enone group (about -1.65 volts), the fluoro group is reduced at more negative potentials (about -2.0 to -2.2 volts) than the A4-3-keto group (about -1.7 volts) in ethanol-aqueous media. The epimeric 6-fluoro-A4-3-ketosteroids reduce with the same relative ease in ethanol-water and DMF-Le., the ,%isomer preceding the a-isomer. In DMF, a second wave appears a t a more negative potential because of the reduction of the enone. This second reduction step is not reported in the protonated solvent.
ment throughout the investigation and E. J. Becker, B. Berk, P. A. Diassi, J. Fried, L. B. High, and F. L. Weisenborn for the donation of steroids.
(6) Kabasakalian, P., DeLorenzo, S., McGlotten. J.. ANAL. CHEM.28. 1669
LITERATURE CITED
(1) Brezina, M., Zuman, P., “Polar-
ography in Medicine, Biochemistry, and Pharmacy,” Interscience, New York,
1958. (2) Cohen, A. I., Keeler, B. T., Coy, N. H., Yale, H. L., ANAL.CHEM.34, 216 (1962). (3) Cohen, A. I., Snyder, R. E., un-
published results. P., “New Instrumental Methods in Electrochemistry,” Interscience, New York, 1954. (5) Dorfman, L., Chem. Reus. 53, 47 (4) Delahay,
ACKNOWLEDGMENT
The author thanks If,H. Coy and K. Florey for their help and encourage-
(1953).
RECEIVEDfor review Julv 20, 1962. Accepted November 30, 1962.
Amperometric Titrations with Very Dilute Solutions of Permanganate H.
P. SILVERMAN’
and
D. A. SKOOG
Department o f Chemistry, Stanford University, Stanford, Calif.
b A satisfactory amperometric end point can b e obtained with permanganate solutions as dilute as 1 X 10-+le Titrations of very dilute solutions of Fe(ll), U(IV), and oxalate ion revealed the presence of a constant error of approximately 2 X lo-‘ meq. of KMn04. This error appears to arise from an induced reaction of the oxidizing agent with the solvent. A blank titration will not permit correction for the error and with very dilute permanganate solutions an empirical calibration curve must b e employed.
T
permanganate ion is sufficiently intense in color so that solutions of this reagent as dilute as 0.01 to 0.02N can be employed for titrations without the necessity of an indicator material. Knop and Kubelkova ( 2 ) have shown that milligram quantities of iron can be titrated accurately with 0.005N permanganate solutions, if certain triarylmethane dyes are employed as indicators. Kirk and Tompkins ( 1 ) have used the o-phenanthroline-ferrous complex as an indicator for oxalate titrations with permanganate solutions of similar strengths. The amperometric method appeared to offer a means by which end points could be determined with permanganate solutions more dilute than those heretofore employed. Kolthoff and Jordan HE
Present address, Magna Corp., 1001 South East St., Anaheim, Calif.
(4) have mentioned briefly that currentvoltage waves for permanganate ion are obtainable with a rotating platinum electrode from 131 sulfuric acid, and have described the use of 0.002N solutions as a reagent for the determination of micro quantities of iodide ion. V e have undertaken the further investigation of the amperometric end point for titrations with very dilute solutions of permanganate ion. These studies have shown that n ell-defined and reproducible end points are obtained n-ith reagent concentrations appreciably lower than those required to give a satisfactory end point by other means. Titration of ferrous iron and other reducing agents has revealed, however, the existence of a constant positive error which is large enough to have serious effects on the outcome of analysis based on permanganate solutions more dilute than about 5 x 10-3N. We have made some preliminary inrestigations of the source of the error, but have only been able to come to some tentative conclusions regarding its cause. Unfortunately, the error is not revealed by a blank titration and satisfactory analyses with very dilute permanganate solutions require the use of an empirical calibration. REAGENTS AND PROCEDURES
Techniques. Current-voltage curves were obtained with a Sargent Model XXI polarograph. The electrolysis cell included a platinum wire microelectrode 3 mm. Apparatus and
