with a finite bound (z,) and in the B, terms. Validity of the former approximation (Equation A-4) was proved by using values of zslarger than those calculated from Equation A-4 and noting no change in calculated current functions. Booman and Pence ( I ) discuss various approximations of the B, terms, and justify use of either Equation A-11 or A-13. All preliminary calculations were performed in duplicate using both of these approximations. Comparison of results showed variations that were negligible with respect to those resulting from changes of 6 and Az. Because Equation A-1 1 required
fewer iterations, however, Equation A-1 1 was employed for all of the results presented in the text.
RECEIVED for review August 1, 1968. Accepted October 23, 1968. Research supported by the National Science Foundation and United States Army Research Office-Durham (Contract No. DA-31-124-ARO-D-308). One of us (M.L.O.) thanks the Phillips Petroleum Company for the fellowship during the summer of 1968.
Precipitation Titrations with Electrochemically Generated Lanthanum Ion Potentiometric Titration of Fluoride and Turbidimetric Titration of Oxalate D. J. Curran and K. S . Fletcher 111' Dppartment of Chemistry, University of Massachusetts, Amherst, Mass. 01002 Lanthanum ion electrochemically generated from a lanthanum hexaboride anode has been used as a precipitant for fluoride and oxalate ions. A lanthanum fluoride membrane electrode was used for end point detection in the fluoride work and a turbidimetric end point technique was used in the oxalate titrations. The pH conditions for the fluoride reaction were studied and 0.5 to 2.0 mg of fluoride in about 100 ml of solution have been determined with a precision and accuracy of a part per thousand at a pH electrochemically controlled at 5.0. The techniques of pretitration and titration back to a predetermined end point potential were used. An equation for the fluoride titration curve is discussed. Approximately 0.5- to 2.6-mg samples of oxalate ion in acidic solution (approximately 20-1111 volumes) have been titrated with a precision and accuracy in the 1 to 2% range.
IN A RECENT REPORT (1) a lanthanum hexaboride anode was used to generate known amounts of lanthanum ion in solution. The current efficiency (defined as the ratio of the number of moles of lanthanum generated at constant current as found by chemical analysis of the electrolysis solution to the number of moles of lanthanum ion predicted in solution from Faraday's law on the basis of pure LaBG of ideal stoichiometry) exceeded 100% and was a function only of the pH of the solution. Application was made to the determination of several metal ions by back titration of excess EDTA added to the solution of metal ion with electrochemically generated lanthanum ion. Lanthanum forms stoichiometric precipitates with a number of anions and this paper reports on the potentiometric titration of fluoride ion and the turbidimetric titration of oxalate ion with electrogenerated lanthanum ion. Present address, Research Center, The Foxboro Co, Foxboro, Mass. 02035 (1) D. J. Curran and K. S. Fletcher 111, ANAL.CHEM.,40, 1809
(1968).
Classical methods for fluoride analyses usually involve time consuming laboratory procedures. The recent development of a solid state electrode with a selective potentiometric response to fluoride activity has provided a simple procedure for fluoride determinations (2). Because the potential of this electrode has a theoretical response of 59.16 mV per decade in activity of fluoride at 25 "C, are lative error of 11 in activity of fluoride would require reliability of the potential measurement to be +0.25 mV. While the response stability of this electrode has been reported to be &0.1 mV (3), relative errors in the range 0.1 to 1% are difficult to obtain by direct potentiometry because the determination of concentration from a measurement of activity requires independent knowledge of activity coefficients to at least this degree of accuracy. Further, response stability of the fluoride and reference electrodes, liquid junction potentials, ionic strength changes, and pH effects all render analyses to accuracies better than 1 % doubtful. Lingane has recently described the potentiometric titration of fluoride with lanthanum nitrate as titrant and a commercially available lanthanum fluoride membrane electrode for end point detection (4). This work indicates that relative errors of 1 0 . 1 % are possible for the titration of 7.6-mg samples of fluoride ion in 100 ml of solution if the equivalence point is measured to ~ k 0 . 3mV. In the present study, conditions for the titration of fluoride ion using electrogenerated lanthanum ion and a fluoride ion selective membrane electrode for end point detection are described. An equation for the titration curve has been developed and 0.5- to 2-mg samples of fluoride ion in 105 ml of solution have been titrated with a precision and accuracy of about =t0.1%by use of the techniques of pretitration and titration to a predetermined end point potential.
