 6 ) G. H. Ayres and W. N. Wells, ANAL.CHEM., 22, 317 (1950). ( 5 ) R. D.
(3) G. F. Smith and W. H. Fly, ANAL.CHEM., 21, 1233 (1949). (4) I. M. Kolthoff, 2. A n d . Chem., 60, 393 (1921).
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Figure 1. End point detail of effects of osmium and direction in potentiometric titration of As(II1) and Ce(1V) in 1N &SO4 A and C , 0.033 pmoles Os04; B and D,0.81 pmoles 0 ~ 0 4 ;D‘ is 2nd end point for D (see text). Triangles with apex indicating direction signify cell potentials still drifting after 5-min. wait. Vertical
dashed lines are calculated stoichiometric points
in that time its “standard” potential os. NHE has changed by only 9 mV. Cell potentials were measured to the nearest millivolt using apparatus previously described (7), but with the sensitivity greatly reduced. Any laboratory pH meter could have served as well. Weight burets were used for the bulk of all titrations with the final 1 to 2 % added from a Manostat Digi-Pet pipet of 1-ml capacity. In the immediate vicinity of the end point, increments of 0.001 ml were added at 1-minute intervals. This was increased to 5 minutes if the cell potential was drifting appreciably, which was arbitrarily taken as >5 mV/minute. Direct observation usually fixed the potentiometric end point within 10-3 ml as compared to a total titrant volume of 20 or 30 ml. As a further refinement, end points were calculated to ml using the equal increment version of Yank procedure (8). Indicator end points were taken to be the first appearance of a red tint in the titration of Ce(1V) by As(II1) and of a blue or colorless solution for the reverse titration. Color changes that faded in less than 1 minute were discounted. In all cases, solution densities could be used to convert the small volume fraction of the titrant back to the weight concentration scale with more than adequate accuracy. The weight burets employed were 2-02 polyethylene wash bottles used as described by Seils, Meyer, and Larsen (9). They proved very convenient and performed well, but special care must be taken to select leakproof caps. Also they were sensitive to electrostatic weighing errors. With the relatively large quantities used in this research, this was not a serious problem; but as a precaution the bottles were allowed to stand on the balance pan at least 15 minutes before all final weighings. Buoyancy corrections for the weight burets were not needed in this work; hence, the concentration scale employed throughout was milliequivalents per gram of solution weighed in air. Frequent use was made of a standard titration with As(I1I) to serve as a fixed reference point. This standard, which anticipates the present results as a procedure that gives the correct answer, was the Potentiometric titration of 2 meq of Ce(1V) by ‘ilSNAs(II1) with a 100-~1aliquot (ca. 0.16 p-noles) of the Os(VII1) stock added in a final solution volume of 65 5 ml of 1N sulfuric acid. Other As(II1) standardiza-
*
(7) A. J. Zielen, J . Phys. Chem., 67, 1471 (1963). 37, 1588 (1965). (8) J. F. Yan, ANAL.CHEM., (9) C. A. Seils, R. J. Meyer, and R. P. Larsen, Zbid., 35, 1873 (1963).
