End-Point Detection and Current Efficiencies for Coulometric Titrations

End-Point Detection and Current Efficiencies for Coulometric Titrations Using the Dual Intermediates Manganese(III) and Iron (II). R. P. Buck. Anal. C...
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(14) James, J. C., T r a n s . Faraday Soc. 47, 1240 (1951). (15) Johnson, M. F., Robinson, R. J., ANAL.CHEILI.24, 366 (1952). (16) Kolthoff, I. M.,Harris, IT. E.. Matsuyama, G., J . A m . Chem. SOC.6 6 , 1782 (1912). (17) Kolthoff, I. M., Lingane, J. J., “Polarography,” 2nd ed., Vol. 1, p. 81, Interscience, Sew York, 1952. (18) Zbid.,pp. 90-3. (19) Lingane, J. J., “Electroanalj-tical

Chemistry,” 2nd ed., p. 362, Interscience, Sew York, 1958. (20) Macdonald, A. M. G., Ind. Chemist 31, 515 (1955). (21) Zbid.,p. 568. (22) M e i p , L., “Polarographic Techniques, Interscience, New York, 1955. (23) Pearson, J., T r a n s . Faraday SOC.44, 683 (1948). (21) Rand, 11.C., Heukelekian, H., ANAL. CHEhf. 25, 878 (1953). (25) Sabato, .I.,Hol. Infornz. Petrol.

(Buenos Aires) 27, 59 (1950); 45,

1333 (1951).

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RECEIVED for review August 15, 1960. Resubmitted November 2, 1962. ACcepted February 8, 1963. Taken in part from the Ph.D. thesis of D. J. Curran. Kork supported in part by a Grant from the Sational Institutes of Health. Presented in part before the Division of i\nalytical Chemistry, 138th Meeting, -4CS, Sew Tork, September 1960.

End-Point Detection and Current Efficiencies for Coulometric Titrations Using the Dual Intermediates M a nga nese(ll1) and Iron(II) RICHARD

P. BUCK

Bell & Howell Research Center, Pasadena, Calif.

b Several proposed versions of amperometric and potentiometric endpoint detection systems have been investigated. For routine applications the null potentiometric method has been most satisfactory. Efficiencies were determined b y a potentiostatic method for the generation of manganese(ll1) and iron(l1) on paraffin-impregnated carbon, boron carbide, and platinum foil for a wide range of current densities. Efficiencies were confirmed by generating Mn(lll) for a known time and back-titrating with Fe(ll). Carbon i s preferred as generator anode material.

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of electrolytically generated Xn(II1) for the coulometric titration of Fe(II), As(III), and oxalic acid was introduced by Tutundzic and Mladenovic (7‘). Subsequently, current efficiencies for the generation of Mn(II1) on smooth platinum in sulfuric acid media and disproportionation equilibria of Mn(II), (111), and (IT’) were investigated by Selim and Lingane (6). Conditions for the efficient generation of hln(II1) as a function of Mn(II), and sulfuric acid concentrations and current density on platinum were confirmed and extended to gold anodes by Fenton and Furman ( 3 ) . Both groups agreed that current efficiencies for the generation of Mn(II1) were less than 1 0 0 ~ by o 0.2 to lyOunder optimum circumstances,-Le., Mn(I1) greater than 0.28’; sulfuric acid between 2F and 7 F ; current densities between approximately 1 and 4 ma. per square centimeter. I n this paper, results are reported on the current efficiencies for the generation of Mn(II1) and Fe(l1) on platinum foil, paraffinimpregnated carbon, and boron carHE USE

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bide which confirm and extend the earlier LTork. The resp0n.e of several forms of amperometric and potentiometric endpoint detection systems was measured for the dual intermediates in the vicinity of the equivalence point. The amperometric end pointq include use of two platinum foils with defined, impressed potential difference, with cathode held a t a constant potential difference (more negative) with respect to the solution potential, and with the cathode held a t a constant potential with respect to a calomel reference electrode. The potentiometric end points include using direct measurement of solution potential a t a platinum wire us. a calomel cell, null mcasurement of solution potential us. a preset value corresponding to the equivalence point potential, and constant current potentiometric method a t two platinum electrodes. EXPERIMENTAL

