these elements are not eluted and can be separated from Ba. The heaviest rare earths are eluted almost together with Sr when 3.00M HC1 in 20% ethanol is used as eluent, while La appears almost together with Ba. The rare earths therefore interfere with the method and, when present, have to be separated. This can be done by cation exchange chromatography using a 75-ml (25-gram) column of AG50W-X8 resin of 200- to 400-mesh particle size. Ba and Sr can be eluted with 500 ml of 2.00M H N 0 3 while the rare earths (up to 2 mmole) are retained quantitatively. The separation factor of asrBa= 3.5 in 3.00M HC1 20z ethanol with the AG50W-X8 resin is slightly higher than those obtained with organic complexing agents except EDTA and DCyTA, and the method has the important advantage that the eluting agent can very easily be removed by evaporation. Exchange rates in the above eluent concentration are reasonably fast and flow rates of 2 to 3 ml per minute (linear flow rate 0.6 to 0.9 ml per minute per cmz) can be employed. Increasing the ethanol concentration gives higher separation factors but slower exchange rates. The same applies to using resin of higher cross-linkage. Larger amounts of Ba precipitate as the chloride from 3M HCl in 50% ethanol or 4 M HCl in 40% ethanol. Disturbing effects in the column operation appear already at somewhat lower concentrations. This and the fact that the distribution coefficients of Sr increase more sharply at higher concentrations of ethanol, limit the favorable conditions for separation to a fairly narrow range. The most convenient separations for most purposes are obtained with an 8% cross-linked resin of 200to 400- mesh particle size and 3.00M HCl in 20% ethanol. Smaller columns can be used when only several milligrams or less of Ba plus Sr are present. Ba (0.1 mmole) could be
+
FIuoride MicroanaIysis by Linear
Table V. Distribution Coefficients in Ethanol AG50W-Xl2 Resin 3.00N HC1 4.00N HC1 Ethanol Sr Ba Sr Ba 0 12.0 29.8 8.1 19.9 15.5 47.8 11.6 35.2 10 20 21.5 82 14.7 64 30 32.3 133 24.2 120 40 52.8 235 41.5 prec. 60 207 prec. ... prec.
z
separated from 0.1 mmole Sr on a column of 15 ml (5 g dry weight) of AG50W-X8 resin of 200- to 400-mesh particle size. The resin bed was 13.5 cm in length and 1.1 cm in diameter, and the Sr was eluted quantitatively with 140 ml of 3.00M HC1 in 20% ethanol at a flow rate of 0.8 f 0.1 ml per minute. When very small amounts of Sr have to be separated from very large amounts of Ba or vice versa, 3.00M HC1 in 30% ethanol is a better eluting agent because of the higher separation factor of 4.3. Resin of 12% cross-linkage does not offer advantages with ethanolic HCl eluents. Separations are less satisfactory when resins of 100- or 200-mesh particle size and high flow rates are used. The distribution coefficients in Table I show that " 0 3 is a much more effective eluting agent than HC1 for Ba from a 12% cross-linked resin. This is in accordance with results for an 8% crosslinked resin obtained previously ( I 4 , 2 0 ) . RECEIVED for review October 24, 1967. Accepted February 12, 1968.
Nu II-Point Potentiometry
Richard A. Durst Division of Analytical Chemistry, Institute for Materials Research, National Bureau of Standards, Washington, D . C . 20234 The modified fluoride activity electrode is used as the sample electrode in the technique of linear null-point potentiometry for the determination of fluoride at subnanogram levels in sample volumes of 10 , I. The emf VS. titrant concentration data are plotted semilogarithmically, and the equivalence point is obtained by a linear interpolation to the null-point potential. Data analysis is also accomplished by computer techniques whereby the equivalence point is obtained from the intercept of a linear least squares fit of the data. Fluoride solutions 10-3 to 2 X 10-'jM (containing 190 to 0.38 nanograms of fluoride in 10 @I)were determined with an accuracy of approximately 1% over the entire range and a relative standard deviation of the mean of about 0.5% for 5 determinations. At the lowest concentration level, 2 x lO-'jM fluoride, the error in determining 380 picograms of fluoride was approximately 2 picograms.
