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
-
Itoo
1
NaF
+ NoN03 a i constant
ionic strengih
200 mg NaF In 100 cc
t
47
x
’ */
,Ic
t t
__
/-
I
ol/+? I - 200 I I
/-
I’I
I
I I - 100
I
I
MILLIVOLTS
0.04738E Lo(NO,),
,c c
In both cases 200.0 mg of NaF in an original volume of 100 cc was titrated
available for the activity coefficients of sodium fluoride in ethanol-water mixtures. In each case the solutions were composed of a mixture of sodium fluoride and sodium nitrate at a constant ionic strength of 0.100M for curves I and 2, and 0.0100M for curve 3. The straight lines were drawn with the theoretical slope of 59.15 mV per pF unit corresponding to the relation = E
+ 59.15 pF
(1)
Equation 1 is obeyed as well in 60 vol % ethanol as in water, but the constant E is about 100 mV more negative. A minor factor contributing to this shift of E is that the activity coefficient of fluoride ion is smaller in 60% ethanol than in water, which is not taken into account when pF values are expressed in terms of concentration. A second small factor is that the liquid-junction potential between the aqueous saturated calomel electrode and the test solution is different in the presence of ethanol. However, the major factor probably is the development of an asymmetry potential across the lanthanum fluoride membrane of the electrode because of the different solvents on either side of it. The data in Figure 2 also demonstrate that Equation 1 is obeyed up to a larger value of pF (smaller fluoride ion concentration) when the solution is well stirred than when it is quiet. The open circle points were measured with the solution quiet, and the solid circle points (curve 2) were obtained when the solution was stirred moderately rapidly with a magnetic stirrer. Referring to curve 2, failure of Equation 1 begins at pF = 4.9 when the solution is quiet, but not until pF = 5.5 when the solution is stirred. At pF values below about 5 stirring has no effect on the observed potential. This beneficial effect of stirring is also observed in aqueous media, and it is consonant with the explanation advanced by Frant and Ross (2) that failure of the electrode ultimately occurs when the concentration of fluoride ion contributed by the solubility of the lanthanum fluoride membrane becomes appreciable compared to the concentration originally present. Stirring prevents the accumulation of fluoride ion at the surface of the membrane due to its solubility. This effect of stirring is pertinent to data recently reported 936
ANALYTICAL CHEMISTRY
I 0
I
I
I
I
I I 100
I
I
lo
I 200
Figure 2. Calibration data in aqueous and alcoholic media at 25’ C
Figure 1. Influence of ethanol on the titration curve of fluoride ion with lanthanum ion in neutral, unbuffered medium
E
I
+
I Aqueous solution at constant ionic strength (NaF NaNOa) of 0.1OOM. 2 In 60vol % ethanol at constant ionic strength of 0.1OOM. 3 In 60 vol % ethanol at constant ionic strength of 0.OlOOM. The open circle points for lines I and 2 were obtained with a quiet, unstirred solution. The solid circle points of curve 2 and all the points of curve 3 were obtained with the solution efficiently stirred. In all cases the straight lines were drawn with the theoretical slope of 59.15 mV/pF
by Durst and Taylor (3). These authors very ingeniously adapted the Orion fluoride electrode to measurement with only 0.05 cc of the fluoride test solution by replacing the internal solution with an agar gel, inverting the electrode, fitting a ring cut fromplastic tubing over the protuberant lanthanum fluoride disk to retain the solution, and dipping the tip of a saturated calomel reference electrode into the very small volume of the solution to complete the cell. Under these conditions of a very small volume of a quiet solution it is understandable that Durst and Taylor observed failure of Equation 1 at a smaller pF value (about 4.5) than under the more usual conditions of a much larger volume of a well stirred solution. Because the solubility of precipitated LaF, (and presumably also that of the single crystal lanthanum fluoride membrane) is decreased in the presence of ethanol, one would expect that Equation 1 would be obeyed up to a larger pF value in the presence of ethanol than in an aqueous medium. At first glance the data shown in Figure 2 do not seem to support this expectation, but the contradiction is apparent rather than real. The electrode responds to the thermodynamic activity rather than molar concentration (and still less to formal concentration) of fluoride ion at its surface. Specific data for the activity coefficient of fluoride ion in sodium fluoride solutions in 6 0 x ethanol are not available, but, judging from the data for other alkali metal halides (4,it must be less than one half the value in water at an ionic strength of 0.1M. Consequently the concentration pF values of curve 2 are at least 0.3 unit smaller than the actual activity pF values. This conclusion is supported by the fact that when the ionic strength in 60z ethanol is decreased to 0.01M (line 3 in Figure 2) the observed potentials at a given concentration pF are about 15 mV more negative than at an ionic strength of O.lM, corresponding to a nearly twofold increase in the activity coefficient. Also at this much smaller ionic strength Equation 1 is obeyed up to a considerably larger value of the concentration pF-ca. 5.9. Even though the solution is stirred efficiently a thin im(3) R. A. Durst and J. K. Taylor, ANAL.CHEM., 39,1483 (1967). (4) R. Parsons, “Handbook of Electrochemical Constants,” Butterworths, London, 1959.