Apparatus and Reagents. Currents

constant t o 0.1% from approximately 100 pa. to 250 ma. mere obtained from an electronically controlled constant current supply following the t n o-electrode designs of DeFord (g), and shown schematically in Figure 1. The modular arrangement selected uSes a high gain d.c. amplifier as an adder-inverter and normally provides currents up to 25 ma. For currents between 25 and 250 ma., a second booster stage, indicated by B . is used. Generation times were measured TTith a precision timer Model 8-10 of the Standard Electric Time Co. The titration vesael was a waterjacketed 150-ml. lipless beaker fitted with a plastic cap into which were inserted the electrodes, salt bridge, gas dispersion tube for deaeration with prepurified nitrogen, and isolation tubes

terminating in frittcd glass disks Solution volume of 7 5 nil. nas used. The generator electrode pair was 0.003in. thick platinum foil electrodes sealed into soft glass. The generator anode wm selected from three foils with areas of 2, 3, or 6 sq em. The generator cathode had an area of 2 sq. em. and n-as separated from the bulk of the solution by a tube containing 4.5F H2S04 terminating in a fine fritted glass disk. The carbon generator anode n-as Spex Industries, Inc , spectrographic grade carbon rod, 0.3-cm. diameter, n hich had been imp:egnated a i t h paraffin !\ax Rods were vaxed into glass tubes ‘0 that 0.34 and 1.14 sq. em mere eyposed. The exposed portion n a. poliqhed with carboiundum The cloth to remole surface n a x boron carbide anode was fine porosity solid cylinder, O..km. diameter, made by the Korton Co., and was sealed into glass JTith sealing T T ~ Y so , that 0.91 sq. em. was exposed. Nercury contacts ivere used n i t h all of the electrodes. A liquid, a t u r a t e d K2S04 bridge separated the referrnce calomel cell from the coulometric vessel. Tefloncovered magnetic Etirring bar R as used. The stock qolution uwd in this study was 0.4F 1\InS04, 0 12F Fe2(S0J3, and 4F H2S01. and n as prepared according to the procedure of Fenton and Furman ( 3 ) . Potential drift, indicating a loss of generated X€n(III), n a s eliminated by boiling the stock splution n i t h a fen- crystals of p o t a s w m permanganate and filtering. The constant impresqed potential amperometric end-point source, current meter, and shunts n ere constructed from the schematic given by Meier, Myers, and Snift ( 6 ) . The potential was impressed across a pair of 2-sq. em. platinum foil of the same construction as the generator pair. For the amperometric end point in which one electrode of the polarized pair was held at a constant potential difference n ith respect to the 3olution potential,

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a three-electrode potmtiostat arrangement. shown in Figure 2, was used. The same arrangement mas used for the more conventional amperometric end-point system to control the potential of the indicator cathode, with respect to a 13eckman calomel reference electrode. - n p e r o m e t r i c indicator current flowed between the polarized foil pair, and essentially no current was d r a n n betn een the arnperometric cathode and the potentionetric or calomel reference electrode. The impressed

potential was autoinatically adjusted to give a value necessary to maintain the desired indicator cathode potential. h simple, approximately zero current potentiometric end point n ith a 0,018-inch diameter platinum wire inch exposed) indicator electrode and a Beckman calomel reference electrode were used. The resulting potential was applied to a Beckman Model G p H meter or through follower amplifiers and voltage divider to a Model C-11 Varian potentiometric recorder. The more sensitive null potentiometric endpoint system using the same indicator electrode and low-resistance calomel electrode follon ed the description of Cooke, Reilly, and Furman ( 1 ) . An opposing voltage provided by a 1.5volt dry crll and Helipot voltage divider was applied to the indicator pair and the null measured with a Leeds & Sorthrup S u l l Detector S o . 9531 The potentiometric end point a t constant current used the three-electrode amperostat arrangement in Figure 2 for application of current to the platinum foil pair, previously employed in the amperometric end-point system. The difference potential nhich d e veloped was measured with a p H meter and individual electrode potentials us. a calomel reference cell could be measured alternately.

