Lanthanum Hexaboride as an Electrochemical Generant of Lanthanum(ll1) for Titrations: Application to Determination of Nickel(ll), Copper(ll), and Zinc(l1) D. J. Curran and K. S . Fletcher 111’ Department of Chemistry, University of Massachusetts, Amherst, Mass. 01002
Electrooxidation of a lanthanum hexaboride anode in aqueous supporting electrolytes releases lanthanum( I l l ) and boric acid or borate ion as major products. Current efficiency for the constant current generation of lanthanum(lll) ion has been defined as the ratio of the number of moles of La(lll) produced by electrolysis as determined by chemical analysis to the number of moles of La(lll) produced by electrolyses as calculated from Faraday’s law on the basis of pure LaB6of ideal stoichiometry. The current efficiency was found for various conditions of pH, supporting electrolyte, current density, and stirring rate and showed some dependence on pH only. In the pH range 1-6.5, the result was 109.0 & 0.1% while that in the pH range 8-13 was 108.1 & 0.1%. Constant current electrooxidation of lanthanum hexaboride in solutions in which the pH is controlled permits the generation of known amounts of lanthanum ion, once the current efficiency has been established. This procedure has been utilized for indirect titrations with EDTA of Ni(ll), Co(ll), or Zn(ll) in synthetic samples. Precision and accuracy of a few parts per thousand are possible for these titrations.
INPREVIOUS WORK it was shown that constant current oxidation of a lanthanum hexaboride anode produced lanthanum(111) ion and boron(II1) as major products (1). For material of ideal stoichiometry the following reaction was indicated: LaBe
+ 18 HzO
-P
La(II1)
+ 6 H3BOa + 18 Hf + 21 e-
(1)
In addition to the products shown in Equation 1 a small amount of hydrogen gas was produced and the current efficiency for the process, based on 21 equivalents per mole of reaction, was greater than 100%. These observations were explained by postulating hydrolysis of intermediate boron species produced in the course of the electrochemical process. In the present study, the current efficiency for generation of lanthanum(II1) from lanthanum hexaboride was determined under various conditions of stirring rate, current density, and solution pH. The current efficiency, calculated from the number of moles of lanthanum(II1) produced and that predicted on the basis of Faraday’s law, showed some dependence on pH alone. In solutions of constant pH, the current efficiency was constant and could be determined with a relative precision of =kO.lx. These facts suggest the use of lanthanum hexaboride as an electrochemical generant for titrations with lanthanum(II1). The current efficiency data reported here are based on either direct titration of EDTA with lanthanum(II1) or on back titration with standard Zn(N03)2of the EDTA remaining after addition of a measured excess of EDTA to the lanthanum(II1) Present address, Research Center, The Foxboro Company, Foxboro, Mass. 02035 1
(1) D. J. Curran and K. S.Fletcher, 111, ANAL.CHEM., 40,78 (1968).
solution. Both titrations were performed to the color change of Eriochrome Black T as indicator (2). These titration procedures are capable of high precision because of the very large formation constants of the EDTA complexes of La(II1) and = 15.5 and log Kz,(II) = 16.5) (3). In Zn(I1) (log KL~(III) principle, use of lanthanum (111) as a back titrant for the determination of metal ions is possible if that metal ion forms a complex with EDTA which has a formation constant larger than that of the complex with lanthanum(II1). This situation prevails for Zn(II), Co(II), and Ni(I1) (log K c ~ ( I=~ 16.3 ) and log KNi(II)= 18.6) (3). In the case of Co(I1) and Ni(II), these metal ions form such strong complexes with Eriochrome Black T that direct titration with EDTA to the color change of this indicator is not possible, and either an alternative means of end point detection or a back titration procedure must be employed. The back titration procedure generally employed uses standard solutions of magnesium or zinc ion. By using electrooxidation of lanthanum hexaboride as a source of lanthanum(III), a useful back titration procedure for the determination of Zn(II), Co(II), or Ni(I1) has been demonstrated. EXPERIMENTAL
