Activity Measurements with a Fluoride-Selective Membrane Electrode K. Srinivasan and G . A. Rechnitz Departrnenl of Chemistry, State University of New York, Buffalo, N . Y . 14214
The nature of the fluoride species present in acidic solutions has been elucidated by means of the fluorideselective membrane electrode. Results obtained by direct measurement of free fluoride ion concentration can be fully explained in terms of the species F-, HF, and HFP-and do not require postulation of polynuclear complexes. The electrode is shown to respond to Factivity in highly acidic media.
A NEW FLUORIDE-SELECTIVE membrane electrode, as developed by Frant and Ross (1)) consists of a single crystal of doped lanthanum fluoride cemented into a plastic tube containing an internal reference solution. A detailed description of the electrode and a statement of the theoretical basis of its operation has been given by Lingane (2) who also employed it for the detection of the end point in titrations of fluoride with thorium, lanthanum, and calcium. The electrode has proved to be a convenient sensor for the rapid determination of fluoride activity and has been employed for the direct determination of fluoride in tungsten (3). Frant and Ross ( 1 ) noted the decrease in fluoride activity measured by the electrode in the acidic region (pH 4 to 5) and attributed this effect to formation of H F , which is not sensed by the electrode. The present work was undertaken to study, in detail, the behavior of the fluoride electrode in acidic solutions and to gain a clear understanding of its performance in terms of the complex fluoride species existing in such solutions. The nature of complex fluoride species present in acidic solutions has been previously investigated by indirect methods. Ciavatta (4) has summarized the findings of earlier authors and has concluded that his own results could be explained by the following equilibria existing in acidic solutions of fluoride:
+ F- S H F H F + FHF2H+
(1 )
Previously, however, Ciavatta and Liberti ( 5 ) had found it necessary to postulate an additional polynuclear species-Le., H+
+ 3HF
H(HF)a+
(3)
It has now become possible to measure directly the free fluoride concentration in equilibrium with complex species; thus, the use of the fluoride-selective membrane electrode would permit an unambiguous decision as to the nature of the species involved.
suitable dilution of the stock solutions, keeping the ionic strength constant at 1.OM by the addition of required volumes of 4M sodium nitrate solution. Solutions containing known amounts of total fluoride and total acid were prepared by mixing calculated volumes of the stock solutions of sodium fluoride, nitric acid, and sodium nitrate, always keeping the ionic strength constant at 1.OM. The solutions were transferred to polyethylene bottles immediately after preparation. A radiometer pH meter with the expanded scale was used for measuring the potential of the fluoride electrode us. a saturated calomel electrode connected to the solution by means of a saturated potassium chloride agar bridge prepared in polyethylene tubing. The solution measurements were made in a polyethylene beaker, therrnostated at 25" + 0.1" C. The potential readings were taken after about 15 minutes to ensure attainment of thermal equilibrium. Two different fluoride electrodes (both supplied by Orion Research, Inc.) were initially examined. Although both showed almost instantaneous response, there was a large difference in the E" readings of the two. The fresh electrode showed a cell emf which was 52 mV more negative than the one already in use, and this difference remained practically constant in all solutions, although the calibration curves for both the electrodes gave the same slope. The fresh electrode gave a millivolt reading of -61.5 mV in a quiet solution and of -55.5 mV in a stirred solution at a fluoride concentration of lO-3M; the instruction manual for the electrode predicts a value of +5.0 mV for this solution. The difference between the millivolt readings in the stirred and quiet solutions was found to be less at high concentrations of the fluoride (0.4 rnV in 0.1M solution of fluoride) and steadily increased with dilution (d difference of 6 mV in 0.001M solution of fluoride). However, in the presence of a high concentration of electrolyte such as 1M sodium nitrate, there was no difference between the millivolt readings in stirred and unstirred solutions as dilute as 5 X 10-SM F-. During this study the readings were taken while keeping the solution stirred at a low constant rate by means of a Teflon-coated magnetic stirring bar. The potentials were found to be quite stable, changing not more than 0.1 mV even after an hour. The reproducibility on the same day for two different solutions of the same concentration was within 0.1 mV. However, the electrode's potential tended to drift slightly over an extended period; thus, after a period of 2 weeks, the electrode gave a reading 3 mV more negative, and after a month, 7 mV more negative for the same solution. The slope of the calibration curve was found to be unchanged. Because the potential of the fluoride electrode is given by the equation
EXPERIMENTAL
Stock solutions of sodium fluoride were prepared by weighing the reagent grade salt after drying at 100' C for 24 hours. A series of standard solutions of fluoride was prepared by (1) M. S . Frant and J. W. Ross, Jr., Science, 154, 1553 (1966). (2) J. J. Lingane, ANAL.CHEM.,39, 881 (1967). (3) B. A. Raby and W. E. Sunderland, Ibid., 39, 1304 (1967). (4) L. Ciavatta, Arkio Kemi, 21, 129 (1963). (5) L. Ciavatta and A. Liberti, International Conference on Coordination Chemistry, London, 1959, pp. 133-4.