Khcn deteimining current efficiencies by the constant potential method. the three-electrode potentiostat arrangement n a s again used. In this cabe, the generator electrode pair received the variable impressed potential, and the generator anode nas controlled a t a fixed potential nitli respect t o the calomel electrode. To pro\ d e voltage sneep, the output voltage of an integrator sn eep generator, SG, was added a t the input of the control amplifier. DISCUSSION AND RESULTS

End-Point Detection. Current response curves for the two-platinum electrode amperoniet'ric end point a t constant impressed potential are s h o m in Figure 3 , wit'h a plot of t h e simultaneous measurement of solution pot'entiali's. S.C.E. These were nieasured in t h e vieinit>- of the equimlence point a t applied potentials of from 50 to 500 mv. Impressed potentials were adjusted for iR drop in the niicroammeter by meaarement of thv actual applied potentials a t the amperometric pair Tvith a Leeds & Kort'hrup millivolt potentionietcr. The minimum amperometric current occurs precicely at the potent'iometric equivalence lmint. However, the minimum current is not zero above an applied potential of 250 mv. and increases with further increasing applicd potential. With applied potential.5 below 250 n ' t ~ . cur~ rents on the excess l I n ( I I 1 ) sidc of the equivalence point, are nonlincwr and

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the usual linear extrapolation is not possible. At higher applied potentials, extrapolation of both branches of the amperometric current is necessary to locate the end point. The slope of the Fe(I1)-Fe(1II) branch is markedly steeper than the Mn(I1)-Mn(II1) branch. For this system, the amperometric end point is not as sensitive to small changes of intermediate concentration in the vicinity of the equivalence point as is experienced when using halogen intermediates. Analysis of current response for this type of amperometric end point involving reversible couples by Lingane and Anson (4) suggests that the potential of the current limiting electrode should be held constant relative to the solution potential. The potential impressed on the indicator pair will necessarily vary as the end point is approached. The indicator cathode was maintained a t a potential 40 mv. more negative than the solution potential. The impressed potential varied from 100 mv. in the presence of excess Mn (111) to about 50 mv. a t the equivalence point. The current a t the equivalence point was less than 0.1 pa. However, the amperometric current in excess ANALYTICAL CHEMISTRY

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Figure 5. Potentiometric end point a t constant current Platinum foil pair, 2-sq. cm. each. Curve A Anode potential at 5 p a . B Anode potential at 2 pa. C Anode potential at 1 pa. D Zero current or soluiion potential E Cathode polential at 1 pa. F Cathode potential at 2 pa. G Cathode potential at 5 ~ a . x-x Measured difference potential at 5 pa. a-a Measured difference potential at 2 p a . Measured difference potential at 1 pa.

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Mn(II1) was not linear and gave no advantage in extrapolation compared with the simpler method. A third amperometric end-point system in which the indicator cathode was held a t constant potential with respect to a reference electrode was investigated. Choosing values of +600, 700, 800, 900 mv., and 1000 mv. us. S.C.E., the resulting amperometric current in the vicinity of the equivalence point is shown in Figure 4. I n excess Mn(III), the current response is not linear but is quite linear and suitable for extrapolation in excess Fe(I1). At potential values of +800 or +900 mv. vs. S.C.E., extrapolation of these values to zero current gives precise indication of the equivalence point while deviations of increasing magnitude occur as the controlled potential is selected farther from the equivalence potential. Potentiometric titration curves are shown in Figures 3 and 4. Rapid response in excess Mn(II1) requires a well preconditioned platinum wire. P r e conditioning is done by shorting the platinum indicator electrode to the

generator anode and generating Mn (111) a t approximately 10 ma. for at least 30 seconds. This treatment is required before a series of titrations, but need not be done between samples. Slow attainment of the equilibrium potential upon increasing Mn(II1) concentration was observed early in this study. The zero current potentiometric response on platinum was followed during the generation of Mn(II1) a t several generation rates from 64.33 ma. to very slow, incremental generations with allowance for establishment of stable readings. Slow indicator response was encountered a t all finite rates studied on both platinum and carbon; but response was always more rapid during generation of Fe(1I). The slow response on generating Mn(II1) was magnified greatly when a platinized platinum electrode was used. I n a qualitative experiment, a 4-sq. cm. heavily platinized platinum foil was plunged into a deaerated solution containing Mn(1II) a t a steady potential. The indicator potential dropped to a new value over several minutes. The