The sample was obtained from Cerac Chemicals, Butler, Wis., in the form of a hot-pressed rod (3 inches long by inch diameter). The density of the rod was measured with a Beckman Model 930 Air Comparison Pycnometer as 4.29 g/cm3. The rod was cut into three 1-inch pieces and one of these pieces was used for all work reported in this study. The procedure for mounting the LaB6 rod has been described (1). The cell used for these constant current studies was a 200-ml glass beaker fitted with a Lucite cover through which holes were drilled to permit introduction of the LaBe electrode, a Corning Model 476020 pH-glass electrode, a Corning Model 47600 SCE, and a buret tip. The constant current source and the procedure used for its calibration have been described ( I ) . The constant current source used for electrical adjustment of pH consisted of a module, described by Brubaker (4), which plugged into a Heath Model EUW-19A Operational Amplifier System (Heath Co., Benton Harbor, Mich.). The pH was measured using a Corning Model 12 pH meter which was standardized at pH 4.0 and 9.18 with 0.05M potassium hydrogen phthalate and 0.01M sodium borate, respectively. Determinate solutions of EDTA were prepared from weighed portions of Fisher Primary Standard sodium diethylenediamine tetraacetate, prepared as primary standard following the procedure of Blaedel and Knight (5) and were diluted to volume with water redistilled from alkaline permanganate. Determinate zinc solutions were prepared from (2) G . Schwarzenbach, “Complexometric Titrations,” translated by H. Irving, Methuen, London, 1957, pp 29-35. (3) Ibid.,p 8. (4) R. Brubaker, Ph.D. Thesis, Department of Chemistry, Princeton University, Princeton, N. J., 1966. ( 5 ) W. J. Blaedel and H. J. Knight, ANAL.CHEM., 26,741 (1954). VOL. 40, NO. 12, OCTOBER 1968
1809
Table I. Current Efficiency for Electrogeneration of Lanthanum(II1) at pH 8.0 and 9.8 8.0 4 96.39 1006.7 f 0.3 0.04790 0.05179 108.1 f 0.1
PH Number of determinations Current, mA Time, seta Ne, mmolesb N,,mmolese C.E. Xd
Determination by direct procedure 9.8 2 48.19 3102.4 f 0 . 2 0.07379 0.07968 108.0 f 0.0
9.8
9.8 2 192.8 774.3 f 0.2 0.07368 0.07968 108.1 f 0.0
1
96.38 1549.0 0.07369 0.07968 108.1
Time shown is the average and standard deviation calculated for the number of determinations shown. Electrochemical mmoles, N e ,was calculated using Faraday’s law with i and t values shown, n = 21.00 eq/mole, and F c For the runs at pH 8.0, N , is given by (9.973 ml) (0.005193M) and for the runs at pH 9.8 by (9.973 ml) (0.007990M). d Current efficiencieswere calculated using Equation 2. a
b
=
96,487 coul/equiv.
Table II. Current Efficiency for Electrochemical Generation of Lanthanum(II1) at pH 1.0, 4.6, and 13.0 and in the pH ranges 6.0-6.5 and 7.0-7.5 1.o PH Number of determinations 3 48.20 Current, mA 2000 Time, sec 0.04758 Ne, mmolesa 0.004113 Molarity of Zn(NO+ Volume Zn(N03)*to titrate 48.52 total EDTA (ml) Volume Zn(NO& to titrate 35.91 f 0.00 excess EDTA (ml) 0.05186 N E ,mmoles 109.0 C.E. %* fO.0 a
b
1 .o 3 96.38 lo00 0.04757 0.004113 48.52
Determination by indirect procedure 6.0-6.5 4.6 4.6 1.o 3 2 2 2 96.39 96.39 192.8 192.8 lo00 lo00 500 500 0.04758 0.04758 0.04758 0.04758 0.004113 0.005027 0.005027 0.005042 44.84 45.15 48.52 44.84
35.91
35.91
f 0.00
f 0.00
0.05186 109.0 rto.0
0.05186 109.0
Calculated using Faraday’s law with n Calculated from Equation 2.
=
&O.O
34.51 f 0.01 0.05193 109.1 fO.1
21.00 eq/mole, and F
Baker Analyzed zinc pellets (assayed at lOO.O%, which were washed with acetone, rinsed with water, and dried at 150 “C. Weighed portions of the zinc were dissolved in 20 ml of 6N HN03, and the solution was evaporated to dryness to remove excess HN03. The Zn(NO& was redissolved with water and quantitatively transferred to volumetric flasks for dilution to volume. The titers of the solutions were verified, within 0.2$, by titration against each other at pH 10 to the color change of Eriochrome Black T (EBT) (2). Baker Reagent Grade C O ( N O ~ 6Hz0 ) ~ - and Ni(NO&. 6Hz0 were used as sources of Co(I1) and Ni(II), respectively. These solutions were standardized against standard EDTA to the color change of murexide as indicator (6). The EBT indicator solution was prepared by dissolving 0.15 g of EBT and 0.5 g of sodium tetraborate in 25 ml of methanol. The murexide was used in its solid form diluted to 50 wt % with NaC1.
