A Study of tlhe Lanthanum Fluoride Membrane Electrode for End Poinit Detection in Titrations of Fluoride with Thorium, Lanthanum, and Calcium J a m e s J. Lingane Department of Chemistry, Harvard University, Cambridge, Mass. 02138 The titration curves of fluoride ion with thorium, lanthanum, and calcium ions under various solution conditions have been defined by means of a commercially available lanthanum fluoride membrane electrode, which responds specifically to fluoride ion activity. The excellent reprodiucibility of this membrane electrode and the precise definition of the equivalence points which it provildes make possible the titration of fluoride with an accuracy hitherto unattainable with visual indicators.
UNTIL RECENTLY the only way of measuring fluoride ion activity has been indirectly by its effect on the redox potentials of metal ion couples, such as ceric-cerous or ferric-ferrous, via unequal complexation of the two conjugate oxidation states. No doubt this is why there is such a lack of specific information on the thermodynamic properties of fluorih salts and complex compounds, arid why the development of fluoride titrations has had to proceed highly empirically. The whole difficult field of the analytical chemistry of fluorine compounds has been reviewed masterfully by C. A. Horton ( I ) . However, very recently Frant and Ross (2) announced the invention of a single crystal lanthanum fluoride membrane electrode which is so specific that fluoride ion activity can be measured as easily as pH is measured with a glass electrode. This membrane electrode is available from Orion Research Inc., 11 Blackstone St., Cambridge, Mass. 02139, and the essential features of its construction are indicated in Figure 1. The fluoride-sensitive membrane is a single crystal of LaF3, doped with E r g , in the form of a disk about 1 cm in diameter and a few millimeters thick, cemented into the end of a polyvinyl chloride plastic tube. The internal solution typically is a mixture of 0.1M sodium fluoride and 0.1M sodium chloride, although other concentrations of chloride and fluoride ions may be employed to adjust the range of operating potential. The potential of the infernal silver-silver chloride electrode is fixed by the chloride ion activity, and the fluoride ion activity controls the potential of the inner surface of the LaF3 membrane. When the electrode is immersed in a fluoride solution an electrical potmtial difference is established across the membrane, and its magnitude depends on the ratio of fluoride ion activities in i.he inner and outer solutions. The potential of the electrode is measured against a reference electrode (usually a saturated calomel electrode), in a manner exactly analogous to the use of a glass electrode. Unlike the glass electrode, the fluoride membrane electrode requires no conditioning in water before use. The measured cell may be represented by Agl AgCl, C1- (O.l), F- (0.l)l LaF,/ test solnl SCE (1) C. A. Horton, “Treatise on Analytical Chemistry,” Part 11, Vol. 7, I. M. Kolthoff and P. J. Elving, eds., Interscience, New York, 1961, p. 207. (2) M. S. Frant and J. W. Ross,Jr., Science, 154, 1553 (1966).