E
= E"
- gFl n [ F - ]
(4)
it is clear that the value of E" shows a drift over a period of time, In the present study, the fluoride concentrations were calculated on the basis of the potentials given by solutions of known fluoride concentrations measured on the same day, the concentrations of the standard solutions being so chosen as to give millivolt readings close to those given by the test solutions. Because the slope of the calibration curve was not found to change, the same slope was employed in calculaVOL. 40, NO. 3, MARCH 1968
509
Table I. Free Fluoride Concentration and Average Number of Fluoride Ions Bound per Hydrogen Ion at Different Total Fluoride and Acid Concentrations [F-IT
[H+lT
-Log [F-]
ii
0.0040 0.0040
0.1500 0.1162 0.1500 0.0581 0.1162 0.0291 0.1500 0.1500 0.0020 0.01 162 0.0010 0.1500 0.001162 0.1500 0.01162 0.05809
4.430 4.347 4.222 4.066 4.061 3.735 3.683 3.331 3.328 3.298 3.176 3.071 2.934 2.863 2.810 2.660 2.648 2.652 2.498 2.442 2.348 2.298 1.943 1.848 1.463 1.331 0.939 0.799 0.837
0.026 0.034 0.053 0.067 0.068 0.131 0.132 0.264 0.265 0.301 0.333 0.394 0.471 0.524 0.555 0.651 0.652 0.669 0,708 0.755 0.815 0.855 0.985 0.998 1.129 1.237 1.389 1.454 1.522
0.0080 0.0040
0.0080 0.0040
0.0200 0,0400 0.0010 0.0040
0.0010 0.0600 0.0080 0.0800 0.0080 0.0400 0.1Ooo 0.0100 0.0040
0.0080 0.0400 0.0100 0.0400
0.0200 0.1Ooo 0.2981 0.3974 0.4968 0.5347
0.1500
0.01162 0.001162 0.005809 0.04357 0.005809 0.02905 0.005809 0.0581 0.2033 0.2033 0.2324 0.2558
tions without obtaining the full calibration curve each day. Because the ionic strength of all solutions was kept constant at 1.OM, the millivolt readings could be directly converted to concentration values. RESULTS
Two typical calibration curves, obtained with the fluorideselective membrane electrode employed in the present study, are given in Figure 1. The calibration curve for higher concentrations of fluoride was obtained nearly 2 months after the first curve was prepared. It can be seen that both have the same theoretical slope as given by Equation 4, although the actual potentials are shifted to more negative values in the more recent curve. Table I gives the total fluoride concentration, the total acid concentration, the free fluoride concentration, and the average number of fluoride ions bound per hydrogen ion for each solution, The first two quantities were calculated from the concentrations of the stock solutions of sodium fluoride and nitric acid, while the free fluoride concentration was calculated employing Equation 4 and assuming that the fluoride electrode responds only to the free fluoride ion. As will be explained later, the data did not reveal any significant response of the electrode to the HFz- ion. Table I gives the calculated values of A, defined by Bjerrum (6) as the average number of fluoride ions bound to a hydrogen ion in any given solution-i.e.,
(6) J. Bjerrum, “Metal Ammine Formation in Aqueous Solution,” P. Haase and Son, Pub. Copenhagen, 1957.
510
ANALYTICAL CHEMISTRY
slope
-4
i ~
1
I
i
I -5
‘
-200
-150
-100
-50
0
t50
E, millivolts
Figure 1. Calibration curve of F - electrode Potential US. saturated calomel electrode Curve 2 constructed 2 months after curve 1
It can be seen from Table I that ii is essentially the same for any given free fluoride concentration and is independent of the total hydrogen ion concentration. This is demonstrated graphically in Figure 2 in which A is plotted against log [F-Ifree.T o draw the A(log[F-1) curve, the curve fitting method of Sillen (7) was used. The manner in which A increased with the free fluoride concentration suggested HFzas the highest complex. A can therefore be written as
where
and Pz =
4Kz
where
If we introduce, as Sillen (7)
(7) L. G . Sillen, Acta Chern. Scand., 10, 194 (1956).
is-
and
A could be written as
1.0.
