Titration of Subnanomole Quantities of Fluoride Ions in Polar Nonaqueous Solvents

Edgar Heckel and P. F. Marsh Department of Chemistry, East Carolina Unicersity, Greencille, N.C. 27834

Titration of subnanomole quantities of fluoride ions can conveniently be carried out with lanthanum ion solution in polar solvents containing 5% water. De- tailed results have been obtained for solutions of ethanol and acetone, respectively. Solutions of meth- anol, 2-propano1, and 1,4-dioxane also have been in- vestigated. All salts pertinent to this study behave as weak electrolytes in the polar solvents. Consequently, the potential of the fluoride ion sensitive electrode greatly depends upon the degree of hydrolysis of both the lanthanum nitrate and the fluoride salts. Buffer solutions containing NH,CI, NH,CH,COO, and NH4HCO0 are not suitable since they interfere with the electrode response either because of enhanced hydrolysis or through the formation of undissociated fluoride and/or lanthanum compounds. Amino acid buffers greatly expand the concentration range of the fluoride sensi- tive electrode as well as the selection of polar solvents. Since the electrode response is rather slow in non- aqueous solutions, the titration process was acceler- ated by a method of graphical extrapolation of the electrode potential to infinite time using time response graph paper.

IN ‘THE PAST FEW YEARS, several papers (I) have been published dealing with the application of the lanthanum fluoride elec- trode in aqueous solution where the electrode obeys the Nernst equation over a range of fluoride ion activity from 1 M to 10-6M as first reported by Frant and Ross (2) . The determination of unknown amounts of fluoride can be most successfully carried out in a titration with lanthanum nitrate solution a t a pH between 5 and 7 (3). This relatively small pH interval requires that the lanthanum fluoride electrode be used in buffered fluoride solutions. In addition, complexing agents may be added to eliminate any interferences of ions such as AI3+, Fe3+, Pod3-, etc. When the fluoride ion activity is decreased below 10-6M, the potential approaches a con- stant value because the contribution of fluoride from the electrode membrane exceeds the fluoride concentration of the original solution.

molarity were accurately determined by Lingane (3, 4 ) using a LaF3 mem- brane electrode in aqueous solution of 60 volume per cent ethanol. The rate of change of the electrode potential a t the equivalence point was considerably enhanced in ethanol- water compared to that in pure water as the solvent.

Very small amounts of fluoride were quantitatively analyzed with a modified membrane electrode by direct and null- point potentiometry as reported by Durst and Taylor (5, 6). The volume of the fluoride solution was only 10 microliters, and because the analysis was carried out in aqueous solutions, the practical limit of this technique was about 5 nanomoles of fluoride.

Fluoride ion concentrations of less than

(1) Orion Research, Inc., Cambridge, Mass., “Bibliography of

(2) M. S. Frant and J. W. Ross, Jr., Scierzce, 154, 1553 (1966). (3) J. J. Lingane. ANAL. CHEM., 39, 833 (1967). (4) Zbid., 40, 931 (1968). (5) R. A. Durst and J. K. Taylor, ibid., 39, 1483 (1967). (6) R. A. Durst, ibid., 40, 935 (1968).

Orion Specific Ion Electrodes,” Dec. 1, 1971, pp 11-15.

In the present study, amounts of fluoride as low as 0.5 nanomole were determined in solutions of polar solvents. We also found through both conductivity and apparent p H measurements as well as titrations of fluoride ions with lan- thanum nitrate solutions that the quantitative determination of small amounts of fluoride ions with the LaF electrode is limited by effects such as hydrolysis and formation of un- dissociated fluoride andior lanthanum compounds (including possible complex ion formation) unless amino acids were added as buffers to the polar solvent systems.

EXPERIMEKTAL

The titrations were performed in home-made polyethylene beakers of 20-mm inner diameter and 15-mm height, and mag- netic stirring was employed. The initial volume of the solvent was 2.00 ml to which were added up to S microliters of 6.0 x 10-3M NaF solution, and not more than 20 microliters of 1.0 X 10-3Mlanthan~m nitrate solution was used in any titration. However, the conductivity experiments and the pH measure- ments were carried out in solutions of 25 ml and 5 ml, respec- tively, using 2 X 10-*M aqueous solutions of NaF (up to 50 pl) or La(N0J3 (up to 200 111). Under these conditions the dilution effects through the solute additions were negligibly small.