and Frant and Ross found that its emf obeys a Nernst type relation of the form
This is the expected relation for the potential across a membrane that is permeable to only a single ionic species, and it indicates that the LaF3membrane is permeable only to fluoride ion. Since the activity of fluoride ion in the internal solution is constant, Equation 1 becomes
or at 25”
E
= e
+ 0.05915 pF
(3)
where p F is the negative logarithm of the fluoride ion activity in the test solution, and the constant e is the sum of the potentials at the silver-silver chloride electrode, the saturated calomel reference electrode, the liquid-junction potential between the test solution and the reference electrode, and the potential across the membrane when the fluoride ion activity in the test solution is unity. In practical use the electrode is calibrated-Le., e is evaluated-with known activities or concentrations of fluoride ion. Frant and Ross reported that Equations 2 and 3 are obeyed over a range of fluoride ion activity from 1M down to 10+M (pF from 0 to 6). When the fluoride ion activity is decreased below about 10-6M the potential tends to approach a constant value, presumably because the solubility of lanthanum fluoride from the membrane contributes more fluoride ion to the solution than that originally present. Except for the normal effect of ionic strength on the activity coefficient of fluoride ion, Frant and Ross reported that such common anions as chloride, nitrate, bicarbonate, and sulfate do not interfere. In the present study it was also found that neither phosphate (at pH = 6.4) nor acetate (at pH = 4.9) has any specific effect on the electrode behavior. According to Frant and Ross the only common interfering anion is hydroxide ion, but only when its concentration exceeds that of the fluoride. With 10-6M fluoride the pH must not be above about 8, but with 0.1Mfluoride it can be as high as 12. The resistance of the electrode is of the order of lo6ohms, so that a high input impedance potentiometer (such as a glass electrode pH meter) is required for the potential measurements. The electrode can be used at temperatures between - 5 and 100” C, but it should not be subjected to a sudden temperature change of more than 50” C since a greater thermal shock may damage the seal between the lanthanum fluoride membrane and the plastic body. In this study the Orion fluoride electrode has been used to reveal the course of the change of fluoride ion activity during its titration with thorium, lanthanum, and calcium ions VOL 39, NO. 8, JULY 1967
881
c
7. 6
PLASTIC TUBE 1.6-cm diam. 15-cm length
O.IM NaCl O.IM NaF
5 h
I
LL
G4 0
I
"
3
k 2
't LaF3 SINGLE CRYSTAL
I
MEMBRANE Figure 1. The Orion fluoride membrane electrode
0 Figure 2. Response of the Orion electrode to fluoride ion activity The potentials were measured against a saturated calomel reference electrode, at 25.00' C. The straight line was drawn with the theoretical slope (Equation 3) of 59.15 mv per pF unit
under various pH conditions in both aqueous and alcoholic media, and thus to define optimum conditions for the titrations. End point detection with this electrode is unambiguous and titrations can be performed with a precision and accuracy far better than are possible with visual indicators. EXPERIMENTAL TECHNIQUE
To avoid contact with glass, a polyethylene beaker was used as the titration cell, and magnetic stirrring was employed. The initial volume of the titrated solution was 75 to 100 cc, and the temperature was 24 + 1" C. A Beckman Model GS pH meter was used to measure the potential of the Orion fluoride electrode against a saturated calomel electrode. Stirring was stopped during the potential readings. The source of known amounts of fluoride was purified sodium fluoride, prepared from Merck reagent quality sodium fluoride. The salt was further purified by preparing a saturated solution in water at room temperature in a polyethylene container, filtering off the excess salt through paper in a platinum funnel, and reprecipitating by adding an equal volume of absolute ethanol. The precipitated salt was collected in a platinum Gooch crucible, washed with ethanol and finally with acetone, and then dried in an oven at 150" C. Standard solutions were prepared determinately, and they were stored in polyethylene bottles. The thorium nitrate was Fisher certified Th(N03)44H20 with stated impurities as follows: rare earths (as La) 0.1 %, insoluble matter 0.000 %, substances not precipitated by ammonia 0.07 %, chloride 0.002 %, sulfate 0.010 %, heavy metals (as Pb) 0.001 %, Fe 0.001 %, and Ti 0.01 %. When a 3.8325-gram sample was ignited in a platinum crucible at about 1000" C to constant weight, the residue of Tho2 weighed 1.7746 gram, corresponding to 46.303 % ThOa. This value is very close to the theoretical value 46.312% Tho2 rather than the tetrahydrate. Standard for Th(N03)4 5H20, solutions of this thorium nitrate were prepared determinately in pure water. A 0.02000M solution showed a pH of 2.74. The starting material for the preparation of lanthanum nitrate solutions was a very pure mixture of Lan03 Laa(Co&, which had been prepared in this laboratory by Behrens
+
882
ANALYTICAL CHEMISTRY
(3) in connection with her study of the atomic weight of lanthanum. It was converted completely to L a s 0 3 by ignition in a platinum crucible at a temperature somewhat above 1000" C. An exactly weighed amount of this L a 2 0 3 was dissolved in excess nitric acid in a fused silica beaker, the solution was evaporated to dryness on the steam bath to remove the excess nitric acid, and the residual lanthanum nitrate was then dissolved in pure water and diluted to volume in a calibrated volumetric flask. Standard solutions of calcium chloride were prepared from Mallinckrodt primary standard CaC03. After drying at 190" C, weighed samples of the salt were dissolved in excess hydrochloric acid (fused silica beaker), the solution was evaporated to dryness to remove the excess acid, and the residual calcium chloride was dissolved in water and diluted to a known volume.