long and 0.05 mm. in diameter. It was rotated at a rate of 600 r.p.m. The reference electrode was a saturated calomel half cell coupled to the electrolysis compartment by means of a sodium sulfate bridge. The cell had a resistance of 300 ohms when filled with 1Jf potassium nitrate. A rate of voltage change of 0.074 volt per minute was employed in obtaining currentvoltage curves. The microelectrode was generally stored in a dilute nitric acid solution. When current-voltage curves were t o be obtained, it was covered with concentrated hydrochloric acid, rinsed with distilled water, and placed in 0.1N potassium permanganate solution for 10 minutes. Following this treatment, the electrode was thoroughly washed with distilled water, Biped dry, and allowed to stand 5 minutes in the solution t o be run. This elaborate treatment was not followed for successive amperometric titrations. Amperometric titrations were carried out a t an applied voltage of $0.4 volt us. the saturated calomel electrode. Generally, 100 to 110 ml. of solution were titrated. A microburet readable to 0.002 ml. was employed and the volume of reagent used was small enough to make unnecessary a current correction for volume change. Reagents and Solutions. Reagent grade chemicals were used throughout. I n some instances the water employed was twice distilled, once from alkaline permanganate solution. Deionized water was found to contain oxidizable impurities, and always had to be distilled before use. Standard permanganate solutions having normalities of I x 10-4 to I X VOL 35, NO. 2, FEBRUARY 1963
131
system with a platinum indicator electrode. The theoretical slope for the 0.1 M H2S04reversible 5-electron reduction is -0.095 240 volt per pH unit. Above pH 3, the observed slope becomes less negative, approaching H2S04zero a t pH 5 to 6. pH- 2 35 When more concentrated perman+- 120 ganate solutions were examined (5.0 x 10-4M), the change in electrode process occurred between pH 2.5 and 4. Here 0 80 again a decrease in the current by a I factor of three fifths rras observed. Above pH 6.0 the waves were ill defined and the limiting currents much smaller I I I than those found below this value. 16 12 08 04 00 -04 CURRENT-VOLTAGE CURVES FROM APPLIED POTENTIAL, VOLTS VS S C E SULFURICACIDMEDIA. Current-voltage Figure 1 . Current-voltage curves for curves for the reduction of permanganate 5 X 10-4M solutions of KMnOd ion were obtained from sulfuric acid solutions in which the potassium permanganate concentrations ranged from were prepared by dilutions of a 1X to 8 X lO-4M. For a given 0.1N stock solution of the reagent which sulfuric acid concentration half-wave had been standardized against primary potentials were found to be independent standard grade sodium oxalate. In of the concentration of the reactive most cases dilution was performed a t species. In 0.LV acid, the average value the time the titrations were to be perfor this constant was 0.83 f 0.02 formed; however, carefully prepared dilute solutions were found to be stable volt us. the saturated calomel electrode; for several weeks. in 1-Wacid, it was 0.90 f 0.01 volt. Standard solutions of ferrous iron The limiting currents observed in were prepared by dissolving weighed these experiments were found to be quantities of analyzed primary standard linearly related t o concentration over a grade ferrous ammonium sulfate and considerable range. Thus, in the case diluting t o known volume. of 0.1M acid solutions, a constant value of il/C of 482 pa. per millimole per EXPERIMENTAL liter was obtained for permanganate Voltammetry of Permanganate Ion. concentrations from 1 X l O - 5 M to Current-voltage curves for dilute solu39 X lO-5ilf; the average deviation tions of permanganate ion were obfrom this Talue for eight measurements tained with a rotating platinum was zt.12. For the 1.OM sulfuric acid cathode. Some typical curves are solutions a constant of 412 was obtained, shown in Figure 1; well-defined with an average deviation of f14. The limiting currents were observed in lower value in the more concentrated acidic media. acid probably arises from the greater EFFECTOF PH ON CURRENT-VOLTAGE viscosity of this solvent. I n 1M acid, CURVES. Both the limiting currents linearity was observed over a permanand the half-wave potentials for the ganate concentration range of 2 X reduction waves of permanganate ion 10-5X to 78 X 10-5M. At both acid were found to be pH-dependent. This is shown by the data in Table I for 1 X 10-4:M solutions of permanganate. Essentially constant currents were obTable I, Effect of pH on Currentserved in the pH range of 1t o 3. Above Voltage Curves for Permanganate Ion" this range the currents decreased and Halfapproached a value which is approxiwave mately three fifths that of the more poten- Limiting Type of tial, current, acidic solutions. This change suggests buffer* pH volt Ma. an alteration in the electrode process Sulfate 1.03 0.83 50 from a 5-electron reduction giving 1.52 0.81 49 manganous ion to a 3-electron reaction 1.60 0.76 48 with manganese dioxide as the product. 2.03 0.73 48 The foregoing conclusion is in part 2.21 0.71 48 2.55 0.67 47 borne out by a plot of the observed 3.00 0.61 49 half-wave potential as a function of Acetate 3.00 0.62 51 pH. Below pH 3 a straight line is 4.07 0.57 39 found, having a slope of -0.105 volt 5.00 0 51 29 per pH unit. This value corresponds 6.10 0.51 29 reasonably well with the slope of -0.096 Solutionsall 1.00 X lO-4M in KMnOd. volt per p H unit reported by Kolthoff b Total buffer concentration 1 . O M in and Furman (3) for potentiometric each case. studies of the permanganate-manganous