L I
4
L/ I
Table I. Titration Data and Solubility Product of Lanthanum Fluoride in Aqueous Medium
o In 0.100 M NaN03 e In 0.100
M HCI
100 cc of 0.03095M NaF titrated at 25.00' C. Theoretical equivalence point is at 31.10 cc 0.03318M La(NO& (Laa+)(F-)3 cc E mV (F-) M (La3+)M X 10'8
With stirring in both coses.
I 50
I 100
I 150 MILLIVOLTS
I
200
250
Figure 3. Calibration data in acidic (0.100M HCI) and neutral (0.100M NaN0,) media, with efficient stirring mobile layer of solution persists at the surface of the lanthanum fluoride membrane, and transfer of fluoride ion across this layer proceeds only by diffusion. From polarographic experience it is well known that ionic diffusion coefficients in 60% ethanol are as much as a factor of two smaller than in water. Consequently, the accumulation of fluoride ion at the surface of the membrane due to its solubility is relatively greater in the presence of ethanol. In Figure 3 calibration data for the Orion electrode in neutral and acidic aqueous media are compared. In both cases the ionic strength was kept constant at 0.100M with sodium nitrate and hydrochloric acid, respectively, and the fluoride was added as sodium fluoride. The p F values are in terms of the actual activity of fluoride ion, computed by using the value 0.77 for the activity coefficients of all the singly charged ions in both media. I n the 0.100M hydrochloric acid solution most of the added fluoride is, of course, converted to HF. The activity of free fluoride ion was computed via the dissociation constant of HF (6.71 X using 0.77 as the activity coefficient of fluoride and hydrogen ions, and assuming that the activity coefficient of undissociated HF is unity. Note that the constant e in Equation 1 is the same in both neutral and acid medium, which simply reflects the very effective elimination of a liquid-junction potential between the test solution and reference electrode (SCE) by the saturated potassium chloride solution in the salt bridge. The important fact, however, is that, in spite of the enhanced solubility of the lanthanum fluoride membrane in the acid medium, Equation 1 is obeyed up to a considerably larger p F value (ca. 6.7) than in neutral medium (5.7). The most likely explanation is that most of the fluoride contributed by the solubility of the lanthanum fluoride membrane is converted to HF, leaving a contribution of free fluoride ion which is much smaller than in neutral medium. Furthermore, in acid medium, the concentration of lanthanum ion produced at the surface of the membrane must be larger than in a neutral solution, and this acts to further suppress the concentration of free fluoride ion. SOLUBILITY PRODUCT OF LANTHANUM FLUORIDE
The solubility product of lanthanum fluoride in aqueous medium was evaluated from data obtained in careful titrations of neutral, unbuffered solutions of sodium fluoride. Typical
0 29.00 30.00 30.30 30.60 30.90 31.20 31.50 32.50 36.00 41 .OO 50.00
-104.6
0.03095
- 24.9
-
+
4.7 4.1 17.9 41 .O 65.6 76.9 88.8 100.7 106.9 111.8
3.98 X 2.56 X 1.62 X 1.03 X 8.00 X 6.61 X
3.9 X 1.1 X 3.6 X 1.2 X
2.4 X 4.2 X
2.5 1.8 1.5 1.3
1.2 1.2
data obtained in the titration of 100 cc of an originally 0.03095M solution of sodium fluoride at 25 O C are shown in Table I. The solution was stirred continuously, and at each point care was taken to wait until the potential became constant (drift less than 0.05 mV/min) before adding the next increment of the lanthanum nitrate solution. Constant potential was obtained within about 3 minutes prior to the equivalence point, but 5 to 10 minutes was required at and beyond the equivalence point. The potential observed with the original solution served to calibrate the electrode (Le., to evaluate e in Equation 1)) and the fluoride ion concentrations at other points in the titration were then calculated via Equation 1 from the observed potentials. Prior to the equivalence point the fluoride ion concentration decreases in direct proportion to the volume of lanthanum nitrate solution added, which means that soluble anionic lanthanum fluoride complexes are not formed. This also is evident from the fact that the quantity of precipitate increases continuously from the start of the titration up to the equivalence point for LaF3. The concentrations of lanthanum ion beyond the equivalence point were calculated from the excess volume of lanthanum nitrate solution added, and the total volume of the solution, assuming that cationic complexes (LaFzf and LaF2+)are not formed. The smooth course of the