RESULTS AND DISCUSSION Current Efficiency for Electrochemical Generation of Lanthanum(II1). Because lanthanum hexaboride is generally not available with the ideal stoichiometry noted in Equation 1 and because there is a side reaction present, it is necessary to calibrate the LaB6 electrode with regard to the electrochemical yield of lanthanum(II1). This empirical calibration is conveniently based on a comparison of the actual quantity of lanthanum(II1) produced under a given set of electrolysis conditions with the theoretical quantity based on Equation 1 (6) G. Schwarzenbach, “Complexometric Titrations,” translated by H. Irving, Methuen, London, 1957, pp 78-81. 1 8 10
ANALYTICAL CHEMISTRY
=
34.52 =t0.01 0.05188 109.0 fO.1
34.86 i 0.01 0.05188 109.0 fO.1
7.0-7.5 2 96.39 1000 0.04758 0.005042 45.15
13.0 2 48.20 2000 0.04758 0.004141 48.10
13.0 2 96.39 1000 0.04758 0.004141 48.10
13.0 1 192.8 500 0.04758 0.004141 48.10
34.90
35.69
35.69
35.70
f 0.01
f 0.0
f 0.0
0.05168 108.6
0.05139 108.0
0.05139 108.0
f0.1
rt 0.0
f0,o
0.05135 107.9
96,487 coul/equiv.
and Faraday’s law. Thus, the current efficiency (C.E.) may be defined as:
C C.E. = N - X 100 Ne where the chemical mmoles of La(III), N,, is determined by chemical analysis for lanthanum of the electrolytic solution, and the electrochemical mmoles, Ne, is calculated from Faraday’s law with TI taken as 21 .OO eq/mole. A direct titration procedure was employed for the determination of the current efficiencies at pH 8.0 and 9.8. For the determination at pH 8.0, 50 ml of 0.5M THAM buffer were used as supporting electrolyte, and for the determination at pH 9.8, 50 ml of 0.5M ammonia buffer were used. Three drops of EBT and 9.973 ml of standard EDTA were added to each solution, and lanthanum(II1) was generated in stirred solution with constant current for the length of time required to reach the color change of the indicator. N , was equated to the mmoles of EDTA taken and Ne was calculated from Faraday’s law. The data and current efficiencies are shown in Table I. The average current efficiency determined at each pH was 108.1 i 0.1%. Current efficiency data at other pH values were obtained using a back titration procedure. For the determination at pH 1.0, 25 ml of 0.10N HCL were used as supporting electrolyte and for the determination at pH 13.0, 25 ml of 0.10N NaOH were used, Lanthanum(II1) was generated both with and without stirring. After the electrolyses, the solutions were neutralized by addition of 25 ml of 0.10N NaOH or HCL, respectively, and were adjusted to pH 9.8 by addition of
Table 111. Data and Results of Indirect Titrations of Zn(II), Co(II), and Ni(I1) Total EDTA added = 0.05179 mmoles
Metal determined Metal taken, mrnoles Current, mA Time to end point, seca La(II1) generated, mmolesb Metal ion found, mmoles
Zn 0.02254 96.38 569.9 3~ 0 . 7 0.02930 0.02249 i0.2z -0.2%
Zn 0.00898 96.37 834.3 zt 0 . 9 0.04290 0.00889 &0.6% -1 .O%
co 0.02262 96.37 566.5 zt 2 . 0 0.02913 0.02266 &0.3% Relative error +0.2% a Time to end point is the average and standard deviation of five trials. b mmoles La(II1) generated was calculated using Equation 3 with quoted values of and C.E. = 108.1 2.