t
q
b:I
4:lJ
1
0
132
ANALYTICAL CHEMISTRY
i
01
0
I
I
I
'
I
I
I
I
2
4
6
8
VOLUME OF I12 X
41
N KMnOq, M L
Figure 2. Amperometric titration curve of a dilute solution of Fef2 concentrations, marked departures from linear behavior were observed a t concentrations smaller than 1 x 10-6M. The observed decrease in il/C may well have been caused by decomposition of the permanganate ion, which becomes proportionately more significant a t the low concentrations. Amperometric Titrations with Dilute Permanganate. To investigate the applicability of the amperometric end point t o titrations with dilute permanganate. carefully measured quantities of ferrous ammonium sulfate in 1M sulfuric acid were titrated; a rotating platinum electrode operated a t an applied potential of $0.4 volt vs. the saturated calomel electrode was employed in each case. Welldefined end points were observed with permanganate solutions as dilute as 1 X 10-4Ar. A typical titration curve is shown in Figure 2. -4perfectly linear relationship between volume of permanganate and limiting current was observed in the case of a blank titration. In this case the extrapolated line passed through the origin, indicating a negligible consumption of the standard reagent. A4CCURACY OF TITRATIONS OF FERrow Iron. To establish the accuracy of titrations employing the amperometric end point, standard ferrous iron solutions were analyzed (Table 11). It is apparent from these data that the amperometric end point yields reproducible results, the average deviation from the mean for duplicate results being 0.2% relative. On the other hand there is a large positive, absolute error associated with the titrations. The data in Table I1 were treated by assuming a straight-line relationship between the number of milliequivalents of ferrous iron taken (column 1) and of milliequivalents of permanganate consumed (column 3). A least squares treatment of these data yielded a slope of 0.993 meq. of ferrous ion per milliequivalent of permanganate as compared t o a theoretical value of 1.000. The standard
deviation for the slope was iO.002. The intercept of the line had a numerical value of 2.06 X meq. of permanganate. These calculations demonstrate the presence of two types of errors in the titrations. The first i3 a small proportionate error indicated by the deviation of the slope from unity. This discrepancy was not examined further, since it was small enough to be of little consequence in the titration of such dilute solutions. It is noteworthy, however, that the discrepancy appeared to be independent of the age and the concentrations of the. permanganate solutions. The second error is a constant one involving a n overconsumption of about 2 x io-* meq. of permanganate. With standard solutions having a the normality of less than 5 X error becomes significant, and, therefore, the attempt mas made to determine its causes. BLAKKDETERMINATIONS. The constant error described above is not detected by titrations of a blank. Even with the most dilute solutions of permanganate studied, the blanks were negligible. Thus it must be concluded that the excess consumption of the reagent in actual titrations results from a reaction induced by the analytical reaction. TITRATIOXS OF OXALIC ACID AND TRA~SYL IONS. To determine whether or not the observed constant error was peculiar t o the titration of ferrous ions, known quantities of sodium oxalate and uranium(1V) were titrated. I n the case of the titration of approximately 4 x meq. of oxalate, a positive error of 4.03 X 10-4 meq. of permanganate was observed. Titrations of approximately 27 X 10-4 meq. of uranyl ion with 1 x 1 0 - 3 ~ permanganate exhibited a n overconsumption of permanganate of 1.8 X meq., comparable t o the errors observed in the titrations of ferrous ions. The somewhat greater error in the case of oxalate ion may well have resulted from the elevated temperatures employed. COMPz4RISOX OF ERRORS I N VISUAL AND AMPEROMCTRIC EXDPOINTS.Several experiments were carried out which showed clearly that the constant error in the permanganate titrations with dilute solutions did not arise from the amperometric end point or the apparatus used to determine the end point. I n this work, a comparison was made between the data from amperometric titrations and the results from titrations employing o-phenanthroline-ferrous complex as a n indicator. -4s shown in Table 111, substantially the same constant error arises in both instances.