RESULTS AND DISCUSSION The potential of the Orion fluoride electrode us. the saturated calomel electrode as a function of fluoride ion activity is demonstrated in Figure 2. These measurements were made at 25.00" C with solutions containing sodium nitrate and sodium fluoride at a constant ionic strength of 0.100M over a range of fluoride ion concentrations from 0.1 to lO-7M. The straight line has been drawn with the theoretical slope of 59.15 mv per pF unit. Within the precision of the potential measurements (=kl mv), Equation 3 is strictly obeyed up to p F = 6. The pF scale in Figure 2 is in terms of concentration rather than activity of fluoride ion, but since the activity coefficient of fluoride ion was kept constant by the constant ionic strength, it differs from the true pF scale only by a small additive constant. Since the activity coefficient of fluoride ion is 0.77 at an ionic strength of 0.1M , this constant amounts to 0.1 1 pF in this particular case. For the particular electrode used in this study the value of E in Equation 3 remained constant to i l mv for several (3) E. E. Behrens, Ph.D. thesis, Harvard University, 1931.
.
200-
0
2
4 6 8 1 0 1 2 1 4 0.02000 M Th(N03)4, cc
Figure 3. Titration curves of fluoride with thorium under various pH conditions In all cases 5.00 cc of 0.08000M NaF (7.60 mg of fluoride ion) was diluted to ail initial volume of 100 CC. (1) No additions-i.e., approximately neutral and unbuffered. (2) 10 cc of 0.100M HCl added, to produce an initial excess concentration of hydrogen ion of O.O06M, which increased to 0.01M at the equivalence point. (3) 10 cc of 1M sodium acetate-acetic acid buffer added, to produce a pH of 4.88
weeks. However, just as with the glass electrode, it is advisable to verify the constancy of E by frequent calibration. The electrode responds. rapidly to a change in fluoride ion activity, only a few seconds being required to attain the new potential. Hence, in titrations of fluoride the potential readings can be taken immediately after each addition of titrant. Although stirring of the solution did not seem to have much effect on the potential, stirring was stopped during all the measurements rep0 rted herein, Titration of Fluoride with Thorium. Titration curves of fluoride ion with thorium ion, which demonstrate the effect of the pH of the medium, are shown in Figure 3. In all cases, 5.00 cc of 0.08000M sodium fluoride, diluted to an initial volume of 100 cc, were titrated with 0.02000M thorium nitrate. Curve 1, obtained with the unbuffered sodium fluoride solution, shows the 1arg:st potential change at the ThF4 equivalence point. The point of maximal rate of change of potential coincides with the theoretical equivalence point. Because the fluoride ion and thoric ion react in a 4 :1 mole ratio, one would not expect such coincidence but rather would expect the titration curve to be asymmetrical with the point of maximum slope slightly in advance of the equivalence point. The observed symmetry results from the fact that the originally neutral solution becomes acidic beyond the equivalence point, due to the acidic dissociation (“hydrolysis”)
of the excess aquo thoric ion. Hence the fluoride ion activity is decreased beyond the equivalence point to a greater degree than if the solution had remained neutral, because of its partial conversion to HF. Consequently the potential is larger than it would have been if the solution had remained neutral, and this effect partially counteracts the intrinsic asymmetric character of the titration reaction. From the hydrolysis constant of fluoride ion ( K w / K ~=~ 1.49 X lo-”) the pH was about 7.4 in the initial pure 4 x 10-3M sodium fluoride solution at the start of Curve 1. Up to the equivalence point it decreased