I I
I-
I
too Figure 5. Current-potential curves of Au on a RPRDE 0
C A ~ C =I ~2 - X 10-6M; CH2504 = 0.2M. Rotation speed = 2500 rpm, scan rate = 100 mV/sec. The number of pC of gold deposited (a) 11 pC, (b) 110 pC, (c) 238 p C , ( d ) 370 IC. Quantity of hydrogen adsorbed (a) 143 pC, (6) 110 pC, (c) 77pC, ( d ) 58
=\ I--
$0
a
3 0
PC
- 100 I .2
0.8
0.4 VOLTS
surface and the monolayer of metal atoms have the same geometrical structure. Our results on copper d o not agree with the work by Bowles. We find a 1 :1 relationship between the deposition of copper at underpotential and the inhibition of hydrogen adsorption. This result was also found by Breiter (18). Suppose we assume there is a random distribution of active sites o n the platinum surface and that the spacing between sites is equal t o the spacing of the platinum atoms. Then, it might be expected that large atoms such a s lead and bismuth, whose cross-sectional areas are 1.5 times that of a platinum atom, would not be able t o show site preference
0 .o during deposition. A smaller atom, however, could show site preference. In this regard, we find that only copper atoms, rcu = 0.92 rRt, and silver atoms rAg = 1.04 rRt, exhibit a preference for one of the hydrogen adsorption sites. All of the larger atoms simultaneously inhibit both the weakly and strongly adsorbed hydrogen sites equally. Curiously, gold, which is the same size as the silver atom, shows no site preference. RECEIVED for review April 23, 1971. Accepted July 23, 1971. Support of the US. Air Force Ofice of Scientific Research under Grant No. AFSOR 70-1832 is gratefully acknowledged.
Potassium Fluoride-A Reference Standard for Fluoride Ion Activity R. A. Robinson, Wayne C. Duer, and Roger G . Bates Department of Chemistry, Unioersity o j Florida, Gainesville, Fla. 32601
Potassium fluoride i s superior to sodium fluoride as a reference standard for the calibration of fluorideselective electrodes because of its higher solubility and i t s relative freedom f r o m ion association. Ion pairing i n sodium fluoride solutions is demonstrated by an analysis of activity coefficient data i n terms of t h e hydration theory developed by Stokes and Robinson. The fluoride ion has a n average hydration number of about 1.9, virtually identical with that f o r potassium ion. Accordingly, the activity coefficients of potassium and fluoride ions are equal in solutions of potassium fluoride. The ion pair dissociation constant for sodium fluoride i s 1.88 on the scale of molality a t 25 O C , and conductivity measurements are consistent with the conclusion that less ion pairing occurs in solutions of potassium fluoride than in solutions of t h e sodium salt. Standard values of pF (-log aF-) useful for the calibration of fluoride ion-selective electrodes over a wide range of fluoride activity are listed.
THEFLUORIDEION-SELECTIVE electrode developed by Frant and Ross (1) is characterized by a high reproducibility and selec~
~~
(1) M. Frant and J. W. Ross, Jr., Scieme, 154, 1553 (1966). 1862
tivity. These favorable properties have led to its extensive use for routine determinations of fluoride as well as for thermodynamic investigations of fluoride solutions (2). The determination of fluoride by other means is inconvenient and timeconsuming; hence, this electrode is a welcome addition t o the tools available to the analytical chemist. The fluoride electrode is one of the class of solid-state membrane electrodes. The membrane, which consists of a doped lanthanum fluoride crystal, is permeable to fluoride ion and capable of rejecting virtually all other ions with the exception of hydroxide. Several investigations have demonstrated (3-7) that the potential of the electrode changes with fluoride (2) J. N. Butler in “Ion-Selective Electrodes,” R. A. Durst, Ed., Chap. 5, NBS Special Publication 314, U. S. Government Printing
Office, Washington, D. C., 1969. (3) J. J. Lingane, ANAL.CHEM., 39, 881 (1967). (4) R . A. Durst and J. K . Taylor, ibid., p 1483. (5) R. Bock and S. Strecker, Z . Anal. Chem., 235, 322 (1968). (6) R . G. Bates and M. Alfenaar in “Ion-Selective Electrodes,” R. A. Durst, Ed., Chap. 6, NBS Special Publication 314, U. S. Government Printing Office, Washington, D. C., 1969. (7) G. Neumann, A r k . Kemi, 32,229 (1970).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
ion activity in accordance with the Nernst equation when the concentration of fluoride ion is between lO-5M and 0.1M. The response of the electrode at concentrations above 0.1M is more difficult t o evaluate because of the indeterminate nature of both the fluoride ion activity in reference solutions and the liquid-junction potential of the cell most commonly used for measurements of this sort, namely LaF3 membrane electrode, F-
( 1 KCI (satd), HgK12; Hg
(I)