tions differed only in the titration direction, the amount of osmium, and the possible presence of a redox indicator. The oxalate standardizations closely followed the suggestions of Smith (IO), whereby an excess of ceric sulfate (2.5 meq) was added to a sodium oxalate solution (2 meq) in 1N sulfuric acid and heated to 50” C for 5 minutes. After cooling, the excess Ce(1V) was titrated potentiometrically with 0.1Nferrous sulfate in 1Nsulfuric acid. The relative titer of the Fe(I1) solution was determined either immediately prior to or after the oxalate titration by a second, direct comparison with the ceric sulfate stock. All titrations involving ferrous were run with a stream of nitrogen sweeping the cell solution. In the potassium dichromate procedure, ferrous sulfate was standardized as an intermediate; and a portion of the same solution sample was immediately used to titrate ceric sulfate. Two versions were tried and found to give slightly different results, which will be discussed later. In both procedures 10 ml each of 5M sulfuric acid and concentrated phosphoric acid were added to 20 ml of 0.1N potassium dichromate. Titration to the potentiometric end point was made with 0.1N ferrous sulfate in 1N sulfuric acid; or in the modified version, a 1 to 2 % excess of ferrous was added and back-titrated with the dichromate solution. A few attempts were also made using pure iron wire as a standard substance ( I I ) , and the iodine monochloride catalyst potentiometric standardization at room temperature 6s. sodium oxalate (12). The iron wire results were very poor, possibly because solution was made in sulfuric instead of the suggested hydrochloric acid. The IC1 method worked well in one attempt using freshly prepared catalyst but failed dismally when a commercial preparation was used. Further efforts with these methods did not seem warranted when compared to the ease and simplicity of the other procedures, especially the osmium tetroxide method. RESULTS AND DISCUSSION
A typical example of the Gleu ( I ) procedure given by Smith
(IO) calls for approximately 1.5 lmoles of osmium tetroxide in a final solution volume of 125 ml. Other authorities suggest osmium-volume combinations covering about a 3to 4-fold concentration range ( I I , 1 3 ) . Obviously the amount of catalyst has not been considered a critical point. And invariably Ce(1V) is specified as the titrating agent with little attention given to the reverse titration. A notable exception is Kolthoff and Belcher (13) who specifically warn against titrating with As(II1) and suggest instead a back-titration with Ce(1V). Figures 1 to 3 present potentiometric and colorimetric end point data to illustrate that these ignored and misunderstood factors are of importance. For this purpose the ultramicro buret proved especially opportune for revealing end point details that would be completely missed in an ordinary titration. In Figures 1-3 all the abscissa values have been arbitrarily selected and successively displaced for clarity. However, in each case a vertical dashed line is included which is the calculated end point as obtained from a standard titration (previously described) with the same arsenious and ceric solutions. An end point difference from the standard of 2 peq (10) G. F. Smith, “Cerate Oxidimetry,” The G. Frederick Smith Chemical Co., Columbus, Ohio, 1942, pp. 32-3, 42. (11) H. H. Willard and N. H. Furman, “Elementary Quantitative Analysis,” 3rd ed., Van Nostrand, New York, 1940, pp. 246-8, 258. (12) H. H. Willard and P. Young, J . Am. CAem. Soc., 50, 1322 (1928); 55, 3260 (1933). (13) I. M. Kolthoff and R. Belcher, “Volumetric Analysis,” Interscience, New York, 1957, Vol. 111, pp. 131, 137. VOL 40, NO. 1, JANUARY 1968
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Figure 2. Potentiometric os. indicator end points for titration of Ce(1V) by As(II1)
Figure 3. Effects of Os04 on potentiometric and ferroin end points in titration of As(1II) by Ce(1V)
E and F, 1.25 pmoles ferroin with, respectively, 0.18 and 2.9 pmoles OsOa; G,1.25 pmoles of 5,6-dimethyl derivative of ferroin with 0.18 pmoles 0 ~ 0 4 . Key same as Figure 1 plus horizontal arrows showing the indicator end points
H,I, J, K, 0.033, 0.16, 0.82, and 2.85 pmoles, respectively, of os04 and 1.25 pmoles of ferroin in each. Key same as Figure 2
corresponds to a 0.1% error. A horizontal arrow marks the visual end point if a redox indicator is present. Titrations A and B of Figure 1 differ from the standard only in a respective 5-fold decrease and increase in the amount of osmium added. For this pair, within the experimental uncertainty, there is no observed effect on the ceric titer. Titrations C and D match A and B, respectively, with a reversal of titration direction as the only variable. Here the discrepancy between the calculated and observed end points clearly indicates an osmium dependence. Moreover, at high osmium the sharpness of the end point has been curtailed, and the curve is distorted beyond the potential break. Curve D‘ is a second end point result obtained with titration D. Here, after the addition of a definite excess of ceric (21 peq beyond the calculated end point), As(II1) was added again until barely in excess (ca. 3 peq); and a repeat titration with Ce(1V) was carried out. The resulting improvement in the sharpness of the potential break and the removal of most of the distortion that occurred in D is very evident. In addition, the titration error in D ’ has been reduced 3-fold to 0.055% from the 0.170% observed in D. These results are consistent with a reduction of osmium in excess As(II1) to a lower oxidation state and the failure to return completely to the VI11 state at the end point of the As (III)-Ce(IV) reaction. This, of course, would cause a titration error proportional to the amount of osmium present and the extent of its reduction. The latter fact would explain the improved results in D ’where only a very small excess of As(1II) was used. The distorted region of D beyond the potential break is caused by the titration of osmium back to the VI11 state. On a more quantitative basis, in D the ratio of the titration error as peq of Ce(1V) to the pmoles of Os (VIII) added was 3.41/0.82 = 4.16. This corresponds closely to the bulk of the osmium being in the IV state at the observed potential break. For D’ a similar calculation gave 1.34, indicating an intermediate mixture of the VI and VI11 (or VII) states of osmium. As yet the mechanism of the osmium catalyst in this reaction has not been definitely established. Laitinen (14) has
