respect to t. The d1’2C(0,t)/dt1’2 may now be eliminated between Equations 8 and 9 to produce the first order ordinary differential equation
d
- C(0,t) =
k2C(0,t) ~
dt
D
c exp
‘
kC
--
6;
Standard methods [see, for example, Murphy to the solution
C(0,t)=
C(r,r) =
[$1 [ $1. erfc k
(a)] thence lead
(11)
Equation 11 is a well-known result (9, IO), and its derivation here is noteworthy only in the novelty of its appearance other than as a special case of the expression (8) G. M. Murphy, “Ordinary Differential Equations and Their Solutions,” D. van Nostrand Co., Inc., Princeton, N. J. (1960). (9) M. Smutek, Chem. Listy, 45,241 (1951). (10) M. Smutek, Collect. Czech. Chem. Commun., 18, 171 (1953).
A more powerful application of this novel approach is to a situation in which the electrode potential is not a known analytical function of time. A description of the numerical technique required in this instance will be deferred until a full presentation of the mathematical treatment can be given. KEITHB. OLDHAM
Science Center North American Rockwell Corp. Thousand Oaks, Calif. 91360 RECEIVED for review June 5, 1969. Accepted September 5, 1969.
Additional Comments on the Precision Standardization of Ceric Sulfate Solutions SIR: In recent work Schlitt and Simpson ( I ) failed to observe the directional-dependent titration error we reported ( 2 ) for the standardization of ceric sulfate against arsenious oxide in the presence of osmium tetroxide-the Gleu (3) procedureand which we attributed to incomplete reoxidation of the osmium catalyst when ceric was the titrating agent. Schlitt and Simpson did find entirely similar behavior but only in the presence of nitrate ion. Furthermore, both investigations agreed in that the reverse titration with As(II1) eliminated all errors. This led Schlitt and Simpson to suggest that our ceric reagent, which was obtained from the G . F. Smith Chemical Co. supposedly as a pure solution of 0.1N ceric sulfate in 1 N sulfuric acid, was probably a solution of ceric ammonium nitrate in sulfuric acid. Fortunately a portion of the ceric solution from our earlier work was still on hand, and tests did indeed show the presence of substantial amounts of both nitrate and ammonium ions. Quantitative analyses were carried out by standard procedures of this Laboratory: ammonia by distillation after the addition of excess sodium hydroxide and nitrate by difference after reduction with ferrous and silver(1) catalyst to ammonia followed by the same distillation (4, 5). The results were 0.0569M and 0.0678M, respectively, for ammonium and nitrate ions, and the ceric concentration was 0.0982M. These values, while far from stoichiometric agreement with (NH& Ce(NO&, amply confirm the suspicion of Schlitt and Simpson. The presence of nitrate and ammonium impurities would certainly not be expected on the basis of information pub(1) R. C. Schlitt and K. Simpson, ANAL.CHEM., 41, 1722 (1969). (2) A. J. Zielen, ibid., 40, 139 (1968). (3) K. Gleu, 2.Anal. Chem., 95, 305 (1933). (4) J. E. Varner, W. A. Bulen, S. Vanecko, and R. C. Burrel, ANAL.CHEM., 25, 1528 (1953). (5) J. M. Pappenhagen, ibid., 30,282 (1958).
lished by Smith (6) on the preparation of his reagents. The sulfato-ceric acid solution is, in fact, specificallyrecommended for direct use by the consumer because dissolving ceric bisulfate in dilute sulfuric acid is a troublesome procedure. Also this was not a case of a single bottle of contaminated reagent. Another type and batch of G. F. Smith sulfato-ceric acid solution (0.5Nceric in 2N sulfuric acid) was on hand, and this solution gave a much stronger “brown ring” nitrate test than the 0.1Nceric solution. The critical experiment and confirmation of the Schlitt and Simpson results remained to be done-namely, if the use of a nitrate-free ceric reagent would eliminate the directional-dependent error reported in our earlier work. Accordingly a solution of 0.1N ceric sulfate in 1N sulfuric acid was prepared as suggested by Schlitt and Simpson using G . F. Smith crystalline Ce(HS04)4 as the starting material. The ceric bisulfate and hot solution were equilibrated for 6 hours on a hot platemagnetic stirrer; and the solution was then cooled, filtered, stored in a brown glass bottle, and allowed to age for 2 days before use. This ceric solution gave a negative “brown ring” nitrate test. Inasmuch as directional dependence of the titration was the only variable to be tested, potentiometric titrations on 2-meq samples were performed in both directions with a single 0.067N arsenious oxide solution and a constant 0.76 pmole of osmium tetroxide per titration. Other than the ceric reagent, the equipment and procedures used were all identical to the earlier work (2). This simple comparison of the two solutions was selected in order to obtain the highest possible precision in the titrations without undue concern over the absolute accuracy of the standardization. The results are summarized in ( 6 ) G. F. Smith, “Cerate Oxidimetry,” The G. Frederick Smith Chemical Co., Columbus, Ohio, 1942, pp 1 - 1 1 ; ibid., 2nd ed.,
1964, pp 33--36.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
1905
Table I. Directional Comparison in the Potentiometric Titration of Nitrate-Free Ceric Sulfate and Arsenious Oxide in 1N Sulfuric Acid. Titration Titration with As(II1) with Ce(1V) 0. 098786b 0.098819b 0,098770 0,098821 0,098792 0.098824 0.098777 0.098807 0.098781 Mean 0.098818 9.7 u x 106 7.5 0
b
Two meq samples and 0.76 pmole of OsOc per titration. All results as meq of Ce(1V) per g of solution.