THE DETERMINATION of fluoride at subnanogram levels in sample volumes of 10 p1 has been achieved for the first time using the modified fluoride activity electrode ( I ) in combina-
tion with the concentration cell technique of linear nullpoint potentiometry [LNPP] (2). The fluoride sample in the inverted fluoride electrode microcell is titrated by the addition of a standard fluoride solution to a second electrochemical half cell connected to the former by a salt bridge. The emf U S . titrant concentration data are plotted semilogarithmically, and the equivalence point is obtained by a linear interpolation to the null-point potential. The concentration cell employed is LaFalF-(CA), KN03(0.1WI IKNO@lM)I 10 pl
salt bndge
I I
KN03(0.lM), F-(CT) LaF3 100 ml.
where LaF3 is the fluoride-specific membrane of the fluoride activity electrode, C, is the concentration of the fluoride solution being analyzed (z'.e., analate solution), and CT is the concentration of fluoride in the titrant half cell. The, emf of this cell is given by the Nernst equation for a concentration cell : ~~~~
(1) R. A. Durst and J. K. Taylor, ANAL.CHEM., 39, 1483 (1967).
(2) R. A. Durst and J. K. Taylor, ANAL.CHEM., 39,1374 (1967). VOL 40, NO. 6, MAY 1968
931
POLYETHYLENE CAPILLARY
SAMPLE SOLUTION
( 4 % AGAR-0
I y KNOJ
L a F-j MEMBRANE LYETHYLENE CAPS
TYGON
SLEEVE LYETHYLENE RING
MODIFIED FLUORIDE ACTIVITY ELECTRODE
C
Y
Figure 1. Concentration cell for LNPP determination of fluoride Modified fluoride activity electrode Sample microcell (see enlargementin Figure 2) Ag/AgCl inner reference electrode O.lMNaF, O.lMKC1, 4 % agar gel Polyethylene capillary containing 0.1M KN03-4 agar gel Salt bridge-4.1M KN03 F. Tygon tubing G . Porous Vycor salt bridgejunction H. Stirrer I. Variable fluoride concentration solution-100 ml 0.1M KNO, f xMNaF J . Polyethylenecapillary tube K. Fluoride activity electrode L . Titrant solution-standard NaF in 0.1MKN03 M. Microburet N . Electrode leads to pH meter A. A'. B. C. D. E.
+--- lornrn -4 Figure 2. Details of the 10 p1 sample microcell
Becausc the titrant solution is added volumetrically, a dilution correction must be applied to the concentration of fluoride in the titration half cell-Le.,
(3) where CT is the fluoride concentration in the titration half cell, C, is the concentration of the titrant solution, V, is the original volume of inert electrolyte in the titration half cell, and Vuis the volume of titrant added. EXPERIMENTAL
where AE is a bias potential between the two fluoride activity electrodes caused by differences in the inner reference solutions, (F-)A and (F-)T are the activities of fluoride in the analate and titrant half cells, respectively, and Ej is the liquid junction potential. By the use of an excess of inert electrolyte (0.1M KN03) throughout, the liquid junction potential between half cells becomes negligible, and the activity coefficients of fluoride will be practically equal because of the constant ionic strength maintained in the two half cells. Equation 1 thus simplifies to
E=AE--
RTIn 10
F
CA log CT
where the cell emf, corrected for the bias potential, is solely dependent on the ratio of fluoride concentrations in the analate and titration half cells (Ca and C T )when both half cells are at the same temperature. Therefore at the null point, where the cell emf is equal to zero, C A = C T . 932
ANALYTICAL CHEMISTRY
The complete concentration cell is illustrated in Figure 1. The 10-p1 sample microcell portion of the diagram is enlarged in Figure 2 to show details of the assembly. This microcell comprises the analate half cell. It consists of a fluoride activity electrode which has been modified ( I ) to operate in an inverted position by conversion of the inner reference solution (0.1M NaF, 0.1M KCl) to a ge1-4z agar. The fluoride-specific membrane itself can then serve as the sample container for the analysis of 25-75 pl of sample solution by surrounding it with a Tygon tubing sleeve. By inserting a polyethylene ring, as shown in Figure 2, the sample requirement is further reduced to as little as 10 pl. An inner polyethylene cap serves to hold the ring tightly in place while a second cap reduces sample evaporation. A thin film of silicone lubricant between the polyethylene ring and the LaF3 membrane prevents entrapment and cross contamination of sample solutions. Because the LaF3membrane in the more recently produced fluoride activity electrodes is set flush with the body of the electrode tube, enclosing the membrane with a sleeve of Tygon tubing is no longer feasible, but the same purpose can be achieved in other ways, such as encircling the membrane with an epoxy dike to confine the sample to the desired area of the LaF,. The modifica-