potential change beyond the equivalence point, with no evident additional inflections, supports this assumption. Correction was applied for the lanthanum ion contributed by the solubility of the lanthanum fluoride (equal to one third the observed fluoride ion concentration at each point), but this correction becomes negligible beyond 2 % excess lanthanum nitrate solution. Notice that the data extend over a large range of excess lanthanum nitrate solution from only 0.3 to 61 beyond the equivalence point for LaF,. In view of the fourth power concentration dependence, the values of the solubility product of LaF, shown in the last column of Table I are remarkably constant over this very large range of excess concentration of lanthanum ion. To be sure, there does seem to be a downward trend from 2.5 X lo-'* to 1.2 x 10-18, but, as equilibrium constants go, this is not very large. Because the first point is only 0.10 cc, or 0.3 %, beyond the equivalence point a cumulative error of only 0.15% in the quantity of fluoride taken and the concentration of the lanVOL 40, NO. 6, MAY 1 9 6 8
937
thanum nitrate titrant solution would account for the apparent trend. In another trial in which a 0.01190M solution of sodium fluoride was titrated, the average observed solubility product was 1.2 X in agreement with the data in Table I, and it was constant to 1 0 . 1 X 10-’8 over a range of excess lanthanum nitrate from 7 % to 260z. From activity coefficient data ( 4 , 5 ) , the activity solubility product of LaF3 should be very nearly five times smaller than the concentration solubility product (1.2 x 10-’8) at the ionic strength at which the data in Table I were obtained, and thus is close to 3 x The lanthanum nitrate titrant solution was slightly acidic (pH = 3.90) because of incomplete removal of nitric acid during its preparation. At the end of the titration of Table I, the pH was 4.05, and, because the pK of hydrofluoric acid is 3.17, about 13% of the fluoride must have been present as HF. However, because the actual extant fluoride ion concentrations were measured,this does not cause any significant error in evaluating the solubility product. The only error involved is in the correction for the concentration of lanthanum ion contributed by the solubility of the LaF3 (which actually is 13% greater than one third the observed fluoride ion concentration), but this entire correction becomes negligible about 2% beyond the equivalence point. When only 0.05 cc of solution is in contact with the lanthanum fluoride membrane of the Orion electrode, so that equilibrium with respect to the solubility of the membrane is at least approximately attained, the data reported by Durst and Taylor (3) demonstrate that deviation from Equation 1 begins in the neighborhood of pF = 4.5. From the solubility product 1.2 x 10-18, the pF value in a saturated solution of LaF3 in pure water should be 4.36. In other words, the solubility of the single crystal lanthanum fluoride membrane appears to be nearly (and perhaps exactly) the same as that of freshly precipitated LaF3. Beyond the equivalence point in titrations of fluoride with lanthanum, the solution becomes much less opaque-Le., tends to “clear up,’’ This could be caused by actual dissolution of the precipitate uia the reactions
+ La3+ = 3 LaF2+ LaF2+ + La3+ = 2 LaF2+
2 LaF3(S)
(2)
(3)
Another possibility is that in the presence of excess lanthanum ion, the precipitate is converted to a more colloidal form (peptization resulting from adsorption of lanthanum ion), so that the solution appears to become less opaque. The writer inclines to the latter interpretation, because if reactions 2 and 3 did occur to any significant extent it seems very unlikely that values of the apparent solubility product as constant as those in Table I over such a large range of excess lanthanum ion concentration would result. Referring to Table I, the maximal rate of potential change, AEJAV, occurs at 30.93 cc, and thus nearly 0.6% before the true equivalence point, This is as expected for such an asymmetrical titration reaction. In practice, one should either titrate to the true equivalence point potential, or, and this is the most practical, use the point of maximal slope as an arbitrary end point but standardize the lanthanum nitrate titrant solution against a known quantity of fluoride. Although it is evident that the solubility of LaF3is decreased in the presence of ethanol (see Figure I), the solubility product ( 5 ) J. Kielland, J. Am. Chem. SOC.,59, 1675 (1937).