_(2) M. S . Frant and J. W. Rose, Jr., Science, 154, 1553 (1966). (3) T. S. Light, Pittsburgh Conference on Analytical Chemistry
and Applied Spectroscopy, March 1967.
(4) J. J. Lingane, ANAL.CHEW., 39, 881 (1967). VOL. 41,NO. 2, FEBRUARY 1969
267
The titration of oxalic acid with lanthanum solutions as the titrant and turbidimetric end point detection has been reported (5). While no specific experimental detail or figures of precision are available, the method was claimed to be reliable to 5 z . A procedure for the turbidimetric titration of oxalate ion in aqueous acid solution with electrogenerated lanthanum ion is reported here which is simple and fast and which has a precision and accuracy of about 1to 2 x . EXPERIMENTAL
Reagents and Materials. All chemicals were reagent grade unless otherwise stated. Baker analyzed sodium fluoride (assayed at 1OO.Oz) was purified by the procedure described by Lingane (4), and determinate fluoride solutions were prepared in a constant ionic background of 0.100N KNO, by transferring weighed portions of the salts to volumetric flasks and diluting to volume with water redistilled from alkaline permanganate. The solutions were immediately transferred to polyethylene bottles for storage. Determinate solutions of oxalate ion were obtained by dissolving dried (150 “C.) and weighed portions of Thorn Smith Na2C204 (99.96z) in redistilled water and diluting to volume. A 2 M acetate buffer was prepared by diluting 115 ml of glacial acetic acid and a solution of 40 grams of NaOH to one liter with water. The pH of this solution was 4.6 as read with a standardized pH-glass electrode-calomel pair and pH meter. The lanthanum hexaboride rod used as the anode measured inch in diameter by 1 inch in length and was cut from the same piece of material used in earlier work ( I ) . Mounting of the rod has also been described (6). Apparatus. Fluoride titrations were performed in a 250-ml Nalgene beaker equipped with the lanthanum hexaboride anode, a l-cm2 platinum flag cathode, an Orion Model 94-09 fluoride electrode (Orion Researches, Cambridge, Mass.), a Corning Model 476020 pH-glass electrode (Corning Co., Medfield, Mass.), and the saturated calomel electrode described by Lingane (7) with “J” tip filled with saturated KCl. The potentials of both the fluoride and pH-glass electrodes were measured against this reference electrode. The glassSCE pair was standardized at pH 4.00 with 0.05M potassium hydrogen phthalate at 25.0 “C. The pH measurements were obtained with a Leeds and Northrup Model 7401 pH meter (Philadelphia, Pa.) and fluoride measurements were obtained with a Corning Model 12 pH meter. Electrochemical adjustment of pH was accomplished by use of the constant current source described by Brubaker (8) connected to the platinum flag electrode described above and a second platinum electrode separated from the rest of the cell by an agar plug containing KNOI. The constant current source used for generation of lanthanum ion and the procedure used for its calibration have been described (6). Electrolysis times were measured with a standard Model S-10 precision timer (The Standard Electric Time Co., Springfield, Mass.) by manual operation. A single switch operated both the timer and the constant current source. With incremental approach to equivalence points, we estimate the accuracy of time measurements to be better than =tO.lzrelative for titration times of 300 seconds. The solutions were stirred with a 1-inch coated stirring bar made of Teflon (Dupont) driven by an air driven magnetic stirrer (G. F. Smith Chemical CO., Columbus, Ohio). All titrations of fluoride were performed at 25.00 =t0.02 “Cby immersing the cell in a P. M. Tamson (Zoetemer, Holland) Model T9 constant temperature bath. (5) M. Bobtelski, A m / . Chini. Acta, 13, 172 (1955). (6) D. J. Curran and K. S. Fletcher 111, ANAL.CHEM.,40, 78
(1968). (7) J. J. Lingane, “Electroanalytical Chemistry,” 2nd ed., Interscience, New York, N. Y., 1958, p 362. (8) R. Brubaker, Ph.D. Thesis, Department of Chemistry, Princeton University, Princeton, N. J., 1966. 268
ANALYTICAL CHEMISTRY
200
400
600 800 1000 1200 TIME, S E C O N D S
1400