tion of the inner reference solution by conversion to a gel is still applicable to the newer types of electrodes. A 0.1M K N 0 3 salt bridge connects the analate and titration half cells. The salt-bridge junction to the microcell is made from a polyethylene tube drawn out to a fine capillary and filled with a 4z agar gel of 0.1M KN03. The junction to the titration half cell is made through a porous Vycor plug (3). The titration half cell consists of a 180-ml tall form beaker in which are inserted a second fluoride activity electrode (unmodified), a stirrer, and a polyethylene capillary tube from the microburet. The microburet, readable to 0.01 ml, contains the standard fluoride titrant solution. The titrant is prepared containing the 0.1M K N 0 3 inert electrolyte background to prevent ionic strength changes when it is added to the titration half cell. The cell emf may be conveniently measured by connecting the electrode leads to an expanded scale pH meter (100 mV full scale) which serves as a voltage follower amplifier for a multirange potentiometric record, The cell emf can also be read directly from the pH meter with only slightly reduced precision, but the recorder facilitates continuous observation of the emf equilibration and stability. The microelectrode lead is connected to the glass electrode input jack of the pH meter while the second fluoride electrode connects to the unshielded reference electrode input. The pickup of electrical noise at this electrode does not constitute a serious problem in the emf measurement because of the relatively low resistance of the fluoride electrode (approximately 500k 52). The emf is read from the recorder to the nearest 0.1 mV. Because the ratio of solution volumes in the titration (100 ml) and analate (10 pl) half cells is 10,000 : 1, the number of equivalents of fluoride added to the titration half cell must be lo4 times greater than the amount present in the microcell to achieve the same concentration. This amplification factor permits the determination of amounts of analate too small to be otherwise added with any degree of accuracy or precision. In Table I, the titrant solution concentration and the volume added at the equivalence point are given for the various fluoride concentrations used in this study. Obviously, if an equivolume (10 p l ) null-point titration at these low concentrations were to be attempted, the titrant solutions would have to be prohibitively dilute (and therefore of doubtful titer) and/or accurately added in nano- or microliter quantities. Using such an amplification factor which may be varied to achieve optimum conditions, it is possible to work with convenient volumes and concentrations of the titrant. In addition to evaluating the equivalence point graphically, data analysis is easily accomplished by computer techniques whereby the equivalence point is obtained from the intercept of a linear least squares fit of the data. By this technique, the computer is programmed t o take the logarithm of the Xvalue (Cr) before fitting the data and to print the antilogarithm of the X-intercept (equivalence point concentration, CT = CA)where the cell emf (or Y-value) is zero. The computer readout also provides the slope of the best straight line through the titration data points for comparison with the theoretical Nernstian slope. The results reported below are obtained in this way after an initial graphical inspection to determine any obvious anomalies in the titration data. Prior to the addition of titrant to the titration half cell, the cell potential is indeterminate and off scale in the negative direction (cf. Equation 2). As titrant is added, Cr in Equation 2 increases, causing the negative cell potential to decrease-Le., become more positive. The emf measurements are started when the cell potential decreases to about -30 mV and taken at arbitrary increments of the titrant solution thereafter, depending on the particular concentration range and the reliability of the linear fit desired. The titrant ad(3) R. A. Durst, J. Chem. Educ., 43, 437 (1966).