only to about 7, but then decreased rapidly. The pH of the 0.02000M thorium nitrate titrant solution was found to be 2.74. When this solution was diluted 2 :100, corresponding to 2 cc beyond the equivalence point of Curve 1, the pH was 3.56. Curve 2 in Figure 3 was obtained after adding 10 cc of 0.100M hydrochloric acid to the sodium fluoride solution. This converted most of the fluoride to HF, and left an initial excess concentration of 0.006M hydrogen ion, which increased to 0.01M at the equivalence point. As expected, the potentials prior to the ThF, equivalence point are considerably more positive than for Curve 1, owing to the decreased activity of fluoride ion. From the dissociation constant of H F (6.71 x lo-,), the initial fluoride ion concentration was nearly exactly one-tenth of what it was for Curve 1. (At these small concentrations of total fluoride the Concentration of HF2-, whose dissociation constant to H F and F- is 0.25, is negligibly small). Therefore, the potential at the start of the titration would be expected to be 59 mv more positive than for Curve 1. The observed difference of 58 mv agrees well with this expectation. Note also the asymmetry of Curve 2 at the ThF4equivalence point, and the smaller second potential inflection at the ThF2+2point. This second inflection apparently results from ThF,(s)
+ Th+4 = 2 ThFit2; K
=
1.8
(4) The quoted equilibrium constant has been calculated from data obtained by Dodgen and Rollefson (4) in their thorough study of the various complex thorium fluoride species. Because this constant is relatively small the second inflection is defined only vaguely. Curve 3 in Figure 3 was obtained in the presence of a 0.1M sodium acetate-acetic acid buffer of pH = 4.88, and it shows a much smaller potential change than in an unbuffered solution (Curve 1). Evidently, in the acetate buffer the fluoride ion activity beyond the equivalence point is somewhat more then ten times larger than in unbuffered medium, so the activity of thoric ion must be correspondingly smaller. Presumably, at this pH the excess thoric ion precipitates either as ThO(OH)*, or a basic thorium acetate. According to Gayer and Leider (5) ThO(OH)2 = T h o f 2
+ 2 OH-;
K = 5.5 X
(5)
At pH = 4.88, it follows that ThO(OH)2 will precipitate when the concentration of thorium is greater than lO-bM, and this concentration is reached after addition of only 0.05 cc of 0.02M thorium nitrate beyond the equivalence point of Curve 3. In unbuffered medium (Curve 1) the acidic dissociation of the excess aquo thoric ion decreases the pH enough to prevent such precipitation.
(4) H. W. Dodgen and G. K. Rollefson, J . Am. Chem. SOC.,71, 2600 (1949). (5) K. H. Gayer and H. Leider, Zbid.,76, 5938 (1954). VOL. 39, NO. 8, JULY 1967
883
state the solubility is enhanced so that the fluoride ion activity at the equivalence point is larger, and the potential correspondingly is smaller, than when the solution is in equilibrium with flocculated ThF4. The species ThF3+, ThF2+2,ThF+3,and Thf4 are all present in a saturated solution of ThF,, and from the measurements of Dodgen and Rollefson (4) at 25 O C
+ F-; ThF3+ = ThF2+2 + F-; ThF2+’ = ThF+3 + F-; ThF+’ = Th+4 + F-;
ThFl(s) = ThF3+
K6
1.3 X
(6)
K7 = 2.1 X
(7)
Ks
1.0 X
(8)
Ks = 1.5 X 10-8
(9)
=
=
In unbuffered medium with a large amount of fluoride (Curve 2 in Figure 4) the observed potential at the equivalence point is 99 mv, corresponding to a fluoride ion concentration of 3.7 x lO-5M. From this, and the above equilibrium constants, the relative proportions of the various thorium species at the equivalence point, are (ThF2+2) _ __- 2.1 X low5= 0.57
x (ThFf3) _ _ _ - 1.0 x (ThF3+)
3.7
(ThFz+’) - 3.7 X lo-’
-(Th+4) - 1.5 X (ThF+B) 3.7 x 10-5 0
0.5 I FRACTION TITRATED
1.5