10 ml of 1.OM ammonia buffer. A measured volume of a solution of known concentration of EDTA was then added followed by three drops of EBT, and the excess EDTA was titrated with standard Z ~ I ( N O ~ )To ~ . correct for the possibility of reagent blank, titration of the total EDTA was performed in the presence of the same additions but without electrogenerated lanthanum(II1). The solution at the end point of this titration was saved, and the solution containing lanthanum(111) was titrated to the same color. The difference between the volume of Zn(NO& required to titrate the total EDTA and the volume required to titrate the EDTA remaining after addition to the lanthanum(II1) samples was used to calculate the mmoles of lanthanum(II1) generated, N,. Current efficiency data at pH 4.6 were obtained by electrolyses in stirred solutions containing 50 ml of 0.20MKCL and 10 ml of 1.OM acetate buffer. After these electrolyses the pH was adjusted to 9.8 by addition of 20 ml of 1.OM ammonia buffer, and lanthanum(II1) was determined as described above. Values of Ne were calculated and the data and current efficiencies are shown in Table 11. To complete the characterization of the dependence of current efficiency on pH, the electrooxidation of lanthanum hexaboride in stirred solutions of 0.100N K N 0 3 in the pH ranges 6.0-6.5 and 7.0-7.5 was studied. Because of solubility or complexation problems, a buffer for pH control in this range could not be found, and it was necessary to use electrical control of pH during these electrolyses. For this work, 65 ml of 0.100N KNOa were placed in the electrolysis cell which was equipped with the lanthanum hexaboride anodeplatinum cathode pair, a platinum anode-platinum cathode pair (this cathode was separated from the cell by an agar plug containing 0.1N KN03), and the standardized pH-glass calomel electrode pair. Electrolyses were performed using constant currents of 96.39 mA impressed across the lanthanum hexaboride-platinum pair for 1000 sec. At the anode, Faraday’s law, with n = 21 eq/mole, and Equation 1 predict generation of 0.4758 mmole La(II1) and 0.856 mmole of Hf. At the cathode, Faraday’s law predicts generation of 1.000 mmole of OH- and the effect of electrolysis is to increase the pH of the solution. To counteract this, the pH of the solution was adjusted to the desired pH prior to the run, as noted with the pH meter, and held within the pH range 6.0-6.5 or 7.0-7.5, by simultaneous passage of a second current, variable from about 1 to 12 mA, through the platinum-platinum electrode pair. After these electrolyses, 10 ml of 2M ammonia buffer, three drops of EBT, and a measured excess of EDTA were added to the cell, and lanthanum(II1) was determined by the indirect procedure. These data are also shown in Table 11.
co 0.00901 96.37 829.3 zt 0.4 0.04264 0.00915 50.3z +1.6%
Ni 0.02200 96.38 580.8 & 0.5 0.02987 0.02192 zt0.2% -0.3%
Ni
0.00876 96.38 834.8 i 0 . 4 0.04293 0.00886 zt0.22 +1.1%
i and t , n = 21.00 eq/mole, F = 96,487 coul/equiv,
In summary, the current efficiency for the electrochemical generation of lanthanum(II1) is constant and reproducible under the limitation of controlling the pH. In the pH range 1-6.5, the average current efficiency was 109.0*0.1% and in the range 8-13 was 108.1 zt 0.1%. The change in current efficiency of approximately 1% occurring in the pH range 6.5-8 does not present a major disadvantage to application of lanthanum hexaboride for an electrochemical source of lanthanum(II1) in titrations with this ion as this range of pH can usually be avoided by manipulation of experimental conditions. Back Titrations of Ni(II), Co(II), and Zn(11). Use of electrogenerated lanthanum ion as a back titrant for the determination of some metal ions was based on addition of an accurately known amount of EDTA to solutions of the metal ions buffered at pH 8 and titration to the color change of EBT of the excess EDTA with electrogenerated lanthanum(111). The utility of this procedure was investigated for Ni(II), Co(II), and Zn(I1) which, together with La(II), form 1 :1 complexes with EDTA. At the equivalence point the number of moles of lanthanum ion generated equals the number of moles of excess EDTA, and the difference between the total number of moles of EDTA taken and the number of moles of lanthanum ion generated is the number of moles of metal ion in the original sample. The number of moles of lanthanum ion generated is found by multiplying the current efficiency by the theoretical yield:
N,
=
C.E. -X N 100%
e
C ELit X- 100% nF
(3)
where i is the current in amperes, t is the time in seconds, n is taken as 21.00 eq/mole, F is the Faraday (the current efficiency at pH 8.0 is 108.1%), and the other terms have been defined. For these titrations, 50 ml of 0.5M THAM buffer were placed in an electrolysis cell equipped with the lanthanum hexaboride anodeplatinum cathode pair. The cathode was separated from the cell by an agar plug containing KN03. Additions of the metal ion to be determined and EDTA were made to this solution followed by three drops of the EBT indicator solution. In all cases 9.973 ml of 0.005193M EDTA (0.005179 mmole) were used and either 5.005 or 1.992 ml of 0.004504M Zn(N03)2, 0.004520M C O ( N O ~ ) ~or, 0.004395M Ni(N03)2. The data and results for these analyses are shown in Table 111. The data shown for each determination are the average and standard deviation for five trials. Precision and accuracy for the larger samples was about +0.2%. For the smaller samples overall precision was about 210.3% and overall accuracy was about + l % , VOL. 40, NO. 12, OCTOBER 1968
1811
CONCLUSIONS
A coulometric titration has been defined as one in which a substance is made to undergo a quantitative, stoichiometric reaction with electrons (7). While generation of lanthanum ion by the constant current oxidation of lanthanum hexaboride does not meet either criterion, the process can be made quantitative by application of an empirical factor, the current efficiency, which calibrates the yield of lanthanum ion regardless of the stoichiometry of the starting material or of the stoichiometry of its electro-oxidation reaction. It should be mentioned that different samples of lanthanum hexaboride are likely to have different stoichiometry and, therefore, this calibration procedure must not only be employed but the calibration factor will be different for the different samples. In addition, experiments performed on a sample of lanthanum hexaboride having a density of 3.09 g/cma as opposed to the nearly theoretical density of the material used in this study, showed an irreproducible current efficiency of about 120z (a), indicating that for best results (7) D. D. DeFord and J. W. Miller, in “Treatise on Analytical Chemistry,” Part I, Vol. 4, I. M. Kolthoff, P. J. Elving, and E. B. Sandell, Eds., Interscience, New York, 1963, p 2476. (8) K. S. Fletcher 111, unpublished results, The Foxboro Co.,
Foxboro. Mass.