The conductivity cell (No. 3402 of Yellow Springs Instru- ment Co.) had a cell constant of 0.1. A 1000-Hz conductivity bridge was employed, and in addition an Orion digital pH meter (Model Sol), an Orion fluoride activity combination electrode (Model 96-09 ; the reference electrode matches the potential characteristics of the saturated KCI calomel elec- trode when using filling solution Orion 90-00-01) and a Corn- ing combination glass electrode (Series 100, No. 3) were used in this investigation. All readings were taken during mag- netic stirring. The laboratory temperature was 21 f 0.5 “C.

Except ethanol (superior quality, Commercial Solvent Co., Terre Haute, Ind.), all other chemicals (certified grade) were purchased from Fisher Scientific Company and they were used as supplied. Water was distilled from alkaline potassium permanganate solution.

The rate of diffusion of the reference electrode filling solu- tion may greatly influence the drift of the electrode potential during the titration process since the water concentration of the solvent, the total ionic strength, and the fluoride concen- tration of the sample will simultaneously change. Very satis- factory results were obtained when the rim of the LaF, elec- trode crystal was wet with silicon oil (Dow-Corning 704 diffu- sion pump oil) after the electrode was dismantled and thor- oughly dried and by filling the reassembled electrode with solution to a height of 25 mm measured from the bottom of the electrode. The electrode membrane was immersed in bidis- tilled water during storage. It was necessary to replace the entire reference electrode filling solution with fresh solution once the electrode was kept in bidistilled water for more than half a day. Further pre-treatment involved one or two titra- tions of samples of known fluoride content before the actual measurements were carried out.

Electrode Time Response. By using polar solvents other than water, the electrode response is rather slow a t low con-

ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972 * 2347

I n n I I l l / I I I

1111 I 1 T ' I -

OD 1 0 8 6 5 L 3 2 TIME. min.

Figure 1. Time response plot of the Orion 96-09 fluoride sensitive electrode of a titration of 30 nanoequivalents of fluoride in 2.0 ml of 95 ethanol solution. 1 X 10-3M aqueous lanthanum nitrate solution was added in 2.5-kI portions

centrations of fluoride ions. Orion Research Inc. (7) made a times response graph paper available which permits the extrap- olation of the electrode potential to infinite time-ix., the technique allows the E M F to be calculated after a relatively short period of time from initial readings.

Figure 1 shows a time response study on graph paper that can be used in systems where positive and negative potentials occur during the same titration. The horizontal axis is recip- rocal of time starting at two minutes after solute addition. The vertical axis was empirically found to be a logarithm func- tion such that +lo0 mV correspond to log 300, zero mV to log 200, and -100 mV to log 100, respectively. Various graph papers of suitably expanded scales have shown equally good results like those of Figure 1.

RESULTS AND DISCUSSION

Polar Solvent Solutions. The dependence of the electrode potential as shown in Figures 2 and 3 indicates that solutions containing between 90 and 100% of ethanol extend the ap- plicability of the fluoride ion sensitive electrode into the nanomole range of fluoride concentration. The EMF of the equivalence point shifts from positive potentials to negative potentials with increasing concentrations of ethanol (Figure 2). The titration curves approach the desired S-shape with inflection points which are in the vicinity of the equivalence points. In solutions of 95 % ethanol which contain less than 20 nanoequivalents of fluoride ions (Figure 3), the titration curves show no more inflection points and the equivalence points shift simultaneously to more positive electrode po-

(7) NewsletterJSpecific Ion Electrode Teclinology, 3 (182), 8 (1971 ); published by Orion Research, Inc., Cambridge, Mass. 02139.

75

100 95

I 0 10 20 30 40 50

La(NO3I3 , nanoequiv,

Figure 2. Titration curves of 37.5 nanoequivalents of NaF with 1 X 10-3M La(NO& in 2.5 mi of solutions of various water-ethanol mixtures

tentials. This can be rationalized as indicating either a decrease in fluoride ion concentration or an increase in the La : F concentration ratio.