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foil had been redLced a t constant potential +0.2 volt us. S.C.E. in 4F H2S04for 24 hours to remove platinum oxide and to avoid formation of sorbed hydrogen. The same foil, preanodized in sulfuric acid, produced no effect on the indicator potential. The prereduced foil, after exposure to ?vin(III), was removed, washed in boiling 4F HzS04,and transferred to boiling hydrochloric acid. After an hour, the hydrochloric acid solution was analyzed spectrophotometrically a t 263 mp. for platinum(1V) chloridt:. Platinum chloride corresponding to about 3000 times the amount of platinum oxide on a smooth [lll] plane was observed. These data suggest that Mn(II1) produces an oxidized ,surface layer on platinum and may establish its potential via surface oxidat on. The direct potentiometric end-point system was suitable only for large samples of about 100 peq., where an uncertainty of 0.3 peq. could be tolerated. Precision was limited by the minimum incremental amount of Fe (11) required to cause perceptible indicator response. The null potentiometric end point avoids this defect and has been used in a coulometric titration of nitrite where precision indicated by relative standard deviation (coefficient of variation) cf 0.29& has been achieved for samples of 62 peq. Potential response of the constant current or differentid potentiometric end point is shown in Figure 5 for

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three constant currents, 1, 2, and 5 pa. Measurements of the individual electrode potentials us. S.C.E. in separate experiments are shown also. Current Efficiencies. Current efficiencies for the generation of Mn(II1) in the range 1 to 4 ma. per sq. cm. reported by Fenton and Furman (3) show variability, but also a consistent trend toward efficiencies less than 99.9% a t optimum concentrations. Since the accuracy of a coulometric oxidation depends directly on the Mn(II1) generation efficiency, further study seemed desirable to determine precise current efficiencies on platinum over a wider current density range and to discover why the efficiency appeared to be variable over the narrow range studied by Fenton and Furman (3). Also, measurement of the efficiency for Mn(II1) generation on carbon and on boron carbide was desirable, since it seemed reasonable that one or both of these materials might provide higher efficiencies than is exhibited by either

platinum or gold. On the basis of earlier work, the optimum solution composition, given above, was chosen. Current efficiencies were determined two ways. Potentiostatic electrolyses in stirred solutions were performed and currentrtime curves were recorded. For Mn(II1) generation, potential steps of 0.025 volt in the range +1.00 to +1.70 volts us. S.C.E. were used. For Fe(I1) generation, the potential range studied was $0.525 to $0.300 volt us. S.C.E. in 0.025-volt steps. Immediately afterward, the same experiments were performed in blank solutions containing only sulfuric acid. Current efficiencies were then calculated. The currenbtime curves for Mn(II1) and Fe(I1) generation showed an initial current spike which decayed rapidly to a mean constant value. A ripple about the mean was caused by stirring of the solution. The blank solutions exhibited a spike and a persistent decay, especially a t the most positive potentials. VOL. 35,

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0.4F M n S 0 4 , 0.1 2 F Fe(SOJ3, and 4F H ~ S O I I. 2-sq. cm. platinum foil II. 1.14-sq. cm. carbon rod 111. 0.91 -sq. cm. boron carbide rod

111 a second and independent method. after the efficiency of Fe(I1) generation was confirmed to be 99.97, or better, hIn(II1) \vas generated for a precise time and the amount determined by back-titration with electrolytically generated Fe(I1). 4 precise null potentiometric end point was used. Results for current efficiencies on platinum, carbon, and boron carbide are shown in Figures 6, 7 , and 8. Brackets around points indicate range in the results. Variation in the potentiostatic efficiencies does not result from variation in limiting currents for the generation of Mn(TII), but is due to difficulty in reproducing limiting currents on blank runs. Current efficiencie3 for the generation of Fe(I1)