material having nearly theoretical density should be employed. The requirements of highest possible density should be explicitly stated when ordering the rod from sources of supply since some applications for the rod in other areas of study are better served by material of lesser density. As with most coulometric procedures, use of lanthanum hexaboride as an electrochemical source of lanthanum ion eliminated the need for preparation and storage of standard solutions. Once calibrated, the lanthanum hexaboride rod should be stable indefinitely in the absence of strong oxidants and will provide an extremely convenient source of lanthanum ion. In addition, the small size of the moles per coulomb ratio, l/nF, equal to approximately 5 X 10-7 moles/coul, shows that very small quantities of reagent (electrons) may be added and accurately measured. ACKNOWLEDGMENT
We thank J. W. Anderson for cutting the LaBB rod. RECEIVED for review June 10, 1968. Accepted July 10, 1968. Taken in part from the Ph.D. Thesis of K.S.F. 111. Work supported in part by University of Massachusetts Research Council.
An Automatic Digital Readout System for Reaction-Rate Methods E. M. Cordos,lS. R. Crouch, and H. V. Malmstadt Department of Chemistry and Chemical Engineering, UniGersity of Illinois, Urbana, Ill. 61801
A new integration technique for obtaining direct readout of rates is described that has high noise immunity. The measurement cycle can be varied from milliseconds to hundreds of seconds to provide optimum performance for very fast or slow reactions. Input signals ranging over a million-fold in mV/sec can be readily measured. Results for synthetic signals from a ramp generator show standard deviations and relative errors of about 0.2%. Test results with spectrophotometric reaction-rate methods for phosphate and glucose in the parts-per-million range are also presented.
IN RECENT YEARS several sensitive, selective, and accurate quantitative methods have been reported that are based on the measurement of initial reaction rates and these have been summarized in review articles (1,-.3), Various devices for obtaining a direct readout of the reaction rate data have also been developed to automate the procedures (4,5). Automatic measurements have been made usually by determining the concentration change in a preselected interval of time (fixed time method), or by measuring the time required for a change of concentration between two predetermined Present address, University “Babes-Bolyai,” CIuj, Romania (1) G. A. Rechnitz, ANAL.CHEM., 36,453R (1964). (2) Ibid., 38, 513R (1966). (3) Ibid., 40, 455R (1968). (4) G. E. James and H. L. Pardue, ibid., 40,796 (1968). ( 5 ) H. V. Malmstadt and S. R. Crouch, J . Chem. Educ., 43, 340 (1 966).
18 12
ANALYTICAL CHEMISTRY
levels (variable time method) (6). Both of these techniques involve measurements at two points along the reaction rate curve. With these two-point methods, the accuracy in the determination of Ac or At can be significantly affected by the noise. Because a high signal-noise ratio is necessary for high accuracy and general application of the readout device, it is important to develop new systems that are not greatly affected by noise and can be used for measurements of a wide range of reaction rates. The instrument described here is based on an integration procedure that is characterized by high noise immunity. Instead of making the measurement between two points, two portions of the curve are integrated, subtracted, and the difference automatically displayed on a digital readout. This digital readout is directly related to the reaction-rate and can be made equal to the concentration of the sought-for species. The integration averages the noise so that its contribution to the relative error is greatly reduced. The integrators used in the circuit have a “memory” so that the first portion of the integrated curve is taken as reference for the measurement. When a new measurement is to be made, the operation is repeated, and always the first of two successive integrated portions of the curve becomes the reference, regardless of its absolute value. Accordingly, the in(6) W. J. Blaedel and G. P. Hicks, “Advances in Analytical Chemistry and Instrumentation,” Vol. 3, Wiley, New York, 1964, pp 105-42.