Table I. Standard Fluoride Solutions Used and the Equivalence Point Volumes Titrant conc, M ( V d e.p., ml Analate conc, M 1.00 x 10-3 1.00 x 10-1 1.01 1.00 x 10-4 1.00 x 10-2 1.01 1.00 x lo-* 1.01 1.00 x 10-5 5.0 x 1.00 x 10-3 0.503 2 . 0 0 x 10-4 1.01 2 . 0 x 10-6
dition is carried past the null point into the positive potential region-Le., where CT> CA,and as far beyond as required. A titration value at the equivalence point itself is unnecessary. The data are then graphed semilogarithmically, as shown in Figure 3, to obtain a linear plot of the titration cell concentration (C,) with respect to the cell potential. The equivalence point can then be evaluated by a linear interpolation to the null-point potential as indicated in Figure 3. The limits in the figure indicate the scatter (standard deviation) of the values from the five runs, the runs producing five essentially parallel lines. However, as discussed above, the data analysis can be more accurately accomplished by computer techniques insofar as the linear fit of a set of data and significance of the equivalence-point value are concerned. All chemicals used in this study were reagent grade and used without further purification. The sodium fluoride test solutions and titrant solutions were prepared by a serial dilution with 0.1MKN03 of a standard 0.100MNaF (in O.lMKN0,) solution. Distilled water was used throughout, and all titrations were made at room temperature (controlled at 25" i 0.1" C) in undeaerated solutions. In addition to controlling the ambient temperature to 0.1 O, the concentration cell assembly was completely insulated with 1-2 inches of polyurethane foam to further moderate the temperature fluctuations.
RESULTS Standard 10 p1 sample solutions containing 0.3 to 190 nanograms of fluoride in 0.1M K N 0 3 were analyzed. The results of these determinations are illustrated in Figure 3 and tabulated in Table I1 for five measurements at each concentration level. At the lowest concentrations, the initial titration points exhibit a deviation from linearity caused by the slight dissolution of the lanthanum fluoride membrane not having reached equilibrium. This effect is predictable from the solubility product of LaF3and becomes a significant factor because of the extremely small volume of solution employed. However, this effect does not significantly affect the final results, as verified by the very small error observed, because the emf value used as the null point includes the same dissolution factor. That is, the null-point potential is obtained from measurements on identical half cell solutions over the entire concentration range studied. Because the measurements of these potentials are allowed to reach equilibrium, the concentration of fluoride in the microcell increases caused by the dissolution of LaF3 until the K s pis satisfied-while this effect is negligible in the 100-ml titration half cell. The response of these two electrodes therefore only differs at very low concentrations as is illustrated in Figure 4, which shows the response of the two fluoride electrodes to fluoride concentration. It is seen that the response is almost identical down to a concentration of lO+M fluoride, but decreases more rapidly for the microelectrode at lower concentrations. The large overall potential difference between the two electrodes (approximately 116 mV) is caused by the difference between the inner reference systems-ie., the microelectrode VOL. 40, NO. 6, MAY 1968
933
*
300