In other polar nonaqueous solvents, the effects are very similar as can be seen from Figure 4. The addition of N a N 0 3 was intended to maintain a constant ionic strength of the solutions. However, these additions have very little effect on the raising of the equivalence point potential below a con- centration of 20 nanomoles of fluoride as shown in the case of methanol. The same results were received for the other solvents but data will not be reported. It is interesting to note that in the presence of NaNOa the equivalence potential is more positive than in the absence of the electrolyte. The titration curves also show a less steep slope. This means that the concentration of both free fluoride and lanthanum ions is smaller than in absence of sodium nitrate.

In solutions of acetone and 1,4-dioxane, the slopes are steep but the equivalence point potentials are shifted to much higher positive potentials, whereas the titrations curves of the three investigated alcohols have their inflection points very close to the equjvalence points. It is quite obvious that the free lanthanum ion concentration is much smaller than one would expect from the additions of La(N03)? solu- tion. The formation of lanthanum complex ions may be considered to explain the relative lower free ion concentra- tions in presence of 10-2M NaN03 or in solutions of acetone and dioxane, respectively. Knoeck (8) obtained evidence for lanthanum nitrate complexes in aqueous solution through infrared and Raman spectroscopy and with a nitrate ion- selective electrode. The formation of lanthanum acetate complexes was confirmed by Evans et al. (9). However, it

(8) J. Knoeck, ANAL, CHEM., 41, 2069 (1969). (9) P. A. Evans, G. J. Moody, and J. D. R. Thomas, Lab. Practice,

20, 644 (1971).

2348 ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972

1251 Fluoride nanaquivol.

0 10 20 30 10 50 LalNO&, nanoequiv:

Figure 3. Titration curves of solutions containing various amounts of NaF in 2.0 ml of 95% ethanol. The dashed line shows the equivalence potentials (large circles) in dependence of the fluoride concentrations

appears that in polar solvents several effects may contribute to lower ionic concentrations without the formation of in- soluble salts. It is well known that strong electrolytes in aqueous media are more extensively associated in the solvents having lower dielectric constants. This is demonstrated in Figure 5 for 95% ethanol and 9 5 x acetone solutions where the values of the equivalent conductances of these compounds resemble the weak electrolytes in aqueous solution. This result is in good agreement with our previous observations that the free ion concentrations of both fluoride and lan- thanum decrease in presence of sodium nitrate as expressed by Reactions 1 and 2.

F- -I- N a + N 0 3 - NaF + NO3 (1)

(2 ) 1 1 3 - La3+ 4- NO3- e 3 La(N03),

Furthermore, the fluoride ions as well as the lanthanum ions undergo hydrolysis, Reactions 3 and 4, as this is expected from their behavior as weak electrolytes.

F- -I HzO Ft H F + OH- (3) 1 1 - 3 La3+ + H 2 0 $ 5 La(OH), + H+ (4)

The results on the hydrolysis are shown in Figure 6. It is interesting to note that sodium nitrate solutions in 95% ethanol and 95 % acetone are not subject to hydrolysis. The degrees of hydrolysis of sodium fluoride and lanthanum nitrate are in the order of magnitude of 5 % in 95% acetone and about 1 % in 95% ethanol. Since the proton and the hydroxyl ion exhibit greater mobilities than any other ions in solution, our data reported on the equivalent conductances of Figure 5 are affected with some error. The larger equivalent

/ Propanol*

Figure 4. Titration curves of 30 nanoequivalents of NaF in 2.0 ml of solutions containing various polar solvents in 95% concentrations. The dashed lines indicate the dependencies of the equivalent points upon the fluoride ion concentrations in each solution

conductances of NaF and La(N03)3 in acetone solutions are caused by the higher degree of hydrolysis in acetone than in ethanol. The conductances of NaN02, however, resemble the different mobilities of the ions in either solution. Further evidence of the effects of hydrolysis on the EMF of the fluo- ride ion electrode is obtained by measuring the apparent pH during the titration of NaF with lanthanum nitrate solution as shown in Figure 7. In ethanol solution, the pH changes very little until the equivalence point is reached since the fluoride ions are hydrolyzed to less than 1 % . Additional amounts of lanthanum nitrate solution rapidly change the pH of the solution because of stronger hydrolysis of the lanthanum ion. The same effects are enhanced in acetone solution where we observe a pH change of more than one unit until all free fluoride is converted to LaF3 at the equiva- lence point. Since only 5 7 , of the fluoride undergoes hy- drolysis, the formation of undissociated hydrogen fluoride (Reaction 5)