about 1 to 2 ma. per square centimeter. On platinum, efficiencies of 99.9% could be achieved only in the range 1 to 3.1 ma. per square centimeter, according to potentiometric results; although, efficiencies determined by titration gave equal results up to 3.7 ma. per square centimeter. When using platinum foils in coulometric titrations, areas should be chosen such that current densities are between l and 3 ma. per square centimeter. L-sing carbon, a wider current density choice is available for a desired efficiency. Boron carbide anodes are not suitable because of the rapid drop in efficiency beyond 2 ma. per square centimeter, which may be due to dissolution of the boron to yield boric acid. Voltammetry. Voltammetric scans were made in deaerated and stirred solutions containing excess Mn(II1) on each of the electrode materials. Typical results are shown in Figure 9. The oxidation behavior on platinum, carbon, and boron carbide is similar a t lo^ currents. However. on platinum and boron carbide, a limiting current is approached which does not occur belon- approximately 12 ma. per square centimeter on carbon. On successire scans, the limiting current on platinum incwases as is indicated by the successive peaks -4: B , and C. The niaximum limit,ing current was approximately 3 to 4 ma. per square centimeter. The lower overvoltage and appearance of a peak can also be achieved by storing the working generator electrode in escess FelII) overnight prior to voltage sweep experiments. Conversely, if the working generator is stored in excess Mn(III), the first voltage scans \Till show the maximum overvoltage for Mn(II1) generation without indication of a shoulder. These qualitstive results indieat,? that oxide film formation, produced either electrochemically or from chemical oxidation by I I n ( I I I ) , inhibits the generation of Mn(II1). The reduction of Fe(II1) is comparable on platinum and carbon,

on platinum are 99.97, over the useful range 0.2 to 12 ma. per square centimeter; and on carbon the efficiency is equally good, over the range 0.2 to 15 ma. per square centimeter. However, on boron carbide, the efficiencie. did not exceed 99.8%. Efficiencies for the generation of hIn(II1) were 99.77, or greater on platinum between about 0.4and 3.7 ma. per square centimeter; on carbon, between 0.4 and 15ma. per square centimeter; on boron carbidc, brtmeri

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and 4F H~SOI 2-sq. cm. platinum foil elecirode Scan rote, 10 millivolts per second Solution Dotentials. millivolts vs. S.C.E. Curve A,' 1000; 6; 990; C, 980; D, 976; E, 968; F, 952; G, 930; H, 622; I . 5 8 8 : J. 575 Curves A, E, and C a r e for solutions differing b y 10 microequivalents; curves C, D, E, and F differ b y 4 microequivalents; curves F, G, H, I, and J differ by 2 microequivalents I

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but is more irreversible on boron carbide. For further clarifit ation and interpretation of the axnperometric and potentiometric end-pGnt behavior, a series of voltammetr c sweeps in the low current region on platinum were obtained. Each of the curves in Figure 10 represents s solution of different composition in the vicinity of the equivalence point. It should be noted that the so ution potentials measured for these qolutions do not corrcyiond to the 1 otential of zero

current in the cases of excess Mn(II1). This behavior results from a combination of factors including surface oxidation, double layer charging and great irreversibility. Prior oxidation of the working electrode shifts the anodic portion of the curves to greater positive potentials. LITERATURE CITED

(1) Cooke, W. D., Reilly, C. Tu'., Furman, N. H., ASAL. CHEM. 23, 1662 (1951). (2) .DeFord, D. D., private communication, presented at the 133rd National

Meeting, ACS, San Francisco, Calif., April 1958. (3) Fenton, A. J., Furman, N. H., ANAL. CHEM.32, 748 (1960). (4) ~, Lineane. J. J.. Anson. F. C.. Ibid., 28, 1g71 (1956). ' (5) Meier, D. G., Myers, R. J., Swift E. H., J. Am. Chem. SOC.71, 2340 (1949). (6) Selim, R. G., Lingane, J. J., Anal. Chim. Acta 21,536 (1959). (7) Tutundzic, P. S., Mladenovic, S., Anal. Chim. Acta 12, 382, 390 (1955). RECEIVED for review August 8, 1962. Accepted March 11, 1963. Division of Analytical Chemistry, 142nd Meeting, ACS, A4tlanticCity, N. J., September 1962.

Coulometric Titration of Nitrite Using the Dual Inte rmedi(2tes Manga nese(III) a nd Iron(II) RICHARD P. BUCK (and THOMAS J. CROWE Bell & Howell Research Center, Pasadena, Calif. A, constant current :oulometric titration of nitrite has been devised, based on oxidation of nitrite to nitrate in the presence of excess, pregenerated Mn(ll1). Excess Mn(l1l) i s determined b y back-titration wit1 Fe(l1) using a null potentiometric end point. A relative standard deviation of i0.2% i s readily achieved for samples of 62 peq. of nitrite; but ihe deviation increases with decreasing sample size, becoming about =t1.6% a t the 0.3peq. level. A means for minimizing halide interference is described.

