Analytical Determination of Fluoride Ion Using Gran's semi-antilog Plot Ralph J. Barnhard University of Oregon, Eugene, OR 97403
The use of ion-selective electrodes in research, quality control, and analytical and university chemical laboratories is well established. They have opened the door to a wide variety of very clever procedures and applications. A number of demonstrate their use as teachine articles in THIS JOURNAL devices (1-10). They are simple to operate and can he usei as teachina devices starting from the construction of a simvle electrode i o an analyticG determination for a particuiar ion. We have instituted a quantitative determination for fluoride ion using a commercially available fluoride electrode (Orion Model 94-09A) with success. The procedure referred to as known-addition is employed with the data processed on Gran's Plot Paper to determine fluoride ion concentrations M or 0.19 ppm. The novelty of the deterin the range of mination is the Gran's plot, but the importance of the experiment is the application of the abstract Nernst equation to such practical problems as fluoride ion concentration, and secondly the requirement for careful analytical work so basic for good results. The determination is relatively easy. I t does not require a great time commitment, and i t allows students to practice a modern technique with modern instruments. The systematic approach to the molar concentration of fluoride ion determination begins with the fundamentals of an oxidation-reduction reaction. Simple examples are shown (i.e., a strip of copper metal and a strip of zinc metal). Nothing happens of course until the circuit is completed by simply wettine a salt bridae (NaCI solution on a oaoer towel. newspaper or a piece of blotter paper held between the electrodes). From this simplistic demonstration of a votential between two cells, the system can be sophisticatedsomewhat, using the same metal strivs as electrodes in beakers connected bv the classical salt bridge U-tube. Half reactions that describe the chemistry of this cell are introduced and written with the transfer of electrons between the two half reactions noted. The Nernst equation can then he introduced to account for the myriad of occasions when the half-cells are not a t standard state conditions. Cell potentials are described in terms of the that are strips of metal for easy recognition by the student (i.e., zincand copper), but then replace one of the electrodes (i.e., copper) by a bubbling hydrogen gas electrode. The same concept of electrode potentials still exist but now the pressure of a gas is part of the half reaction which can he demonstrated by the Nernst equation. The concept of the activities (or the effective concentrations) of ions pertinent to the half reactions are introduced. By writing out the complete form of the Nernst equation for the cell (zinc and hydrogen) the potential of the cell can be shown to depend upon the activities of zinc ions and hydrogen ions:
Assuming that careful control of the concentration of zinc ion a t standard state is feasible this expression can be manipnlated to provide the measurement bf hydrogen ion concentration, or the quasi-construction of a pH meter. It becomes
t if quite clear that any practical measurement of o l ~ (pH), done with the apparatus demonstrated, i.e., beakers, salt bridges and bubbling hydrogen apparatus, would be clumsy a t best. Consequently, it becomes the appropriate time to introduce another stvle of electrodes. The calomel electrode
may now he summa&ed by the following form:
(where C is a constant which includes En,, and the asymmetry constant of the glass membrane). With this background the discussion can turn to the fluoride reaction (Fz + 2e 2F-). Substituting this reaction into the Nernst equation for the hydrogen half reaction eqn. (1)becomes:
-
The activity of the hydrogen ion ( o l ~ +from ) the expression for pH is simply replaced by the activity of a new ion, the fluoride ion. The activity of free fluoride ion is related to molar concentration bv the activitv coefficient ( 7 )which deoends upon the total imic strength of chi s~,lutiun.A> the rluoride ivn soluti~msbwnmr mow d i l ~ ~1i.e.. t v in thc rant*. uf I U ' t o 10-6) this activity coefficient approaches one ( l i ). Given this, millivolt readings may be used directly to determine molar concentrations of fluoride ion, provided all the fluoride present is unbound and uncomplexed. A high ionic strength buffered and complexing medium called TISAB (Total Ionic Strength Adjustment Buffer) is employed for the vnrpose of adiusting the pH of the solution, com~lexing . . comprting ions and fixing the ionic strength o i the s o l u ~ i ~ n high twouch S I I thar the iictivitv a.ocfficirnis oiunknown and standard s&utions used for comparison are virtually identical (2,12). Typical procedure for the determination of fluoride is to employ the Nernst equations
E,,i1 + E,I,,~ Em,,,,*
- E; = -0.059 log a p = +0.59
pF-
(3)
and to use a semi-log plot of electrode potential along the ordinate versus fluoride ion concentration a l o n ~the logarithmic abscissa. A better alternative is to plot the measured potentials on semi-antilog paper commonly called a Gran's plot after G. Gran who developed the concept (12-15). The Nernst equation is again the focus of the plot; however, an antilog is taken to permit the direct reading of [F-] versus measured potential. Equation (2) is rewritten in the form Volume 60
Number 8 August 1983
679
rnv along antlog axis
1175940
705470
[F-1 x lo.5
235
0
1
2
3
5
4
ml of "known addltlon"
Plot on Gran's semi-antilog paper of mV versus ml of solution (with a known fluwide concentration)added to the unknown sample. mis is used to complete the F- concentration in the unknown.