H + + F - z 2 H F ( 5 )

from the rem&ining free fluoride ions is negligibly small in the more alkaline acetone solution. Consequently, more free fluoride ions are present in 95 x acetone than in 95 ethanol solution and this may explain the steeper slopes of the titra- tion curves in acetone solutions. The pH in ethanol solution changes more rapidly when approximately 5 x 10-6 equiv I.-' (see insert in Figure 7) of lanthanum nitrate solution has been added after passing the equivalence point. As shown in Figure 5 , larger additions of La(NO& result in less disso- ciated salt and a greater degree of hydrolysis. These results are in accordance with the observation that there is a rela- tively small potential increase beyond the equivalence point in acetone solution (Figure 4).

Furthei evidence of the hydrolysis processes has been ob- tained from titrations of sodium fluoride with lanthanum nitrate by measuring the specific conductance (Figure 8). The specific conductances of the solutions depend upon two effects. First, the formation of sodium nitrate according to Reaction 6

ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972 2349

N ~ , C 8 95%Ethano/ 0 9 5 % A c e t o n e

n\ \ -

I\\ P [ L S % 0 95% Acetone € t h a n i /

c 0

3 C c* , s q u i u l - ~ r l o ~ 0 0 1 5 1 0 25 50 75 100 C , r

\\ 4

0 95% Efhunol 0 95% Acetone

Figure 5. Equivalent conductances of NaF, NaN03, and La(N03)3 in dependence of both the equivalent concentrations C* and .\/p

mostly contributes to the overall conductivity before reaching the equivalence point. This is quite evident in acetone solu- tions where the conductance of NaN03 is approximately twice as large as that of any other species (Figure 5) .

Second, beyond the equivalence point the specific con- ductance depends mostly upon the mobilities of the protons which are formed according to Reaction 4. As expected, the conductance increases in ethanol solution because of the greater degree of hydrolysis of La(NO& compared to NaF, whereas in acetone solution a relative lower specific con- ductance is observed. The later effect is explained by the fact that the contribution to the overall conductivity from the protons formed in the hydrolysis (about 5 %) of La(NOd3 in acetone solution is smalkr than that of the sodium nitrate which is formed prior to the equivalence point.

Buffered Solutions. The behavior of the fluoride ion sensitive electrode in solutions containing salts of carboxylic acids as buffers has been discussed by Evans et al. (9). These salts obviously interfere in aqueous solution below lOW4M fluoride. The nature of this interference is not fully under- stood; however, it appears that complex formation plays an important role. The situation may be even more com- plicated in solvents containing only small concentrations of water since all salts behave as weak electrolytes in such solu- tions. As shown in Figure 9, there is no inflection point ob- servable in solution containing the ammonium salts of ace-

0 20 40 66 SOLUTE. e q u i v r l 0 0

Figure 6. pH of solutions of NaN03, La(NO&, and NaF in 95% ethanol and 95% acetone. The pH here is actually an empirically measured number, Le., an apparent pH value

8

7 PH

6

5

9 i a Ethanol 0 Acetone

e

PH 7

6

5

b M 40 60 La(N173)~ , equk x108

Figure 7. pH measurements during the titrations of 300 nanoequivalents of NaF with 2 X 10-*M La(N03h in 25-ml solutions of both 95 ethanol and 95 % acetone. The data refer to apparent pH values

tate, formate, or an acetate/nitrate mixture. In absence of any lanthanum titrant, the electrode potentials are relatively more positive in the buffered than in the unbuffered ethanol solution. Since the buffer concentrations are much larger than the fluoride concentrations (1.5 X lO-jM), the formation of ammonium fluoride takes place (Reaction 8).

(NH4 - Anion)Buffe, --f NH4+ + Anion NH4+ + F- e NHiF

NH4F + OH- S ",OH + F-

NH4F + H+ @ "4' + H F

(7)

(8)

(9) (10)

In addition, the concentration of the free fluoride depends upon the pH of the solution as expected from Reactions 9 and 10, whereby the hydrofluoric acid is partly dissociated according to Reaction 5. The gradual increases in the EMF to more positive potentials through the additions of lanthanum

2350 ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972

95%Acetone

3.0

LalNO3I3 , equiu: x 108

Figure 8. Specific conductance meas- urements during the titrations of 300 nanoequivalents of NaF with 2 X 50-2M La(N03), in 25-ml solutions of both 95 Z ethanol and 95 %acetone

nitrate into solutions containing the ammonium salts of chloride, formate, acetate, and acetate/nitrate are typical for titrations involving weak electrolytes inasmuch as the EMF’S of each system are determined by the equilibria of Reactions 8 to 12.