Figure 4. Titration curves of relatively small and large amounts of fluoride with thorium in an originally neutral unbuffered aqueous medium, normalized in terms of fraction titrated (1) 7.60 mg. and (2) 76.0 mg of fluoride ion in an initial volume of 100 cc titrated with 0.02000M Th(N03)4 Evidently, if the conditions under which fluoride ion finally is isolated in a complete analysis will permit, it is most advantageous to titrate fluoride ion with thorium nitrate in an originally neutral and unbuffered solution. In Figure 4 the titration curves of a relatively small amount (7.60 mg) and a relatively large amount (76.0 mg) of fluoride ion in about 100 cc of unbuffered solution are compared in terms of the fraction titrated in each case. The differences in potential between the two curves are close to what one would expect from the 10-fold difference in fluoride ion concentration. Note, however, that the expected asymmetry of the titration curve becomes evident with the larger quantity of fluoride, and consequently the point of maximum slope occurs about 0 , 6 x in advance of the equivalence point. The potential (fluoride ion activity) at the equivalence point would be expected to be constant and independent of the quantity of fluoride titrated, provided that the solution is saturated with ThF4 of the same physical characteristics. Actually, the equivalence point potential of Curve 1 in Figure 4 (70 mv) is 29 mv smaller than that (99 mv) for Curve 2. Although with the large amount of fluoride the usual gelatinous precipitate of hydrated ThF, appeared, there was no visible precipitate, and only a slight opalescence, with the small quantity of fluoride. Apparently, in the latter case, most of the ThF4 remains in colloidal suspension. In the colloidal 884
ANALYTICAL CHEMISTRY
= 0.027
= 4
x
10-4
Therefore, the chief species are ThF3+ and ThF2+*,with ThF3+ predominating, and the concentrations of ThF+3 and Th+4 are negligibly small. Alternatively, without employing the observed fluoride ion concentration, but directly neglecting the equilibria expressed by Equations 8 and 9, it follows from Equations 6 and 7 that (F-)
=
(ThF3+)
+ 2(ThFz+’)
(1 3)
Since (ThF3+) = Ks/(F-), and (ThF,+2) = K1 (ThF3+)/(F-), the fluoride ion concentration at the equivalence point should be 4.9 X lO-jM, which agrees well with the observed value (3.7 x 1 0 - 5 ~ ) . The colloidal character of small amounts of ThF, affects (increases) only the primary solubility equilibrium (Equation 6). From the observed equivalence point potential (70 mv) of Curve 1 in Figure 4, the fluoride ion concentration at the equivalence point is 1.2 X 10-4M. From Equations 7 and 13 it then follows that the concentration of ThF3+is 8.9 X 10-5M, and consequently for the colloidal ThF4 the equilibrium constant of Reaction 6 is 1.1 X 10-8, and thus eight times larger than for flocculated ThF,. This is, of course, only an approximate estimate, since it ignores the effect on the activity of fluoride ion of the different ionic strengths extent in Curves 1 and 2 of Figure 4. Because the maximal value of AE/AV occurs somewhat in advance of the equivalence point, the most accurate results are obtained by titrating to the equivalence point potential, which can be established in any given medium from titrations with known amounts of fluoride. For Curve 2 in Figure 4 the rate of potential change at the equivalence point is 23 mv per cc of 0.02000M thoriu mnitrate. With care, the equivalence point potential is reproducible to 1 2 m, corresponding to a precision of =!= 0.1 cc of 0.02000M thorium nitrate, or i 0.16 mg of fluoride. Hence, the titration error should not exceed i 0 . 2 z relative when 80 mg or more of fluoride are titrated in a final volume of about 100 cc.