I
I
-6
-4
I
I
I
I
I
-2
0
2
4
6
1.3
I .2
w f 2 1.1 vi
;1.0 0
>
0.9
0.8
Table I. The standard deviations observed are in reasonable accord with a precision estimate of 1-2 p1 uncertainty in the end point (by microburet) out of a total titrant volume of 20 or 30 ml (by weight buret). The 0.037x directional bias observed in Table I must be judged real on a statistical basis, but it is far less than the 0,165x that would be predicted from Figure 4 of our earlier work, Furthermore, there were striking differences in potentiometric behavior in the end point region. The distortion previously noted with Ce(1V) as the titrant [cfFigure 1-D of (2)] was completely absent, and the ceric and arsenic titration curves became virtual mirror images. Typical results are illustrated in Figure 1 where the observed end point of the As (111)-Ce(1V) reaction has been set at zero peq for each data set. It is especially pertinent to note the small but definite potential break that occurred in both curves at about 0.87 V. This break is assumed to be due to the osmium(V1-VIII) couple, and the vertical dashed lines in the figure indicate the calculated value based on the pmoles of osmium added and a twoequivalent change. An entirely similar result was previously observed with As(II1) as the titrant [cfFigure 1-B of ( 2 ) 1, but the present work is the first clear evidence that osmium is returned to the (VIII) state before the end point when titrating with Ce(1V). Thus a standardization should be independent of the amount of catalyst added. The observed values in the four ceric titrations for the difference between the main and osmium potential breaks were 1.6, 1.7, 1.3, and 1.4 peq compared to the calculated 1.52 peq. Only one arsenic titration (the third) was carried far enough to observe both breaks and the difference was 1.5 peq. All end points were calculated by Yank method (7). The combination of sharply decreased directional bias and visible evidence of return of the osmium to the (VIII) state indicates that Schlitt and Simpson were correct, and the directional error that we previously observed was due to nitrate ion interference. Apparently osmium can catalyze, albeit inefficiently, the oxidation of As(II1) by nitrate. Hence, a high oxidizing titer is obtained where ceric is the titrating agent because an excess of As(II1) is available for slow oxidation by nitrate; but in the reverse titration with As(III), the stronger and more efficient Ce(1V) oxidizes the As(II1) as fast as it is added without the occurrence of an appreciable error. On this basis it is readily understandable that the titration error or extent of nitrate oxidation would be dependent upon the con-
(7) J. F. Yan, ANAL. CHEM., 37,1588 (1965). 1906
M ICROEQU IVALENTS
Figure 1. Potentiometric end point detail in the OsOl catalyzed As(IIItCe(1V) reaction in 1N H S O 4 illustrating the mirror image results with nitrate-free solution Open circles: titration with Ce(1V); solid circles: titration with As(II1). Vertical dashed lines are calculated Os(V1-VIII) break points on basis of 0.76 pmole of osmium per titration
centration of osmium and hydrogen ion, as observed, and probably also on the speed of the titration. The 0.037x directional difference observed in Table I remains unaccountable at present, but it would not be significant in most analytical work. Also it should be recalled that Schlitt and Simpson did not detect any directional bias at all with a nitrate-free reagent; however, the standard deviation of Titration with their data was a comparatively high 0. 13 As(II1) could perhaps favor the loss L ’ Ce(1V) because of trace reducing impurities in the As(II1) soL*tionor on the surface of the reaction vessel; but on the othe; hand, this was the identical procedure that gave results ccrisistent to 0.01 % among three National Bureau of Standa. ds redox reagents (2). Accordingly, we continue to favor ti,(: reverse titration with As(II1); and of course, it is now well established that this procedure is essential to the Gleu method if the ceric reagent contains nitrate (and possibly other, similar oxidizing impurities). Thus the observations and suggested procedures of our earlier work remain unchanged; only the theory of incomplete reoxidation of the osmium catalyst was wrong. One final comment should be made on the use of ferroin indicator. It is now apparent that the cancellation of errors previously observed would be dependent upon the amount of nitrate present. Thus careful consideration must be given whether or not to apply a blank correction when ceric is used as the titrating agent. As previously noted, a blank correction is always needed with ferroin when titrating with As(II1).
x.
A. J. ZIELEN Chemistry Division Argonne National Laboratory Argonne, Ill. 60439 RECEIVED for review July 18, 1969. Accepted August 18, 1969. Work performed under the auspices of the U. S. Atomic Energy Commission.
ANALYTICAL CHEMISTRY, VOL. 41, NO. 13, NOVEMBER 1969