Electrolytically generated bln(I1I) for the coulometric titration of Fe(II), As(II1). and o.talic acid was introduced by Tutundzic and Madenovic (13). Current efficiencies for RSn(II1) generation on smooth platinum in sulfuric acid solutions were investigated by Selim and Lingane (11). Further measurements of current efficiencies on platinum and gold were made by Fenton and Furman ( 4 ) , and on wax-impregnated carbon and boron carbide by Buck (2). EXPERIMENTAL

A

SUJIBER of oxidative titrations of nitrite have been reported. The oxidants permanganatcx (j),dichromate ( 8 ) , cerium(1V) (15). bromate r6), hypochlorite ( 7 ) , or manganese(II1) ( 1 4 ) have been recommended. R e actions with the latter four titrants might reasonably be considered as the basis of secondary coulometric titrations. However, certain difficulties in the use of some of the intermediates can be inferred from t h s behavior of the potentiometric titration.. While electrolytic generation of Ce(1V) at high current efficiency is 1)ossible (3, IO), Willard and Young (15 ) demonstrated that, the titration of nitrite is quantitative only if the reaction mixture is warmed to 50" to 60" C. Electrochemical generation of bromate in basic solutions occurs by disproportionation of hypobromite ( I ) , but has not been shown to occur a t all in acidic solutions. Current efficiency for the generation of hypochlorite has not h e m reported and, in addition, its reaction with nitrite is slow ('7). I n contrast: manganese(II1) was shown by Uhelohde (14) to oxidize nitrite rapidly at room temperature.

Apparatus and Reagents. Currents constant t o 0.1% were obtained from a n electronically controlled constant current supply described elsewhere (2). Generation times were measured with a precision timer Model S-10 of the Standard Electric Time Co. The sensitive null potentiometric end point has been described (2). The titration vessel using a bright platinum wire indicator and low-resistance calomel reference cell was a water-jacketed 150-ml. lipless beaker fitted with a plastic cap into which the electrodes, K2S04-saturated salt bridge, gas dispersion tube for deaeration with prepurified nitrogen, and isolation tubes terminating in fritted glass disks were inserted. -4 solution volume of 75 ml., prior to sample addition, was used. Platinum foil and carbon rod generator electrodes were described previously ( 2 ) . A Teflon-covered magnetic stirring bar was used. The stock solution was 0.4F MnSOa, 0.12F Fe2(S04)3,and 4F H2S04; and was prepared according to the procedure of Fenton and Furman (4). The stock solution should be freed from reducing impurities by boiling with a few crystals of potassium permanganate and filtering. A stock 0.03F sodium nitrite solution was prepared from C.P. material and

standardized against potassium permanganate previously standardized against sodium oxalate. Samples of sodium nitrite, ranging from 0.3 peq. to 62 peq. were determined coulometrically. X calibrated 1-nd. volumetric pipet and a series of calibrated micropipets ranging from 500 to 50 lambda were used for sample addition. Procedure. T h e procedure is based upon oxidation of nitrite t o nitrate in t h e presence of excess, pregenerated hln(II1). This step is necessary because nitrous acid is easily lost from acidic manganous sulfate solutions prior t o and during generation of Mn(II1). Excess N n ( I I 1 ) is backtitrated with electrolytically generated Fe(I1). A carbon or platinum internal generator electrode may be used. Carbon is preferred because the range of current densities yielding high generation efficiencies is n-ider. The solution must be thoroughly deaerated to prevent loss of Fe(I1) during the backtitration. However, nitrogen flow muqt be stopped when the sample is added or low results are obtained, presumably due to loss of intermediate S O n . The potentiometric titration curve for the reaction of Nn(II1) and nitrite spans a more limited potential range than that of the Fe(I1) titration. Latimer (9) reports a formal potential E" = -0.94 for the nitrite-nitrate couple compared n-ith E" = -0.68 for the Fe(I1)-Fe(TI1) couple in sulfuric acid media ( 1 2 ) . An end point potential of 900 mv. 1's. S.C.E. was used throughout. This potential is above the platinum oxide formation potential in this medium so that oxide layer is not reduced during the titration, thus removing a source of potential drift. Use of less positive preset potentials corresponding to a significant concentration of Fe(II), causes fleeting end points because of reduction of nitrate, in addition to oxide layer reduction. Initially, the end point potential is V O L . 35,

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