t
v; I
I
I
I
I
- IO0
0
I
5
I
I I I I
IO
15
0.132 M Th(NO&,, cc Figure 5. Influence of ethanol on the titration of fluoride with thorium In each case 5.00 cc of 0.08000M NaF diluted to an initial volume of 100 cc were titrated. For both Curves 1 and 2 the solution contained 10 cc of 0.100M HlCl (initial excess hydrogen ion concentration of 0.006M), but for Curve 2 the solution also contained 60 vol ethanol. Curves 3 and 4 were both obtained in the presence of 0.1M sodium acetate-acetic acid buffer (aqueous pH = 4.88), but for Curve 4 the solution also c'ontained 60 vol x ethanol
Figure 5 demonstrates the influence of ethanol on the titration curves of fluoride with thorium. In 0.01M hydrochloric acid (Curves 1 and 2) addition of 60 vol ethanol (Curve 2) produces a larger and rnuch more sharply defined potential change than in purely aqueous medium (Curve l), because the second inflection is; eliminated. Presumably, this improvement results from a decrease in the solubility of ThF4 in the presence of ethanol. In the presence of 60 vol ethanol fluoride can be titrated in 0.01M hydrochloric acid as accurately as in an aqueo JS unbuffered solution. As shown by Curve 4 in Figure 5, ethanol also increases the total potential change in a 0.1M sodium acetate-acetic acid buffer, but the sharp potential inflection occurs 2 0 x before the ThF4equivalence point. Indeed, it occurs almost exactly at the point corresponding to ThF,-. This suggests that NaThF, is precipitated, because the little evidence that is available indicates that ThF6- itself is not very stable. Titration of Fluoride with Lanthanum. Titration curves of a small amount (7.60 mg) of fluoride with lanthanum nitrate under various conditions of pH are shown in Figure 6. The total volume of solution was 100 cc. As Curve 1 demonstrates, the largest potential change is obtained when the fluoride solution initially is approximately neutral and unbuffered, just as in the titration with thorium nitrate. The titration curve with lanthanum is more asymmetrical than that with thorium, and the maximal rate of potential change for Curve 1 occurs at 4.05 cc instead of at the theoretical equivalence point at 4.18 cc. Hence, as in the titration with thorium, the titration with lanthanum should
z
z
I
1
I
I
I
I
I
2 3 4 5 6 0.03189M LO(N03)3 , cc
I
7
Figure 6 . Titration curves of fluoride with lanthanum under various pH conditions In each case 5.00 cc of 0.08000M NaF (7.60mg of fluoride ion) were titrated in an initial volume of 100 cc. (1) No additions-i.e., neutral-unbuffered solution. (2) 10 cc of 1M sodium acetate-acetic acid buffer of pH = 4.88 added. (3) 10 cc of 0.2M sodium formate-formic acid buffer of pH = 3.00 added. (4) 10 cc of 0.100M HCl added, to produce an initial excess concentration of 0.006M hydrogen ion, which increased to 0.01M at the equivalence point. (5) As Curve 4 with 0.006M HCl, but 60 vol x ethanol was also present
be completed to the equivalence point potential, determined from titrations of known amounts of fluoride, rather than to the point of maximal rate of potential change. In a 0.1M sodium acetate-acetic acid buffer of pH = 4.88 (Curve 2 of Figure 6) the potential change is much less than in unbuffered medium, and the fluoride ion activity beyond the equivalence point remains relatively large. This suggests that the activity of lanthanum ion is decreased, but exactly why is a moot question. No precipitate forms when the acetate buffer is added to a lanthanum nitrate solution. It is possible that acetate ion forms a soluble complex species with lanthanum ion, but this is still conjectural. The response of the membrane electrode is not influenced by acetate ion, because the potentials during the first part of the titration are identical for Curves 1 and 2. In a 0.02M sodium formate-formic acid buffer of pH = 3.00 (Curve 3 of Figure 6), and in 0.01M hydrochloric acid (Curve 4), the potential changes are smaller than in unbuffered medium because of the conversion of the fluoride ion to HF, and the increase in the solubility of LaF3. Although in a purely aqueous medium titration in the presence of 0.01M hydrochloric acid is not feasible, Curve 5 in Figure 6 demonstrates that it becomes quite satisfactory when 60 vol ethanol is present to decrease the solubility of LaF3. In Figure 7 the titration curves of relatively small and large amounts of fluoride in an originally neutral and unbuffered solution are compared in terms of the fraction titrated in each VOL. 39, NO. 8, JULY 1967