contains a gel while the normal electrode contains an aqueous solution. The null-point potentials (with the 95 confidence limits, each based on 5 measurements) reported in Table I1 therefore reflect the constant 116 mV bias caused by the differences in the inner reference systems and a decreasing emf difference caused by LaFa dissolution in the microelectrode half cell. In Figure 3, the titration curves are normalized by plotting the observed minus the null-point potentials so that the null point occurs at an emf of zero for all cases. There is also a small negative drift in the cell potential during the titration caused by very slight evaporation of the test solution. The drift is constant and reproducible, amounting to approximately 0.02 mV/min. A correction of this amount is applied to the emf readings during the titration, which is completed in about 15 to 35 minutes depending on the concentration. The less concentrated solutions require the longer titration times for the same number of data points because of the longer equilibration times required for a stable emf reading. The titration times could be easily reduced by a factor of two by taking only two points on either side of the equivalence point, instead of four, with some sacrifice in the reliability of the linear fit. The summary of results in Table 11 gives the quantity of fluoride present in the standard test samples, both in terms of concentration and in nanograms per 10 p1 sample, the con-
centration of fluoride found (average of 5 determinations) with the relative standard deviation of the mean, and the error expressed as a percentage and in nanograms. The error of the method is virtually constant at about 1 over the entire concentration range while the standard deviation of the mean as a per cent of the mean increases with decreasing concentration from 0 . 3 x to 1%. At the lowest fluoride concentration studied, 380 picograms of fluoride were determined with an error of only 2 picograms. This clearly ranks this technique as the most sensitive microanalytical method for the determination of fluoride. Below this concentration, however, it is expected that the precision of the technique will rapidly deteriorate because of the difficulty in establishing a meaningful null-point potential. Therefore, increased sensitivity of the method while still maintaining analytical precision, can only be achieved by further reduction in sample size. A tenfold increase in sensitivity should be obtainable by this procedure. The advantage of the nullpoint technique over direct emf measurements using a calibration curve is evident from a comparison of the precision obtained in this study with that found previously ( I ) . Although comparable at higher concentrations, the precision of the LIWP method below 10-5Mfluoride is approximately five to 50 times better-Le., the standard deviation of individual determinations are in the approximate ratio of 5:l to 50:l. To achieve this increased precision, some sacrifice in analysis time and instrumental complexity must be made. An interesting application of this technique has already been
x
Table 11. Results of the Fluoride Determinations by LNPP
Titration 1 2 3 4 5 a
Fluoride taken Conc, M ng 1.00 x 1.00 x 1.00 x 5.0 X 2.0 x
10-6 10-4 10-6
10-
190 19.0 1.90 0.95 0.38
Error F- Found, M 1.013 x lo-* 1.010x lo-' 1.014 x 10-5 4.96 x lo-' 2.01 x lo-'
Standard deviation of the mean as a per cent of the mean.
Re1 std devma 0.3% 0.5%
0.6% 0.6% 1 .O%
* Indicated uncertainties are the 95% confidence limits based on five measurements. 934
0
ANALYTICAL CHEMISTRY
% 1.3% 1 .O% 1.4% -0.8% 0.5%
ng
2.5 0.lg 0.027 0.008 0.002
116.3f 0.3 116.0 0.3 114.4 0.5 113.8 f 0.4 111.5 f 0.6
suggested by scientists at the Woods Hole Oceanographic Institution (4). This application concerns the determination of fluoride in the interstitial water squeezed from deep-sea sediment cores. In these cases, the amount of sample generally available is less than 0.5 ml-a volume sufficient for about 50 replicate LNPP determinations. The addition of inert electrolyte would be unnecessary to maintain a constant ionic strength for the normal constituents of sea water would serve this purpose while introducing no interferences in the fluoride determination. Also, because this technique is nondestructive of the sample solution-Le., the sample only serves as a
reference solution and is not modified or chemically reacted during the determination-it can be reused in subsequent studies. RECEIVED for review January 2 1968. Accepted February 8, 1968. Third Middle Atlantic ACS Meeting, February 1968. (4) D. W. Spencer, Woods Hole Oceanographic Institution, private communication, 1967.