However, the EMF of a cell without liquid junction consisting of a sodium-responsive glass electrode and a lanthanum fluoride membrane electrode furnishes the same values of the mean ionic activity coefficient of sodium fluoride up t o a molality (m)of 1 mol kg-I (6) as have been obtained by the most careful isopiestic vapor pressure measurements (8). The usefulness of the fluoride ion-selective electrode at fluoride concentrations well above O.lm seems therefore to have been demonstrated. Furthermore, the electrochemical behavior of the electrode is good enough t o justify confidence t o a few tenths of a millivolt in the measured potentials, o r 0.002 t o 0.008 unit in -log uF- (pF). To derive the full benefit of this excellent performance o n the part of the membrane electrode, careful consideration must be given t o the manner in which the electrode is standardized. In general, it has been the practice to standardize the lanthanum fluoride membrane electrode in a dilute solution of sodium fluoride o r potassium fluoride. The activity of fluoride in these reference solutions was assumed t o equal the mean ionic activity of the alkali fluoride. It has been recommended (6) that sodium fluoride not be used above O.lm, because ion pairing at higher concentrations was suspected. This procedure is, however, justifiable when the concentration of the reference salt is no greather than 0.01~1. Unfortunately, the standardization of cell I at 0 . 0 1 ~is inadequate when the electrode is t o be used for measurements of fluoride ion activity in the range of concentrations (or ionic strengths) from O.lm t o l m or above. There is ample evidence that the residual liquid-junction potential may amount t o 1 t o 4 mV under these conditions (6). This error of 0.02 t o 0.07 unit in pF can be reduced o r eliminated by standardizing the cell assembly with a fluoride solution of nearly the same concentration or ionic strength as the “unknown” mixture whose p F is to be determined. There is no unique formula, however, by which the activity of fluoride ion in these reference solutions can be calculated o r measured. In a recent contribution ( 9 ) ,we have proposed a reasonable convention based on hydration theory ( I O ) by which ionic activities in concentrated solutions of unassociated chloride salts can be assigned. We now suggest that potassium fluoride be chosen as a standard reference material, in preference t o sodium fluoride which is associated in moderately concentrated solutions. Our earlier treatment was based, with some experimental justification, o n the assumption that the chloride ion is unhydrated. On this basis, it can be shown that the fluoride ion has a hydration number of 1.87, o r alSimimost identical with that (1.9) for the potassium io:. larly, the hydration theory leads t o equal radii (1.82 A) for the hydrated potassium and fluoride ions. These parameters have now been used to calculate single ionic activity coeffi(8) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed., appendix 8.10, Butterworths, London, 1970. (9) R. G . Bates. €3. R. Staples, and R. A. Robinson. ANAL.CHEW, 42, 867 (1970). (10) R. H. Stokes and R . A. Robinson, J . Amer. Chem. SOC.,70,
I870 (1948).
Table I. Mean Activity Coefficients of the Sodium and Potassium Halides: Molality, 1 mole kg-I; 25 “C Sodium Potassium Fluoride 0.573 0.645 Chloride 0,657 0.604 Bromide 0.687 0.617 Iodide 0.736 0.645
cients and fluoride ion activities in solutions of potassium fluoride. The latter are proposed as reference values for the standardization of the lanthanum fluoride membrane electrode. ACTIVITY COEFFICIENTS OF SODIUM FLUORIDE AND POTASSIUM FLUORIDE
As a reference material for the standardization of the lanthanum fluoride membrane electrode at high fluoride concentrations, sodium fluoride is not a good choice. The solubility of sodium fluoride, for example, limits the concentration of fluoride ion that can be achieved to about l m at 25 “C. O n the other hand, potassium fluoride is much more soluble than sodium fluoride. More important, there is evidence of ion pair formation in sodium fluoride solutions that appears to be greatly reduced or absent in solutions of potassium fluoride. The simple conventions relating fluoride ion activity to the mean ionic activity of the electrolyte, therefore, cannot be applied rigorously t o solutions of sodium fluoride at moderate and high concentrations. This qualitative conclusion emerges from a comparison of the mean activity coefficients of the two fluorides with those of the other sodium and potassium halides a t a rather high molality, for example l m , as shown in Table I. The activity coefficient of potassium fluoride a t l m (0.645) is considerably higher than that of potassium chloride (0.604). Probably this difference is attributable t o hydration of the fluoride ion. While the chloride ion has little if any hydration (9), and the same