Figure 1. Potentiometric titration curves for the titration of fluoride with electrogenerated lanthanum(II1) at various pH. Initial fluoride amount = 0.2448 mmole. Constant current = 192.8 mA. V, 0, 0 , pH controlled electrolytically at 4.0, 5.0, and 6.0, respectively; 0 pH controlled with pH 4.6 acetate buffer; V theoretical titration curve
Turbidance measurements were obtained as absorbance readings with a Fisher Electrophotometer I1 (Fisher Scientific Company, Pittsburgh, Pa.). Titrations were performed with the lanthanum hexaboride anode and platinum wire cathode dipping directly into the 25-ml cuvet supplied with the instrument. Care was taken to be sure that the electrodes did not interrupt the light path through the cell. Stirring was achieved with the same type of air-driven stirrer as mentioned above. The unit was mounted in a space below the ceil compartment and Tygon tubing was brought through the side of the instrument to supply air for the stirrer. The cell was illuminated through a blue filter. Fluoride Procedures. Potentiometric titration curves for the titration of fluoride ion with electrogenerated La(II1) were studied with solutions 0.100N in KN03 buffered at pH 4.6 with acetate buffer, and solutions 0.100N in KNO, electrochemically controlled at pH 4.0, 5.0, or 6.0. For titrations in the acetate buffer, 100.0 ml of 0.100N K N 0 3 , 1.0 ml of 2M buffer, and 5.005 ml of 0.04891NNaF in 0.100N KNO, were added to the cell, while for the titrations with electrochemically controlled pH, 100.0 ml of 0.100N K N 0 3 and 5.005 ml of 0.04891N NaF in 0.100N K N 0 , were added to the cell; the pH was electrochemically adjusted to about 2.0; La(II1) was generated at a constant current of 192.8 mA, and the pH was readjusted to 4.0, 5.0, or 6.0 for each reading of the fluoride electrode potential. In all cases, the solutions were stirred. Analysis of known amounts of fluoride in the range 0.5 to 2.0 mg were carried out by pretitration of a known larger sample to the theoretical equivalence point time, followed by addition of the sample and titration back to the equivalence point potential noted for the larger sample. All solutions were titrated in 0.100N K N 0 3 and the pH was controlled either at 4.6 with acetate buffer or at 5.0 with electrochemical
means. For titrations in the acetate buffer, 100.0 ml of 0.100N K N 0 3 and 1.0 ml of 2M acetate buffer were added to the cell. Pretitration of 5.005 ml of 0.04891N NaF in 0.100N K N 0 3 (0.2448 mmole of fluoride) was performed to the theoretical equivalence point time of 786.7 seconds and the equivalence point potential was observed as 55.2 mV us. SCE. Accurately known volumes of 1 to 5 ml of known fluoride solutions were then added to the pretitrated solution, lanthanum ion was generated at constant current, and the time required to return the fluoride electrode to the equivalence point potential was measured. N o more than three or four fluoride additions were made to the same pretitrated solution. Similar procedures were used for titrations with electrochemically controlled pH: 100.0 ml of 0.100N KN03, pretitration to a theoretical equivalence point time, and addition of 1- to 5-ml volumes of known fluoride solutions. The pH of the titrate was adjusted initially by coulometric means to 3.5 to 4.0 prior to generation of La(II1) and readjusted to pH 5.0 by use of a constant current of 10 mA for each measurement of the fluoride electrode potential. Oxalate Procedure. The turbidimetric titration curves for the titration of oxalate ion with electrogenerated lanthanum(II1) were obtained with solutions buffered at pH 4.6 with acetate buffer. Three sets of titrations were performed. For the first, 9.972 ml of 0.003037M Na2CZ04,10 ml of water, and 1.0 ml of 2 M acetate buffer were taken and lanthanum ion was generated at a constant current of 96.39 mA. For the second set, 5.005 ml of 0.003058M Na2C204,15 mI of water, and 1.0 ml of 2 M acetate buffer were taken and the current was 48.20 mA. For the final set, 1.992 ml of the oxalate solution, 15 ml of water, and 1.0 ml of acetate buffer were taken and lanthanum ion was generated at 9.636 mA. The solutions were stirred and the absorbance was measured us. water at several times during the titrations. Before reading the absorbance (turbidance), the current was turned off, the stirring stopped, and the cuvet tapped lightly to remove bubbles of hydrogen gas which were produced at the cathode and which tended to cling to the precipitate.