Further Study of the Lanthanum Fluoride Membrane Electrode for Potentiometric Determination and Titration of Fluoride James J. Lingane Department of Chemistry, Haruard University, Cambridge, Mass. 02138 I n the presence of 60 vol % ethanol the Orion fluoride electrode obeys the expected theoretical relation up to about the same pF value as in aqueous medium. I n aqueous acid medium the upper pF limit of theoretical response-ca. 6.7-is significantly greater than in neutral media-ca. 5.7. In all media, stirring has noeffect below about pF = 4.5 but at larger pF values it extends the limit of theoretical response by minimizing the accumulation of fluoride ion at the surface of the lanthanum fluoride membrane because of its solubility. At an ionic strength of 0.03M in aqueous medium at 25" C, the solubility product of lanthanum fluoride is 1.2 X 10-l8and that of europic fluoride is 2.2 X lo-''.
IN A PREVIOUS COMMUNICATION ( I ) the lanthanum fluoride membrane electrode invented by Frant and Ross (2), which is commercially available from Orion Research Inc., 11 Blackstone Street, Cambridge, Mass. 02139, was employed to study the titration curves of fluoride ion with thorium, lanthanum, and calcium ions, and to define the optimum conditions of these titrations. In the present study additional information has been obtained about the behavior of the Orion electrode in alcoholic and acidic media, and the effect of stirring. The solubility products of lanthanum and europic fluorides, which heretofore were unknown, have also been determined from data obtained in careful titrations of fluoride ion with lanthanum and europic ions. EXPERIMENTAL
Standard solutions of lanthanum nitrate were prepared as previously described ( I ) from pure Laz03. The starting material for the preparation of standard europium solutions was Eu203from K and K Laboratories, Plainview, N. Y.,which was stated to be 99.8% pure with respect to europium (the rarest of the rare earths). When ignited in a platinum crucible at about 1000" C, the loss in weight (presumably water and CO,) was 2.25%. Weighed samples (corrected for ignition loss) were dissolved in excess (1) J. J. Lingane, ANAL.CHEM., 39,881 (1967). (2) M. S. Frant and J. W. Ross, Jr., Science, 154, 1553 (1966).
hydrochloric acid in a fused silica beaker, and were then evaporated to dryness on the steam bath to remove the excess acid, The residual EuC13 was dissolved in water and diluted to a known volume. A 0.03724M solution prepared in this way had a pH of 4.7. Evaporation of europic chloride or nitrate solutions to remove excess acid must not be performed above 100" C, because at higher temperatures hydrolytic decomposition of the salts occurs. Sodium fluoride, purified as previously described ( I ) , served as the source of known amounts of fluoride ion. The potential of the Orion fluoride electrode in the test solution was measured with respect to a saturated calomel electrode. Some of the measurements (to + 1 mV) were made with a Beckman Model GS pH meter. To obtain a precision of 1 0 . 1 mV, other measurements were made with a Keithley Electrometer, whose unity gain output was observed with a precision potentiometer. T o avoid the possible reaction of fluoride ion with glass, a fused silica beaker was used as the titration vessel. The initial volume of solution titrated was usually 100 + l cc. Magnetic stirring [Teflon (DuPont) coated stirring bar] was employed. For measurements at 25.00" C (water thermostat) the submersible magnetic stirring unit of Henry Troemner Inc., Philadelphia, Pa., served very satisfactorily. BEHAVIOR OF THE ORION FLUORIDE ELECTRODE IN ALCOHOLIC AND ACIDIC MEQIA
It was found in the previous study ( I ) that lanthanum ion is the best of the titrant metal ions studied to date for the titration of fluoride, and the optimum pH condition is a neutral, unbuffered solution. As demonstrated in Figure 1, the titration curve is further improved very considerably by the addition of 60 to 70 vol ethanol, for this decreases the solubility of the LaF, and enhances the rate of potential change at the equivalence point. Therefore, it was of interest to study the response characteristics of the Orion fluoride electrode in the presence of ethanol. In Figure 2 calibration curves in the presence of 60 vol ethanol are compared with the calibration curve in purely aqueous medium. The pF values are in terms of concentration rather than activity of fluoride, because data were not VOL 40, NO. 6, M A Y
1968
935