938
e
ANALYTICAL CHEMISTRY
ifl
I
I
I
4I
u = -
,Or
I
1 ,
I
I I
I
I
I I
I
I
I
11.4nig F - i n IVV Inn-- Irk Neutrol , Unbuffered
I
’I I
I
in alcoholic medium cannot be evaluated readily from titration data because the response of the electrode deviates from linearity too soon beyond the equivalence point. However, from the observed p F at the equivalence point (4.98) in the presence of 70 vol ethanol, the solubility product is approximately 4 x Consequently the molar solubility itself is about one fourth the value in aqueous medium. TITRATION OF FLUORIDE WITH EUROPIC ION
Because the lanthanum fluoride membrane is doped with a small amount of europium, the titration of fluoride with europic ion is of special interest. Frant and Ross ( 2 ) state that the europium is added in the + 2 oxidation state, presumably to obtain a nonstoichiometric crystal to favor transfer of fluoride ion through it. However, europium in the + 2 oxidation state is so strongly reducing and so easily air oxidized that, quite aside from the question of how much of it survives during the preparation of the single crystal membrane, it seems likely that whatever the role of europium may be within the crystal, it must play its role in the + 3 state at the surface of the membrane which is exposed to dissolved oxygen. Fortified by this prejudice the titration of fluoride was studied with +3 europium. A typical titration curve in neutral, unbuffered aqueous solution (5.00 cc of 0.1200M NaF diluted to 100 cc) is shown in Figure 4. Prior to the EuF3 equivalence point, the concentration of fluoride ion decreases in direct proportion to the quantity of EuF3 precipitated-Le., there is no indication of the formation of anionic complexes. The smooth course of the potential change after the equivalence point also shows that the cationic species EuF2+and EuF2+are not formed. That the sole reaction during the titration is simply precipitation of EuF3 is demonstrated conclusively by the fact that the value of the solubility product of EuFBcalculated from data just slightly beyond to very far beyond the equivalence point remains constant. Typical data obtained in the titration at 25.00’ of 100 cc of a 0.03000Maqueous solution of pure sodium fluoride are shown in Table 11. The solution was stirred continuously, and at each point care was taken to wait until the potential became
constant before adding the next increment of europic chloride solution. Prior to the equivalence point, the potential became constant (drift not greater than 0.2 mV/S min) almost immediately. During this stage the precipitate was so translucent that the solution was only slightly turbid. Very close to the equivalence point, the precipitate transformed, rather suddenly, to a much more opaque, “white” form, and this change was accompanied by an increase in potential,-decrease of fluoride ion activity. When the 0.30 cc increment of EuC13 solution was added to reach the 26.80 cc point in Table 11, which is the theoretical equivalence point, the potential increased immediately from its previous value of 3.2 mV to 16 mV and remained there for about 4 min, the precipitate being still translucent, But, with the solution continuously stirred, the potential suddenly began to increase quite rapidly (while the solution rapidly became opaque) and finally it became constant at 44.3 mV after 20 minutes. Apparently the freshly precipitated EuF3is highly hydrated, and, prior to the equivalence point, it is kept in a nearly colloidal condition by the adsorption of fluoride ion. The translucent to opaque transformation close to the equivalence point probably results from the formation of a less hydrated form, and, as indicated by the concomitant increase in potential, this final stable form is considerably less soluble than the original precipitate. If one titrates so rapidly that insufficient time is allowed for this transformation to complete itself at the equivalence point, it occurs somewhat later. Consequently the maximal rate of potential change will occur somewhat after the true equivalence point, whereas under equilibrium conditions it actually occurs slightly in advance of the equivalence point because of the asymmetric character of the titration reaction. Under the near equilibrium conditions of Table 11, the maximal rate of potential change is at 26.65 cc, and thus 0.15 cc or 0 . 