ii
A family of theoretical curves satisfying Equation 13 was constructed with p 2 = 9, 10, 1 1 , 12, 13, and 14, and for each value of p2, the function y was calculated letting u take arbitrary values covering the values of [F-] used in the study. Each theoretical curve consisted of the function y plotted against log U. Each of these theoretical curves was on a graph on which the experimental ii values had been plotted against log [F-1. It was found that the theoretical curve with p2 = 1 1 best fitted the experimental points. Figure 2 shows the ii {log [F-] ] plot in which the experimental points are joined by the theoretical curve with p2 = 11. The fact that ii values over a wide range of acid concentrations, from 0.25M to 0.001M, fall on a single ii {log [F-] 1 curve can be taken as evidence for the absence of polynuclear species (8), containing more than one hydrogen ion, in the region of acid concentration studied. Thus, the species F-, HF and HFz- are prevalent in this region of F- and H+ concentrations. For the calculation of the stability constants of HF and HFz- the method of Bjerrum (6) was adopted. The values of [F-] at ii = 0.5 and ii = 1.5 were taken from the graph and approximate values of K1 and KZwere obtained (6, 9) via
0
A
KiK2 =
ii
Table 11. Formation Constants of H F and HFz- Calculated for Each Experimental Set of F-]and n Kl = -;[HFI
- (1 - ii)Ki[F-] (2 - ii)[F-]'
1
Ki
- 771.7 771.7
- Kz - 5.6241 5.624
for R
< 1,
(18)
Kz
[H+lIF-l
- ii)[F-]
[+
l.OM, 25" C)
(p =
The approximate value of KlK2is introduced into Equation 16 for each experimental set of ii and [F-] and the value of Kl is obtained. Because K1K2 is known, KZcan be calculated. To obtain the optimum values of K1 and KZ from each experimental set, the following equations were employed to arrive at the final value of KIKZby successive approximation KlK2fina1= KiKzproviaiorml
0
1
F-I
Figure 2. Bjerrum plot for F - plus H + system
- (2 - ii)K&[F-I2 (1
-2
-3
Log
The approximate values of Kl and Kz were found to be 771.7 and 5.624, respectively, giving KiK2 v 4340. Rearranging Equation 6 after introducing Kl and K2 in the place of pi and pz, we can write K1 =
-4
-5
=
WFz-I
WFIF-1
ii
[F-I
log KI
log Kz
0.131 0.132 0.264 0.265 0.301 0.333 0.394 0.471 0.524 0.555 0.651 0.652 0.669 0.708 0.755 0.815 0.855 0.985 0.998 1.129 1.237 1.389 1.454 1.522
0.0001842 0.0002075 0.0004666 0.0004700 0.0005035 0.0006670 0.0008491 0.001165 0.001371 0. 001548 0.002188 0.002249 0.002229 0.003176 0.003617 0.004488 0.005035 0.01140 0.01419 0.03443 0.04662 0.1151 0.1589 0.1455
2.91 2.86 2.88 2.88 2.93 2.87 2.88 2.87 2.89 2.89 2.91 2.90 2.94 2.85 2.89 2.93 2.97 2.93 2.89 2.88 2.88 2.88 2.91 2.89
0.72 0.77 0.75 0.75 0.71 0.77 0.76 0.76 0.74 0.74 0.73 0.74 0.70 0.79 0.75 0.70 0.81 0.87 0.80 0.76 0.88 0.76 0.73 0.89
Mean value 2.90 f 0.03 0.77 3=0.05
and K1KZiine.l = KiK2provisional
[
1 -
Ki
- 771.7 771.7
+
Kz
- 5.6241 5.624
fora (8) L. G. Sillen, Rec. Trau. Chim., 75, 705 (1956). (9) G. A. Carlson, I. P. McReynolds, and F. H. Verhoek, J . Am. Chem. Soc., 67, 1334 (1945).
> 1.
(19)
In the neighborhood of ii = 1 , Equation 17 is used to calculate KlKz by introducing the approximate value of C and improvVOL. 40, NO. 3, MARCH 1968
51 1
ing the value by successive approximation using Equation 18 or 19, The values of Kl and K2 calculated in this manner are given in Table 11. The mean values of Kl and K2 are found to be log Kl = 2.90 f 0.03 and log K2 = 0.77 i 0.05 a t the ionic strength of 1.OM. The marked consistency in the values of K 1 and K2 over a wide range of acidities can be taken as providing strong support to the understanding that the fluoride-selective membrane electrode senses selectively the free fluoride ions even in acidic solutions. Calculations were made to test whether the electrode did show any response at all t o the HF2- ion. In this connection, use was made of the equation
E
=
Eo
-E In { [F-1 + K[HFz-]), F
(20)
to calculate the selectivity constant, K , by successive approximations. The results did not show any improvement in the agreement among the values of K1 and K2. On the contrary, there was a greater divergence in the values of K2. I t is, therefore, concluded that the response of the fluoride electrode, if any, to the HF2- ion is negligible. RECEIVED for review October 19, 1967. Accepted December 6, 1967. The financial support of Grants NIH GM-14544 and NSF GP-6485 is gratefully acknowledged.