suggested that it can be reasonably assumed to be a cyclic two-electron reduction of osmium by As(II1) followed by successive one-electron oxidations by Ce(1v). However, a recent study of the reaction kinetics by Habig, Pardue, and Worthington (15) indicates that this is an oversimplification, They made the very significant observation that the osmium could be added in the IV, VI, or VI11 states without affecting the reaction rate. Moreover, it was impossible to account for their results with a single osmium cycle involving as extremes the VI and VI11 states. It was necessary to postulate the simultaneous occurrence of a second catalytic cycle whereby one-electron oxidations of Os(1V) to Os(V1) by Ce(1V) was followed by a single two-electron reduction by As(II1) back to Os(1V). The relative importance of these two cycles would depend on the As(III)/Ce(IV) ratio. Of course, this mechanism is entirely compatible with the results presented in Figure 1 ; and it indicates how the oxidation of As(II1) could go to completion while the osmium remained at least partially reduced. So far no mention has been made of the second potential break that occurred in titration B. Undoubtedly, this also was due to the titration of osmium; but fortunately, in this case, unlike titration D,a fairly good potentiometric end point can be obtained. Since any significant reduction of osmium would cause both an error and osmium dependence in titrations A and B, the results indicate the osmium must still largely be in the VI11 state at the main potential break. The observed difference in the two potentiometric end points of B amounts to 1.5 peq, and 0.81 pmoles of Os(VII1) were added in this run. This is 92% of the calculated value for an Os(VIII) to Os(V1) reduction. Three similar titrations with up to a 4-fold increase in the added osmium yielded values ranging from 88 to 102 % of theoretical with an average of 93 %. Another set of four with a stream of nitrogen sweeping the cell solution gave a mean and average deviation of 83 i 2 x of the theoretical value. This indicates the volatility loss of osmium tetroxide probably contributes to the failure to observe a full two-equivalent change. To date this appears to be the only direct evidence that the reduction of Os(VII1) by As(II1) is indeed a single two-electron step. Also it confirms the Os(VII1)-Os(V1) catalytic cycle at
(14) H. A. Laitinen, “Chemical Analysis,” McGraw-Hill, New York, 1960, pp. 3356,340,441-3, 462.
(15) R. L. Habig, H. L. Pardue, and J. B. Worthington, ANAL. CHEM.,39, 600 (1967).
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Figure 4. Errors for 2-meq sample as function of added Os04 0,potentiometric titrations of Ce(IV) by As(II1); E ferroin (1.25 pmoles) end point titration of Ce(1V) by As(II1); 0, potentiometric titration of As(II1) by Ce(1V). Solid lines
calculated and dashed line empirical high Ce(1V) (1.5). Undoubtedly, the fraction of osmium in the VI and VI1 states remains very low until the reduction of Ce(1V) is complete, clearly indicating why only the titration by As(1II) produces an error-free result that is independent of the amount of osmium added. Effect of Ferroin. The most popular version of the Gleu ( I ) procedure utilizes the redox indicator ferroin. Potentiometric titrations E to K of Figures 2 and 3 present a study of this added factor. Titration F differs from E only by a 16-fold increase in the amount of osmium, and again the added potential break caused by the osmium VI11 to VI reaction is very evident. Other than this it is clear that again the titration of Ce(1V) by As(II1) is independent of the amount of Os(VII1) added. The visual ferroin end point, which appears almost identical to the potential inflection point because of the overpowering intensity of the red reduced form, obviously requires an indicator blank correction. As ca. 1.25 pmoles of the reduced form of the indicator were added per titration, the calculated and observed blank correction are seen to be in good agreement. The second potential break marks the end of the Ce(1V)-As(II1) reaction and checks very well with the calculated end point, These two titrations fully indicate that ferroin actually changes at the wrong potential for an optimum result. Titration G of Figure 2 represents an effort with the 5,6-dimethyl derivative of ferroin. This indicator changes at a potential about 0.1 volt lower than ferroin, which should correspond more closely to the observed potential break for the Ce(1V)As(II1) reaction. The results show that a substantial decrease in the indicator end point error was in fact achieved, Nonetheless, the substitution of this indicator is not recommended because the observed color change was too gradual to give a good end point. Ferroin with a blank correction gives far superior results. Titrations H to K of Figure 3 present a series with increasing osmium as the only variable. This is the common version of the Gleu ( I ) procedure using Ce(1V) as the titrating
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Figure 5. Errors for 2-meq sample in titration of As(II1) by Ce(1V) with 1.25 pmoles of ferroin present 0, first potentiometric end point; 0 , ferroin end point.