E,,u
=E,
- S log ar-
(4)
where E, is made uo of constants and S is the slope of the electrode; typically the Nernst factor of 59.16 mV. G&'S Plot Paoer is uniaue in that it is not only semi-antilog paper .. . hut the'vertical akis is also skewed to allow for up to a 10%change in volume of the original sample (see figure). Supplies of Gran's semi-antilog paper are available from most scientific supply houses or directly from Orion Research, Inc. (12).From ein;.(3) and (4) i t is noted that the values of measured electrode potentials, plotted on the ordinate, must be increasing
intercept along the abscissa will be in error by about one minor division. In these cases semi-antilog paper may be obtained that is designed with a smaller built-in slope, or less than 58 mV Nernstein slope ( 1 2 ) . A useful application of analysis using Gran's plots is the measurement of samples in which the level of fluoride ion being determined is close to the electrode's limit of detection. I n the case of fluoride ion this limit of detection is a concentration of M. For determinations of fluoride ion a t this level the initial millivolt readings do not fall on a Nernstian straight line. However, as additions of fluoride ion are made to the unknown sample, subsequent the straieht line reeion of a tvnical readines .. aooroach .. -. mV \.ersur. p F - pl,,t.'l'he intercept of the eurrapolated straight line at the ahacis>a yiel(l.i thr .xmwnirarion oitluoride iun.
of adding 1ml "known-add solution" is repeated four more times and the recorded potentials plotted on the sequentially numbered vertical lines after each addition. The six plotted points are connected by a straight line which is extended to intersect the horizontal abscissa. The values of the coordinate points along the abscissa to the left of the zero (0) mark depend on the concentration of the "known-add solution." As an example: if the "known-add solution" used for the determination is 2.35 X 10W M in fluoride ion then each of the marks along the abscissa varies by 2.35 and the concentration labels for fluoride ion in the unknown solution (fromright to left starting at the zero line) would be 0,2.35, 4.70,1.05,9.40,and 11.75 X 10-5MF-, respectively. If a straight line plat of the six experimentally determined potentials intersect the abscissa at point A (Fig. I), the concentration of the fluoride ion in the unknown solution would he reported as 5.88 X 10-5 M F- or 0.0012 ppm. Advantages and Dfsadvantages One limitation of this technique is that the Gran's semiversus potention, on the other hand, allows for concentr%ion changes over many decades. If the initial estimation of the decade range for the concentrations of unknown fluoride ion is incorrect, then another "known-add solution" must he carefully prepared, either more dilute or more concentrated, hut still within the range of M fluoride ion. Great to care must be exercised in the preparation of unknown samples and "known-add solutions" to minimize the effects of polyvalent ions iSi4+. A13+. and Fe3+) which comulex F-. Plastic containers mustbe uskd for sto*ing solution$ since fluoride ion is absorbed by glass. The success of this analytical technique depends heavily upon the accurate use of volumetric elassware. It is sueeested that students should ~ r a c t i c eusine h . n n e t r i c pipe&; before attempting to use cHrefu11y made "known-add solutions" and unknown samples in a serious fashion for experimental results. The need for a limited number of potentiometric readings taken after regular increments of the "known-add solution," unlike differential plots of dEldV or dpHIdV against V, make the acquisition of data simplistic. The calculations are quick and straightforward as the molar concentration of fluoride can he read directly from the graph. The accuracy obtained hy students using in-house unknowns (mixtures of NaF and NaCl prepared on semi-micro analytical balances) in our laboratory has been of the order of 1ppt. Literature Cited (1) Lamb, R.E.. Nstusch,D. F., O'Reilly, J. E., and Watkins. N., J. CHEM EDUC., SO. 432 ,>o,m ,.",",.
(21 Lisht.T.
Experimental Procedure To determine fluoride ion concentration in an unknown solution of approximately 10V M the potential (E,n) of a 100-mlsample of the original unknown solution is measured and plotted on the 0 (zero) vertical line of the Gran's plot paper. One milliliter of "known-add solution," a solution of precisely known fluoride ion concentration is added, and the potential is measured again. It is recommended that the concentration of the "known-add solution" should be close to 2.00 X 10-3 M . It is not important that the solution be exactly 2.00 X M hut the concentration must be precisely known. The value of the potential measured following the addition of 1 ml of "known-add solution" is plotted on the number one vertical line. The procedure
680
Journal of Chemical Education
S..andCsoouceino.C.C.. J. CHEM E~uc..52.247(1975)
(1978). (9) Emars, M. M., arid N. A., and in, C. T., J. C H ~ MEDUC., . 56,670 (1979). (10) Christian, G. D.. "Anaiyliesl Chemistry."3rd Ed., John Wiley and Sona, New York, 19s". n W 9 (11) Liherfi. A.,snd Maseini,M.,Anol. Chem.. 41,676 (1969). (12) "NousletterISpeciflc Ion Electnde Teehnoio~~." Orion Research. Ine., 380 Putman Ave.. Cambridge. MA 02139, 1970. (13) Weatcott. C. C..Anai.Chim A d a .86.269(1976l. . . (14 Glan, G., Act.. Chim. Scond., 4,559 (1950). (15) FraZa7.J. W.. Kray, A. M.,Selig, W.,andI.in, R.,Anal. Chem.,17,869(1975)