is true of the bromide and iodide ions, the comparatively small radius of the fluoride ion (1.36 A) may well permit some hydration. The lower ionic conductivity (11) of fluoride ion (55.4) as compared with that for chloride ion (76.4) supports this conclusion. In spite of this, the activity coefficient of sodium fluoride in the 1 molal solution is only 0.573, as compared with 0.657 for sodium chloride at the same molality. This differencesuggests that sodium fluoride, unlike potassium fluoride, is partially associated into ion pairs at this concentration. A more detailed analysis of the activity coefficient data can be made in terms of the Stokes-Robinson hydration treatment (10). The hydration equation may be written as follows In y,
=
hfDH -
h In urn- In [l
+ 0.018 (2 - h)m]
(1)
where urnis the activity of water in the salt solution, h is the hydration number, and f D H is a Debye-Huckel term given by hiDH = --AW*/(l BHl’’2) (2)
+
in which A and B are constants of the Debye-Huckel theory, b is the “ion-size parameter”, and I is the ionic strength. Equation 1 accounts very successfully for the activity coefficients of unassociated uniunivalent electrolytes up t o a molal( I t ) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed., appendix 6.1, Butterworths, London, 1970.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1863
Table 11. Comparison of the Mean Activity Coefficient of Potassium Fluoride with Values Calculated by Equation 1 at 25 “C Yt
Obsd 0.670 0.645 0.658 0.705 0.779
m
0.5
1.0 2.0 3.0 4.0
edge of the effective distances of closest approach ( p l ) and average hydration numbers (h) for the three salts NaC1, KCl, and KF, therefore, it was possible to calculate the corresponding parameters for “unassociated” NaF. This was accomplished by combining the data summarized in Table I11 according t o the additivity formula N a F = NaCl K F - KCI. The ideal activity coefficients of sodium fluoride, calculated by Equation 1 with the parameters given in Table 111, are listed in Table IV, together with the values of 4, the osmotic coefficient, from which the activities of water were derived. The ideal values are the activity coefficients that would be expected if sodium fluoride were a n unassociated salt in aqueous solution, In all instances, they are considerably higher than the experimentally obtained stoichiometric activity coefficients given in the last column of the table.
+
Calcd 0.668 0.644 0.658 0.706 0.779
Table 111. Values of the Parameters h and h for Halides and for Single Ionic Species &,A h NaCl 3.97 3.5 1.9 KCl 3.63 NaF 3.98 5.37 KF 3.64 3.77 CI1.81 0 F1.82 1.87 Na+ 2.16 3.5 K’ 1.82 1.9
DISSOCIATION CONSTANT OF NaF ION PAIRS
A comparison of the last two columns of Table IV provides clear evidence of ion pairing in sodium fluoride solutions. The differences between the stoichiometric activity coefficients and the ideal activity coefficients furnish a n estimate of the magnitude o f K , the dissociation constant of N a F ion pairs. The constant of K is given by
Table IV. Ideal Activity Coefficients of Sodium Fluoride Calculated by Equation 1 with = 3 98 A and h = 5.31 Y*
m 0.1 0.2
0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
Calcd 0.780 0.739 0.720 0.707 0.700 0.698 0.697 0.697 0.699 0.702
9 0.936 0.933 0.933 0.935 0.940 0.946 0.953 0.959 0.966 0.974
Obsd 0.765 0.710 0.676 0.651 0.632 0.616 0.603 0.592 0.582 0.573
Table V. Calculation of the Ion Pair Dissociation Constant, K , for Sodium Fluoride at 25 OC from Activity Coefficient Data m 0.5
0.6 0.7 0.8 0.9 1.0
Yt
0.632 0.616 0.603 0.592 0.582 0.573
Y’
0.704 0.699 0.698 0.697 0.697 0.697
K
01
0.898 0.881 0.864 0.849 0.835 0.822 Mean K
=
1.96 1.91 1.87 1.86 1.85 1.84 1.88
ity limit defined Ioughly by hm = 12. The magnitudes of the two parameters h and H are reasonable in the light of solution theory and the relative dimensions of the ions concerned. Furthermore, the ionic contributions to both h and 8, which appear to be additive, can be derived from the assumption that h = 0 for chloride ion, whereupon 8 for this anion becomes equal to its crystallographic value, 1.81 A. It now becomes possible t o calculate “ideal” mean activity coefficients for sodium fluoride and potassium fluoride at concentrations above O.lm in the following manner. First of all, activity coefficient data for potassium fluoride were fitted t o Equation 1 at molalities up to 4 mole kg-l. Excellent agreement between observed mean activity coefficient: and the values calculated from Equation 1 with i = 3.64 A and h = 3.77 was obtained, as shown in Table 11. With a knowl1864
K
=
a*n~(y’)‘/(l- a )
(3)
where CY is the degree of dissociation and y‘ is the ideal mean activity coefficient of sodium fluoride in a solution of molality am. It may be shown (22)that
Yt where y, Hence,
=
w’
(4)
is the observed stoichiometric activity coefficient.