Solid line calculated and dashed line empirical. Horizontal arrow marks calculated indicator blank agent. At the lowest osmium concentration only one potential break is observed, and it must be attributed to the titration of ferroin. At higher osmium, an earlier potential break occurs that presumably marks the end point of the As (111) to As(V) reaction. There is a definite increase in the microequivalent difference between the two potentiometric end points as the osmium is increased; however, it is less than a linear change. Moveover, there is a steady shift of the true stoichiometric point (the dashed line), which corresponds to the oxidation of As(II1) to As(V) plus complete return of the osmium back to the VI11 state. Thus, the visual ferroin end point has a negative titration error at low osmium that is fairly close to the calculated indicator blank (1.25 peq), then fortuitously passes through a region of very low error in the customarily recommended osmium range, and finally a positive error is obtained at relatively high osmium. These results indicate that the success ferroin has enjoyed is largely due to the fact that its color change occurs at too high a potential. This allows titration of the osmium back to the VI11 state before the ferroin transition occurs. At high osmium the indicator changes color before this process is complete and a positive error results. It is interesting to note that an indicator blank correction, which in principle should be needed if the customary reduced form of the indicator is used, is never recommended with Ce(1V) as the titrating agent. Obviously, failure to apply this correction helps to cancel the error caused by any reduced osmium remaining at the ferroin end point. In the optimum osmium range this leads to complete cancellation of the error. Summary of the Gleu ( I ) Procedure. A summary of the per cent errors for a 2-meq sample observed with various modifications of this method is presented in Figures 4 and 5 . All the results of the preceding figures plus other data covering a wider range of conditions are included. The only procedure completely free of error is seen to be the potentioVOL 40, NO. 1, JANUARY 1968
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metric titration of Ce(1V) by As(II1) without ferroin. The solid line through the points is the true zero error line while the actual mean and standard deviation of the data was 0.0023 i.0.0082%. The titration of Ce(1V) by As(II1) using the ferroin end point also gives reliable results provided a blank correction is applied. The straight line passing slightly above these points in Figure 4 is the calculated error based on the manufacturer’s labeled concentration of 0.025M ferroin. This gave a value of -0.065 % as compared to the actual observed mean of -0.072%. TWOother titrations of this type were carried out using a 5-fold increase in the amount of ferroin. The mean indicator end point was in error by -0.322 %, which checked very well with the calculated value of -0.312%:. The dashed line of Figure 4 is merely an empirical smooth curve that is intended to summarize the potentiometric titration data of As(II1) by Ce(1V) with no ferroin present. As all the titrations used a 2-meq sample, a straight line would have been obtained if all the osmium were in a single oxidation state at the end of the As(II1)-Ce(1V) reaction. Thus a 45” line or slope of 0.1 % error per pmole of osmium would correspond to Os(V1) and so on. The curved line actually observed indicates a mixture of lower osmium oxidation states. There is a considerable uncertainty involved, but as drawn the limiting slope at zero osmium corresponds to Os(I1) as the lowest state. This is not in good agreement with Habig, Pardue, and Worthington (19, who report Os(1V) as the lowest state formed by excess As(II1). And neither result agrees with Meites’ (16) observation that Os (111) is the only reduction product of controlled potential electrolysis in mineral acid media. Whatever the true situation, the present results are definitely sufficient to rule out use of this potentiometric end point. It is ironic that a hidden error of about 0.2% has been the award for any conscientious worker who has attempted to “improve” the standard Gleu ( I ) procedure in this way. Figure 5 presents the data obtained for the two end points in the potentiometric-colorimetric titration of As(II1) by Ce (IV) with ferroin. Here the greatest scatter of all occurred in the results. Thus the final point of both series is actually the mean of three determinations with average deviation indicated by vertical lines. Within a rather large uncertainty the straight line drawn with a slope of 0.1 % error per pmole of osmium fits the open circle data. This corresponds to Os(V1) as the main state at the end of the As(II1) oxidation. This result is very different from the dashed line of Figure 4 for the same end point without ferroin, and it indicates a ferroin interaction that profoundly affects the reaction mechanism. Possibly it is connected to the induced reduction of the oxidized indicator by As(II1) which, as Laitinen (14) points out, occurs only in the presence of both Os(VII1) and Ce(1V). However, the precise nature of this interaction remains unknown. The colorimetric end points, especially at high osmium, were plagued by a competition between ferroin and the reduced osmium. The result was a series of premature color changes followed by slow fading. This undoubtedly contributed to the scatter of the solid circle data of Figure 5. Again the dashed line is intended merely as a summary of the results. Possibly it is too optimistic to attempt any such smooth curve with this data; however, a good deal of the scatter can be removed by plotting the microequivalent difference between the two end points instead of the individual per cent errors
+
(16) L. Meites, J . Am. Chem. Soc., 79,4631 (1957).