1 1 - La3+ + F- - LaF, (11) 3 3

(12) 1 1 - La3+ + H F e - LaF, + H+ 3 3

The free lanthanum ion concentrations are low, probably either through the formation of complex ions (Reaction 13) or due to undissociated lanthanum compounds, e.g., La- acetate (Reaction 14), La-formate, or La-hydroxide.

1 1 - La3+ + x CH3COO-- a - [La(CH3C00),]aC 3 3

1 1 3

(13)

- La3+ + CH3COO- i2 3 La(CH3C00)3 (1 4)

In addition one cannot exclude the possibility that complex ions (e.g. La(OH)?+, La(OH)2-, La(N03)Z+, etc.) are formed which also would reduce the free lanthanum ion concentra- tion. In the more alkaline solutions, La(OH), may be formed in a process competitive to Reaction 11. The pH of 9.10 for a 95 ethanol solution saturated with ammonium acetate (Figure 9) reveals that the acetate ion is more effectively hy- drolyzed than the ammonium ion.

The present study shows that ammonia salt buffers are completely unsuitable in polar solvents containing approxi- mately 5 of water since the fluoride ions form undissociated salts and the lanthanum ions may exist either as coordinated ions or as undissociated salts.

Contrary to the ammonia salt buffers, amino acids such as glycine (amino acetic acid) are very useful compounds to maintain a constant pH in polar solvents (Figure 9). The titration curve in ethanol-water solution containing glycine is identical to those curves shown in Figures 3 and 4-Le., in spite of a pH of 6.50, the fluoride ions are present in the same activity as in absence of the buffer. The glycine forms zwitter ions, but otherwise it is very slightly dissociated (Reactions 15 and 16).

Figure 9. Titrations of 30 nanoequivalents of NaF with 1 X lO-,M La(N03), in 2.5 ml of both 95 % ethanol (o0O.m) and 95 % acetone (0) solutions containing various buffers at satura- tion concentrations

H~NCH~COOH e H~NCH~COO- (15) + H2NCH2COO- + H+ (16)

Whereas the proton and the hydroxyl ion undergo reactions with the zwitterion structure (Reaction 17 and 18),

HaNCH2COO- + H+ HSNCH2COOH (1 7)

H3NCH2COO- + OH- i2 NH2CH2COO- + H 2 0 (18) neither the fluoride ions nor the lanthanum ions are equally reactive. The latter conclusion is supported by the results obtained from a 95 % acetone solution containing glycine. In the case of the unbuffered solution, the equivalence point is shifted to more positive potentials above the inflection of the titration curve (see Figure 4) as a result of the hydrolysis of the lanthanum ions as previously discussed. In presence of glycine, the pH of the solution is 6.35 which constitutes a sufficient concentration of protons to shift Reaction 4 to the left side. Consequently, more free lanthanum ions are available and the equivalence point of the titration curve is located near the inflection of that curve.

This observation is a rather significant result since a great number of solvent systems can be composed, all of which have in common a rather low dielectric constant which ex- tends the limit of fluoride detection rather readily into the subnanomole range. Besides acetone and dioxane solutions, we have so far investigated glycine buffered mixtures of ethanol-acetic anhydride-5 % water, ethanol-chloroform-5 % water, and ethanol-acetic anhydride-chloroform-5 water. The advantage of composed solvents lies in the fact that fluoride ions can be recovered from sample materials by a great variety of solvents and yet to obtain rather symmetrical titration curves--Le., high accuracy even for subnanomole quantities. Because of the slow electrode response in solu- tions of low dielectric properties, an electrode potential- time response extrapolation method as previously described has to be employed.

RECEIVED for review June 2, 1972. Accepted July 31, 1972. We thank for financial support both the National Science Foundation for a grant under COSIP to East Carolina University and the North Carolina Academy of Science for an undergraduate research grant to P. F. Marsh.

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