885
100
CaF2
501 I
0
Figure 7. Titration curves of relatively small and large amounts of fluoride with lanthanum in neutral, unbuffered aqueous solution, normalized in terms of fraction titrated (1) 7.60 mg and (2) 76.0 mg of fluoride ion in an initial volume of 100 cc titrated with 0.03189MLa(NO&
case. The rate of potential change at the equivalence point is 2.3 mv per 0.1 titrated for the larger quantity (76.0 mg) of fluoride, and 0.3 mv per 0.1 % titrated for the smaller quantity (7.60 mg). These values are about twice as great as in the titration with thorium, Since, by careful titration of known amounts of fluoride, the equivalence point potential can be established to *2 mv, the titration of more than about 80 mg of fluoride ion in a volume of about 100 cc should not entail an error due to end point detection of more than = t O . l % . No information is available on the thermodynamic properties of LaF3, nor on the possible existence of the species LaF2+ and LAF+~.Presumably becabse the lanthanum fluoride membrane electrode begins to fail between 10-6 and lO-7M fluoride, Frant and Ross (2) suggested that the solubility product of LaF3 is about However, this value pertains to a massive single crystal of LaF3, and the titration curves of fluoride ion with lanthanum ion indicate that the solubility product of freshly precipitated LaFa is much larger. In common with other rare earth fluorides, freshly precipitated LaF3is hydrated, gelatinous, and very prone to form colloidal suspensions. During the titrations of Figure 7 the solution remained perfectly clear with the smaller amount of ff uoride ion, and even with the larger amount it became only slightly turbid. The equivalence point potential of Curve 2 in Figure 7 is 69 mv, from which the fluoride ion concentration is 1.2 x 10-4M. Assuming that the predominant species at the equivalence point are Laf3 and F-, the solubility product, (La+3)(F-)3,of freshly precipitated LaF3is 7 x lo-”. 886
ANALYTICAL CHEMISTRY
I 4
I 8
I 12
I
I
I
16 20 24 0.01000 M CaCI2, cc
I
28
Figure 8. Titration curves of fluoride with calcium In each case 5.00 cc of 0.OSOOOM NaF, diluted to an initial volume of 100 cc, were titrated. (1) No additions-i.e., neutral, and unbuffered aqueous solution. (2) Neutral and unbuffered, but with 75 vol ethanol originally, which decreased to 60% ethanol at the equivalence point. (3) 10 cc 1M sodium acetate-acetic acid buffer added (aqueous pH = 4.88), and 75 vol ethanol initially
Titration of Fluoride with Calcium. The solubility of calcium fluoride in water is too large to permit the titration of fluoride ion with calcium ion in purely aqueous media. This is demonstrated by Curve 1 in Figure 8, which shows no inflection at the equivalence point. By the conductometric method Kohlrausch (6) obtained a value of 3.9 X 10-11 for the solubility product of CaFz in water. From thermal data Latimer (7) calculated the considerably larger value 1.7 X 10-lo, but Curve 1 in Figure 8 suggests that this value is still too small. The potential at the equivalence point for Curve 1 is -6 mv, corresponding to a fluoride ion concentration of 2.2 X 10-3. Since the concentration of calcium ion is one half this value, the corresponding solubility product is (1.1 X 10-3) (2.2 x lO-3)2, or 5.3 x 10-9. However, in a neutral, unbuffered medium containing a large proportion of ethanol the solubility product is decreased to such an extent that the titration is quite successful. This is demonstrated by Curve 2 in Figure 2, in which case the solution at the start had a volume of 80 cc and contained 75 vol ethanol, which decreased to 60 vol Z at the equivalence point. The asymmetry of the curve is only partly due to the fact that fluoride ion and calcium ion react in a 2 :1 ratio, and its major cause is failure of the electrode response. In a (6) F. Kohlrausch, 2.Physik. Chem., 64, 145 (1908). (7) W. M. Latimer, “Oxidation Potentials,” 2nd ed., PrenticeHall, New York, 1952, p. 320.