144
ANALYTICAL CHEMISTRY
as actually shown. The empirical smooth curve result of such a plot combined with the calculated straight line values obtained for the first end point served to construct the dashed line presented in Figure 5. A horizontal arrow marks the calculated indicator blank that is approached at low osmium. The optimum (zero error) amount of osmium is indicated to be about 1.6 pmoles or 2.5 X 10-5M osmium tetroxide for the 65 ml of solution used here. However, this value probably depends in turn on the amount of ferroin that is used. Dichromate Standardization of Ferrous Solutions. Earlier mention was made of slightly different results obtained, depending on titration direction, in the standardization of ferrous sulfate by potassium dichromate. The remarkable difference that occurs with reversal of titration direction in the potentiometric titration curves for this system is well known (17). Laitinen suggests that this is due to surface oxide formation on the platinum electrode possibly coupled with adsorption of dichromate. [See Ref. 14, pp. 335-36. Note, however, that this may explain the anomalous potentiometric behavior ; but the magnitude of the end point difference about to be reported is too large to correspond to the superficial oxide layer that is produced on platinum. Using the highest value of 40 seconds of 2-mA current for a 60-sq cm electrode observed by F. C. Anson and J. J. Lingane, J. Am. Chem. Soc., 79, 4901 (1957), this amounts to 0.014 peq per sq cm. For a 0.05-inch diameter wire immersed to a 3-cm depth, this totals only 0.017 Ieq or less than 0.001% for a 2-meq sample.] Whatever the reason, the titration with ferrous produces a notably sharper and larger end point break; and at first it was thought to be the superior choice. Subsequent results indicated that it gave a ferrous titer (and thus ceric concentration) 0.01 to 0.02% too high. This is a negligible error in all but the most exacting work and in fact substantiates recent results at a more modest accuracy level by Rao and Krishna (18), who observed no disagreement between the stoichiometric and potentiometric end points. A direct measure of the end point difference was carried out in a series of titrations using a single standard dichromate solution. Triad analyses were run using two titrations of the same type to interpolate the results to the same time as the reverse titration. This was to correct for the small but appreciable air oxidation change of the ferrous sulfate stock which was observed to be about -0.014% per hour. Fifteen analyses combined in five such triads gave a ferrous standardization difference of 0.304 peq (a = 0.094 peq) or 0.0152% for a 2-meq sample. On the basis of a null hypothesis test using the familiars tatistic t or Student’s factor, the observed end point difference must be judged real with an extremely high statistical significance lying between the 99.5 and 99.9% confidence levels. Corrections to the individual end points were also determined by running macro level (2 meq) standardizations on the ferrous stock and comparing this result with the titrations of a 100-fold smaller sample, If a fixed number of equivalents of dichromate are assumed lost per titration, the error generated is greatly magnified with the smaller sample. The blank corrections so obtained in two such titrations with ferrous gave 0.46 and 0.42 peq and similarly two with dichromate gave 0.04 and 0.06 peq. The mean difference of 0.39 peq checks reasonably well with the previous macro level (17) G. F. Smith and W. W. Brandt, ANAL.CHEM., 21,948 (1949). (18) G. G. Rao and U. M. Krishna, Tulanru, 13, 1705 (1966).