Table It.
Results of Amperometric Titration of Ferrous Iron with Dilute Permanganate Solutionsa
Fe +2 taken, meq. X IO4 4 5 5 9
KMn04, Concn.
.v x
60 00 06 20
1 1 1 2 11
21 4
48 6 51
0
b
9 2 8 4
517 538 564 576 583 105 2 114 4 280 5
f 0 1 1 0 1 zkO1
Error Meq. X 104
=to2 f0 4 f0 2 f0 1
I 7 /C
1 24 1 23 1 25
26 24 24 21 8 5
2 02 2 8 1 8
3 2 2 3 2 4 2 4
zkO1
~
9 6 7 9 9 8
6_ 4-
1 8 3 1 4 0 6 1
0 3
4 5 4 3 2 I
2 7 8 9 2 8
Iron contained in approximately 100 ml. of 1M H~SOI. Where precision is indicated, average of duplicate titratione recorded.
Table 111.
Comparison of Amperometric and Indicator End Points in Titrations with Dilute Permanganate"
Type of end point o-Phenanthroline
Amperometric
5
5 84 i- 0 01 6 23 6 30 11 22 342 f01 331 * 0 1
120 120 120 240 20
11 20 11 20 11 20 11 20 11 20 22 40 22 40 11.20
n
54 i 54 5
55 101 111 276
Fe +2 found,* meq. X lo4
104
Taken
Fe+2, mpq. X IO4 Found
55 48 41 31
9 6 7 3
585zt03 51 1 f O 02 44 1 f 0 02 33 1 iz 0 01
55 48 41 31
9 6 9 4
58 3 iz 0 02 517f006 44 8 f 0 01 34.2 zt 0 01
Error, meq. X lo4 2 2 2 1 ilv. 2 2 3 2 2 Av. 2
6 .5 4 8 3 4 1 9 8 8
Ferrous ion contained in approximately 100 ml. of 1M HzSOl; KMnOa concentration
x
10-3~.
IV. Effect of Acids on Titrations with Dilute Permanganateu Composition Fe+*,meq. X IO4 Error, meq. X IO4 of solvent Taken Found 1M HCIO4 6.83 13.02 6.19 Table
1M HC104, 0 . 2 M Na2S04 1M HC104, 0 . 4 M Na2S04 2M HCIO, 2M HC1O4,0 . 2 M Na2S04 2M HC104, 0.4A4 NazS04 0 . 5 M &SO4 1M HnSOd 0
6.18 6.83 6.83 6.62 6.62 6.62 6.18 6.76 6.62
11.69 11.22 10.69 12.79 10.45 9.48 8.93 9.03 9.10
5.51 4.39 3.56 6.17 3.83 2.86 2.78 2.27 2.48
Titrations performed on 100 ml. of solution; KMn04concentration 1 X 10.-4N.
EFFECT OF CONCENTRATION AND KINDOF ACID. To determine whether or not the permanganate-consuming susbtance was present in the acid employed, a number of titrations were performed in various media (Table IV). The error is appreciably greater in perchloric acid solutions than in sulfuric acid. Introduction of sodium sulfate into the perchloric acid, however, reduces the error until it approaches that in sulfuric acid. Furthermore,
the data suggest that the magnitude of the deviation is not markedly affected by the quantity or concentration of acid. EFFECTOF VOLUMEOF SOLUTION. An important variable which mas found to affect the size of the constant error was the initial volume of the solution. This is clearly demonstrated in Table V, where it will be seen that the error is reduced t o half when the starting volume is reduced to approximately VOL. 35, NO. 2, FEBRUARY 1963
133
one quarter of that normally employed. These observations suggested that the reagent was consumed by some impurity in the water. The use of water redistilled from alkaline permanganate did not, however, reduce the discrepancy to any appreciable extent.