where C.E. is the current efficiency, i is the current in mA, 1 is the time in seconds, n is 21.00 equivalents per mole, and F is the Faraday. Substituting, NF- = 3(if/nF) (C.E./100%)
Current efficiency for the electrochemical generation of lanthanum ion over the pH range used here was 109.0% ( I ) . Using this value, N F - = 0.2448 mmole, i = 192.8 mA, n = 21.00 equivalents per mole, and F = 96,487 coulombs per equivalent, the theoretical time to the equivalence point for the titrations in Figure 1 is calculated from Equation 3 as 786.7 seconds. A vertical line indicates this time in the figure. Kury has reported the following equilibria and equilibrium constants for aqueous solutions of lanthanum(II1) and fluoride ion at 25.0 "Cin0.5MNaC104(10):
+F La3+ + HP = LaF2+ + H+ 1 1 . -HzO(s) = La3+ + 3 F + -HzO 2 2 HF
LaF,
=
H+
Ksp
=
[La3+][ P I 3 = 1.4 X lo-'*
where NLas+ is the total mmoles of Laa+ generated and NFis the total mmoles of F- taken. It was previously shown that ( I ) :
(6)
(9)
If u liters of a solution containing c moles of fluoride is titrated with electrogenerated lanthanum ion at conntant current, then, folIowing the formalism developed by Butler ( I I ) , the mass balances can be expressed as:
+
La3+]
(1)
(5)
(7)
[F] [LaF2+]
N L ~ =~ (1/3)N~+
(4)
where the equilibrium constants are, respectively :
RESULTS AND DISCUSSION
Titration of Fluoride with Electrogenerated Lanthanum Ion. As indicated in a previous report (9), application of a constant current across a lanthanum hexaboride anode-platinum cathode electrode pair results in a net increase in the pH of the solution because of the nonequivalency of the hydrolytic reactions occurring at the electrodes. Thus the pH of the solution controlled at pH 4.6 with acetate buffer increased to pH 5.0 after generation of lanthanum(II1) for 1200 seconds. For the titrations with electrochemically controlled pH, the procedure of maintaining the solution pH at about two prior to the generation of La(II1) ensured that the solution would not become basic during the electrolysis, thereby eliminating the possibility of a change in the current efficiency ( I ) . The upper limit for the readjusted pH of 6.0 was chosen to avoid the possibility of OH- interference with the fluoride electrode ( 2 ) . The titration curves resulting from these experiments are shown in Figure 1. At the equivalence point:
(3)
+ 3P = c / u
+ [LaF2+1+ P = Kt/o
(11)
where P is the number of moles of LaF3 precipitated per liter, and Kt is the total number of moles of lanthanum ion added, where K is a constant given by (i/nF) (C.E./100%) and f is the time in seconds. Eliminating P and making appropriate substitutions gives the complete equation for the titration curve as :
[F= ](C - 3Kt)/u
+ 3Ksp/[FI3 + ~ K , S P K ~ / K ~ (12) [F]~
The fraction of the fluoride titrated as a function of time is given by: qi =
3Kt/c
(13)
Rearrangement of Equation 12 in terms of the fraction titrated yields:
4 -1
= (u/c) (3Ksp/[FI3
+ 2KspKr/KJF-l2
- [ P I ) (14)
If formation of the LaF2+ species is neglected, Equation 14 reduces to :
4 -1
= (u/C)
(3Ksp/[FI3 -
F-1)
(1 5 )
Before the equivalence point, 3Ksp/[F-I3