result; and, of more importance, it confirms that the ferrous titration is the (slightly) erroneous procedure. The reason for this error must lie with side reactions involving the intermediates such as Cr(V), Cr(IV), or Fe(1V) that are presumably formed in the Fe(I1)-dichromate reaction (for mechanisms, see Ref. 14, pp. 441-3). For example, the oxidation of water by any of these active species would in effect represent a loss of dichromate. In turn, and as observed, such undesired side reactions would be suppressed when an excess of readily oxidized Fe(I1) is available. This would perhaps indicate that the direct titration of Fe(I1) with dichromate should be superior to the back-titration procedure actually used in this research. In any event, the errors involved are very small. Comparison Standardizations with AszOa, NazC2O4, and K2Cr207. The final check against the three primary redox standards of the National Bureau of Standards was run on a single ceric sulfate solution. Individual stock solutions of the appropriate standard were prepared for each titration, used the same day, and discarded after this single use. The titrations with As(II1) followed the standard method previously described. A summary of results is presented in Table I. The two sets with AszO, indicate any air oxidation loss during the alkaline dissolution step is not statistically significant. p h e null hypothesis t test applied to the two means gave a value of 1.69 for 13 degrees of freedom, which is only in the 80 to 90% confidence range.] Of course, this assumes no undue delay (30 minutes at most) in acidifying the solution; and the effect of heat, which is frequently recommended to speed solution, was not investigated at all. The end point difference previously noted in the two dichromate procedures was used to correct the final pooled result to the titration by dichromate end point. It is readily seen that the final agreement among all three standards exceeds the 0.01 level, which is the reliability limit of the NBS assay values. CONCLUSION It has been shown that the standardization of ceric sulfate solutions by As(II1) with osmium tetroxide catalyst is subject to a number of errors. The direct potentiometric titration of As(II1) by Ce(1V) gives especially poor results and should be abandoned as an analytical method. The more common procedure using the ferroin end point produces errors of opposite sign which cancel at an optimum osmium level, provided an indicator blank correction is not applied. However, this cancellation process is too uncertain and unre-
Table I.
Comparison Standardizations of 0.1N Ce(S032
NBS standard" Sub case
As208 Na2C04 KzCrz07 Nzb No NZ . . . Oxid. Reduc."
No. of determinations 7 (Mean - 0.0939) X lo6 3 . 1 D
x
106
Pooled results: Mead D
x
106
1.1
8
7
4.3 1.6
3.9
3 3.8
6.3
1.2
2.0
1.7
0.093938 1.5
0,093939 1.2
6
0.093946'
1.7
Independent 2-meq samples of each standard per titration. Indicates whether or not As(II1) solution was prepared under an inert atmosphere. c Oxid. is titration by K2Cr2O7 and reduc. is by Fe2S04. All results as meq of Ce(IV) per gram of solution. Blank correction of 0.30 peq applied to each reduc. titration, see text, a
b
producible if any accuracy in excess of 0.1 is desired. Happily a simple and complete solution is obtained merely by reversing the titration direction. The potentiometric end point is the best and sharpest, but very good results can also be obtained with ferroin provided a blank correction is applied. The reverse titration with As(I1I) is hampered somewhat by being slower in the equivalence point region. The kinetic data of Ref. 15 would indicate a 3.1 factor in rate difference with reversal of titration direction ; however, no difficulty was encountered if the final increments are added at 1-minute intervals. There is also the considerable practical advantage that the fading Ce(1V) color gives an excellent advance end point warning. The results are independent of the amount of osmium catalyst added, but the reaction is inconveniently slow at low concentrations. A range of 0.3 to 1.0 pmoles of Os(VII1) per 100 ml of final solution is recommended. In conclusion, it may be stated that the standardization of ceric sulfate solution has been shown to be among the most accurate possible in analytical work. This combined with the remarkable stability of the reagent certainly enhances the versatility of this strong oxidizing agent. The longest continuous use of a single stock solution in this research was 3 months with no appreciable change in its titer. (Other stability studies are presented in Ref. 10, pp. vii, 14-19.) RECEIVED for review September 1, 1967. Accepted October 20, 1967. Based on work performed under the auspices of the U. S. .AtomicEnergy Commission.
'401. 40, NO. 1, JANUARY 1968
145