6 x before the true equivalence point, as expected. Referring to Table 11, the potential (-107.8 mV) observed with the original solution served to calibrate the electrode in terms of fluoride ion concentration, and the concentrations of fluoride ion beyond the equivalence point were calculated from the observed potentials. The concentrations of europic ion were calculated from the volume of excess europic chloride titrant solution added, with respect to the theoretical equivalence point volume of 26.80 cc, and with an additive correction for the europic ion contributed by the solubility of the precipitate (equal to one third the observed fluoride ion concentration). As shown by the last column in Table 11, combination of these concentrations leads to a value for the solubility product (Eu3+) (F-)3 of EuF3 (2.2 X 10-17) which is constant to * l o x over a very large range of excess concentration of europic ion. In view of the fourth power concentration dependence of this solubility product, this degree of constancy certainly is good, and it demonstrates the absence of the cationic species EuF2+ and EuFZ+. Note that this concentration solubility product of EuF3 is about ten times larger than that of LaF3 observed under the same conditions of ionic strength. Neither the quantity of + 2 europium used to dope the lanthanum fluoride membrane to create fluoride holes, nor whether or not this really is necessary, is public knowledge.
Table 11. Titration Data and Solubility Product of Europic Fluoride in Aqueous Medium 100 cc of 0.03000M NaF titrated at 25.00” C with continuous stirring. Theoretical equivalence point is at 26.80 cc 0.03724M EuClB (F-) (Eu *+) (Eu*+)(F)* cc E m V M X 10-6 M x io+” 0 -107.8 0.0300 25.50’ - 22.2 26.20 - 6.6 26.50 3.2 26.80 44.3 27.10 52.6 5.75 1.07 X 1 0 - 4 2.0 27.40 57.1 4.78 1.92 X lO-‘ 2.1 28.60 66.0 3.55 5.32 X lO-‘ 2.4 32.00 74.8 2.40 1.47 X 1 0 - 8 2.0 40.00 81.8 1.91 3.51 X 2.5 2.4 50.00 85.7 1.62 5.75 X Av 2 . 2 5 0 . 2
+
Because the solubility of EuF3 is somewhat greater than that of LaF3 the addition of large quantities of europium would seem to be undesirable because it should decrease the upper limit of pF to which the membrane would respond according to Equation l . Presumably, therefore, only a very small quantity of europium is used. In view of the fact that membranes of other pure, undoped substances (silver halides and barium sulfate) respond correctly to the corresponding activity of their anions, one is inclined to wonder if doping of the lanthanum fluoride membrane with + 2 europium really is necessary. RECEIVED for review January 19, 1968. Accepted February 28,1968.
Correction Direct Determination of Fluoride in Tungsten Using the Fluoride Ion Activity Electrode In this article by Bruce A. Raby and William E. Sunderland [ANAL.CHEM.,39, 1304 (1967)l information regarding the equilibration time found for the p F electrode was not included. Therefore, the following comment should be considered an addendum or correction to the original manuscript. “The electrode which we used for our studies was one of the early Orion Model 94-09 p F electrodes with the white plastic body. This electrode had an interstice between the sensing crystal and the body of the electrode. Slow diffusion of the test solution into the interstice was responsible for the slow rate at which the system came to equilibrium. It should be noted that Orion’s new model p F electrode has its crystal cemented into the body to eliminate the interstice. Consequently, equilibrium is attained in less than 1-3 minutes at a 10-6M fluoride concentration. The response is more rapid at higher concentrations.”
VOL 40, NO. 6, MAY 1968
939