Catalytic Reactions at Tubular Electrodes L. N. Klattl and W. J. Blaedel Department of Chemistry, University of Wisconsin, Madison, Wis. 53706 Current-flow rate equations for the mass transferlimited catalytic regeneration of the reactant at a tubular electrode have been theoretically derived and experimentally verified. The dependence of the concentration profile upon axial distance, flow rate, and rate constant of the chemical reaction are shown graphically. This steady-state hydrodynamic electrochemical system may be used to study reactions with pseudofirst-order rate constants greater than 0.1 sec-’.
Two MAIN ADVANTAGES are associated with hydrodynamic electrochemical systems. First, the forced controlled convection greatly increases the rate of mass transfer, producing a proportionate increase in the current and in the sensitivity when applied to analytical measurements. Second, measurements in these systems may be made under time-independent steady-state conditions, as opposed to the transient, time-dependent measurements that are required of the more conventional techniques. The need for high speed electronics in the readout circuits is diminished. Also, the steady-state nature of the hydrodynamic systems eliminates the charging current, which often limits the sensitivity of the time-dependent techniques. Theoretical description of electrochemical systems applied to the study of chemical kinetics has employed time-dependent techniques almost exclusively. Kinetic studies in hydrodynamic systems have been rare, partly because of success of the time-dependent techniques, and perhaps difficulties associated with the mathematical treatment and experimental measurements in hydrodynamic systems. Galus and Adams (1) considered by means of the reaction layer concept (2, 3) an irreversible first-order chemical reaction succeeding a reversible charge transfer reaction occurring a t the rotating disk electrode. Levich ( 4 ) treated the preceding and catalytic 1 Present address, Chemistry Department, Southern Illinois University, Carbondale, Ill. 62901
(1) Z. Galus and R. N. Adams, J. Electroanal. Chem., 4,248 (1962). (2) K. Wiesner, 2.E/ekrrochem., 49, 164 (1943). (3) R. Brdicka and K. Wiesner, Collection Czech. Chem. Commun., 12, 138 (1947). (4) V. G. Levich, “Physicochemical Hydrodynamics,” PrenticeHall, Englewood Cliffs, N. J., 1962.
5 12
ANALYTICAL CHEMISTRY
chemical reactions a t the rotating disk, neglecting the convective terms in the mass transfer problem by assuming very large rates for the chemical reactions. Albery ( 5 ) and Albery and Bruckenstein (6-9) applied the rotating ring-disk electrode to an irreversible first-order succeeding chemical reaction. With the recently improved techniques for continuous measurements in flowing solutions, and with a n improved understanding of the convective mass transfer-charge transfer interaction, the advantages of making electrochemical kinetic studies in hydrodynamic systems are now more realizable. The following work gives a theoretical description and experimental confirmation of the catalytic mechanism occurring a t a tubular electrode. THEORY
Derivation of Equations. In the discussion that follows the process is considered as a reduction; however, the extension to an oxidation is obvious. The catalytic mechanism involves the heterogeneous reduction of an oxidized species 0 to a reduced species R , which in turn reacts homogeneously with a n electroinactive species Z , present in the bulk of the solution, regenerating substance 0. This mechanism may be depicted by Reactions 1 and 2.
In order to treat this mechanism occurring a t a tubular electrode of circular cross section, with radius p and length X,and with a laminar flow regime, the previously considered equations of convective mass transfer ( 4 , IO, 11) must be modified to accommodate the coupled chemical reaction. This modification involves the addition of kinetic terms expressing the
(5) W. J. Albery, Trans. Faraday SOC.,62, 1915 (1966). (6) W. J. Albery and S. Bruckenstein, Ibid., 62, 1920 (1966). (7) Ibid., p. 1932. ( 8 ) Ibid., p. 1938. (9) lbid., p. 1946. 38, 879 (1966). (10) W. J. Blaedel and L. N. Klatt, ANAL.CHEM., (11) L. N. Klatt and W. J. Blaedel, Ibid., 39, 1065 (1967).