As shown by Curve 3 in Figure 8, the titration curve in 60% ethanol in the presence of a 0.1Msodium acetate-acetic acid buffer is also very unsatisfactory. Why the potentials apparently are normal prior to the equivalence point, but remain depressed beyond it, is a moot question, but a calcium acetate complex is indicated. Although, under the optimum condition of an unbuffered and approximately neutral solution containing 60 ethanol the equivalence point in the titration of fluoride ion with calcium ion can be determined nearly as precisely as in the titrations with thorium and lanthanum ions, it is the least satisfactory of these three titrants.
'"I t
CONCLUSIONS
I
I
I
I
95 100 PER CENT TITRATED
I
I
I
I
I
105
Figure 9. Comparison of thorium and lanthanum titration curves in imm,ediate vicinity of the equivalence point In both cases 76.0 mg of fluoride in 100 cc of unbuffered aqueous solution were titrated, with 0.02000MTh(NO& and 0.03189M La(NO&, recipectively
neutral solution containing 60 vol ethanol the constant E in Equation 3 is about 70 mv more negative than in purely aqueous medium, and Equation 3 begins to fail at about p F = 4.8 which corresponds to about 50 mv. Thus, the potentials beyond the equivalence point of Curve 2 are too small relative to the fluoride ion activity. Apparently it is chiefly because of this that the maximal rrite of potential change for Curve 2 occurs 3 % before the equivalence point. This was also observed in the titration of much larger quantities of fluoride. Comparison of the potlzntials beyond the equivalence points of Curve 2 in Figure 8 with those of Curve 2 in Figure 5 and Curve 5 in Figure 6 suggwts that ethanol has much less effect on the electrode response in acid than in neutral medium. Even in the presence of 60 vol % ethanol it is impossible to titrate fluoride in acid medium (0.006 - 0.01M hydrochloric acid) with calcium ion. The titration curve was nearly a straight line (displaced upward from Curve 1 in Figure 8 by about 40 mv:l with no hint of an inflection at the equivalence point.
Although it can be adduced from the preceding titration curves that lanthanum ion is the best of the three titrants studied, because it yields the largest rate of change of potential at the equivalence point, this is demonstrated more clearly in Figure 9. In this large-scale plot, titration curves with lanthanum nitrate and thorium nitrate of a moderately large quantity of fluoride (76.0 mg in 100 cc of unbuffered solution) are compared directly in terms of percentage titrated in the immediate vicinity of the equivalence points. Not only is the point of maximal rate of potential change closer to the equivalence point with lanthanum as titrant, but the rate of potential change at the equivalence point is somewhat more than twice as great as with thorium. Furthermore, the potential at the equivalence point with small and large amounts of fluoride is the same with lanthanum as titrant, but shows a significant change in the titration with thorium (compare Figures 4 and 7). As mentioned above, but deserving of special emphasis when maximal accuracy is desired, the point of maximal slope should not be taken as an end point, but rather the titration should be performed to the true equivalence point potential, as determined in careful titrations of precisely known amounts of fluoride in the particular medium used. Ignoring this principle will cause a larger negative error in titrations with thorium than with lanthanum. If care is taken to determine this equivalence point potential to =t2 mv, which is quite feasible, moderately large quantities of fluoride can be titrated with lanthanum nitrate with an error as small as =kO.l%, under the optimum condition of a neutral, unbuffered solution. (In Figure 9, the potential at the equivalence point in the titration with lanthanum changes by 2.8 mv per 0.1% titrated.)
RECEIVED for review March 21, 1967. Accepted April 26, 1967.
VOL. 39, NO. 8, JULY 1967
887