ORDEROF
DISCUSSION AND CONCLUSIONS
It seems clear from the voltammetric studies described that the well defined current-voltage curves observed for solutions of permanganate ion having a pH of less than 3 arise from the electrode process
+ 8H+ + 5e
-
Mn+2
+ 4H20
In solutions of pH 5 or greater, the reaction appears to be MnOl-
+ 4H+ + 3e
4
MnOn
+ 2H20
This stoichiometry was suggested by the ratio of 5 to 3 found for the limiting currents in the two cases as well as the slope found for the plot of half-wave potential us. pH in the more acidic region. The voltammetric studies in sulfuric acid solutions revealed a linear relationship between limiting current and concentration down to a permanganate concentration of 2 X 1 0 - ~ xor 1 x However, linearity was found a t appreciably lower concentrations when amperometric titrations were performed. This is shown, for example, by the data in Figure 2, where a straightline relationship is observed inimediately beyond the end point, where the Permanganate concentration is as low Blank titrations also as 5 X lO-’W.
134
Initial vel., ml.
105 105 25 25
ADDITIONOF REAGENT.
The overconsumption of permanganate was increased nearly threefold when the order of mixing was reversed. For example, when a permanganate solution containing approximately 55 x meq. of the oxidant per 100 ml. of 1M sulfuric acid was titrated with a 1 x 10-3N solution of ferrous iron, an error of 6 X meq. of permanganate was observed.
hlnO4-
Table V. Effect of Volume of Solvent on Titrations with Dilute Permanganate4
ANALYTICAL CHEMISTRY
0
1
x
Fe+2,meq. X IO4 Taken Found 48.4 48.6 48.4 48.4
51.3 51.3 49.6 49.8
Error,
meq.
X 104 2.9 2.7 1.2 1.4
Solution titrated, 1M in HzSOd; 10-N.
exhibited linear behavior in the same concentration region. Values for i J C calculated from the slopes of the titration curves beyond the equivalence point were found to be approximately 450, which agrew reasonably well with the data for the voltammetric studies. The difference in minimum concentration for linearity may well have arisen from the greater opportunity for the permanganate to decompose in the voltammetric studies; here an excess of permanganate ion was allowed to stand in the presence of strong sulfuric acid for several minutes while the currentvoltage data were obtained. In acquiring the amperometric titration data, on the other hand, only a short time was required to measure the current a t a single fised potential and the amount of permanganate present was never large. Consequently decomposition would have had less opportunity to occur. The amperoinetric titration data revealed the existence of a serious constant error when solutions more dilute than 5 x lO-3N were employed for titration. This error cannot be detected by an ordinary blank titration, suggesting that the overconsumption of permanganate is brought about by a reaction induced by the analytical reaction itself. Such an effect has been observed in other applications of permanganate, and it has been proposed that intermediates formed in the analytical reaction, perhaps manganese (V), are the cause ( 5 ) . In this instance, such an intermediate may react slowly with water. The fact that the observed
error is not greatly influenced by the amount of reductant suggests that the decomposition occurs primarily a t the outset of the titration and becomes negligible as the concentrations of products of the analytical reaction are built up. The effect of initial volume of solution upon the magnitude of the error can be explained by assuming a difference in concentration dependence of the rates of the various competing reactions. The marked increase in the error observed when a permanganate solution is titrated with the reductant is consistent with the idea of an induced reaction involving manganese intermediates, inasmuch as such intermediates would, in this instance, find a lesser number of ferrous ions with which to react. I t seems probable that the constant error revealed by this study is inherent in all permanganate titrations; it is small enough, however, to be of no consequence with the Permanganate solutions ordinarily employed. With 0.01N solutions it can be expected to cause a relative error of a few parts per thousand a t the most; it is only with solutions more dilute than 5 x l O + N that a correction must be employed. This can best be done by preparing a calibration curve of milliequivalents of permanganate against milliequivalents of reductant. The initial volume of solution must be constant to within about 10 to 207& With these precautions an uncertainty of the order of 5 x meq. is to be expected. LITERATURE CITED
(1) Kirk, P. L., Tompkins, P. C., IND. ENG.CHEM.,ANAL.ED.13, 277 (1941). ( 2 ) Knou, J., Kubelkova, O., Z. anal. Chem.*85, 401 (1931). ’ (3) . , Kolthoff. I. &I.. Furmsn. X. H..
“Potentiometric Titrations,”’ 2nd ed.;
p. 254, Wiley, Kern York, 1931. (4) Kolthoff, I. M., Jordan, J., ANAL. CHEM.25,1833 (1953). ( 5 ) Kolthoff, I. M., Sandell, E. B., “Textbook of Quantitative Inorganic Analvsis.” 3rd ed..,D. . 480. Macmillan. New“York, 1952.
RECEIVED for review July 2, 1962. Accepted Xovember 23, 1962.