The results of the calculation of the ion pair dissociation constant, K, are shown in Table V. The average value of K at 25 “C is 1.88. From E M F measurements with the fluorideselective electrode, Butler and Huston (23) have found this constant to be 6.2 f 0.6 in lm NaC1. Measurements of the conductivity of solutions of sodium fluoride made recently in this laboratory offer some confirmation of the magnitude of the ion pair constant. Details of the measurements and the treatment of the data are given elsewhere (14). Values of A ” , the molar conductivity a t infinite dilution, and of K , the dissociation constant of the ion pairs, were calculated from the conductivities at finite concentrations by the method of Ives (25, 16), modified for use with the equation derived by Pitts (27,18). Nevertheless, the evidence from conductivity data is not unequivocal. The variation of conductivity with concentration can be described either by the equation of Fuoss and Onsager (29, 20), o r that of Pitts (17, 18), both of which include a term 8, the distance of closest approach of two ions. (12) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,’’ 2nd ed., Butterworths, London, 1970, chap. 2. (13) J. N. Butler and R. Huston, ANAL.CHEM., 42, 1308 (1970). (14) W. C. Duer, R. G. Bates, and R. A. Robinson, University of Florida, Gainesville, Fla., to be published, 1971. (15) D. J. G. Ives, J . Chern. SOC.,1933, 731. (16) D. J. G. Ives and K. Sames, ibid., 1943,5 11. (17) E. Pitts, Proc. Roy. SOC., Ser. A , 217,43 (19.53). (18) E. Pitts, B. E. Tabor, and J. Daly, Trmis. Furadcry SOC.,65, 849 (1969). (19) R. M. Fuoss and L. Onsager, J . Phys. Cliem., 61, 668 (1957). (20) R. M. Fuoss, L. Onsager, and J. F. Skinner, ;bid., 69, 2581 (1965).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
Each of these equations gives an adequate representation of the molar conductivity of a solution of a n electrolyte which can be considered t o be completely dissociated, and the value of & required to give the best fit of the experimental data usually lies close t o the sum of the crystallographic radii of the ions. Likewise, solutions of slightly dissociated electrolytes such as acetic acid are also described adequately by these equations by introduction of a dissociation constant. For these weak electrolytes, the fit of the conductivity. data t o the equation is less sensitive to the value of B selected; indeed, a value of d = 0, corresponding t o the Onsager limiting law, is often satisfactory. With electrolytes of high but not necessarily complete dissociation, the results may be ambiguous, as has been shown by Hanna, Pethybridge, and Prue (21). Under these circumstances, the value of the equilibrium constant, K, for a n ionpair dissociation process is very sensitive to the value of & selected, and often a series of values of K and 8. can be selected which will represent the experimental data almost equally well. This difficulty is enhanced in the case of an electrolyte such as sodium fluoride where ion pair formation is slight. Our conductivity data, as well as those of Erdey-Grhz et al. (22), can be interpreted in terms of complete dissociation. Good agreement between the observed and calculated conductivities can be obtained when a value of h = 2.31 A, the sum of the crystallographic radii, is used in the Pitts equation. A somewhat better fit of the data can, however, be obtained by assuming incomplete dissociation and using the sum of the radii of the hjdrured ions (3.9 A) for the value of B in the Pitts equation. This procedure gives K = 1.8 i 0.1 at 25 "C (molar scale), in good agreement with the value obtained by interpreting the activity coefficient data for this salt in terms of the hydration theory. A similar treatment of the conductivity data for potassium fluoride (23) gives K = 6.2 =k 0.6 when the sum of the radii of the hydrated ions (3.64 A) is used for in the Pitts equation. Conductivity data do not demonstrate unequivocally that potassium fluoride is completely dissociated while sodium fluoride is not. However, conductivity data are not inconsistent with the conclusions based on considerations of the hydration of sodium and fluoride ions as set forth earlier in this paper. Nevertheless, sufficient evidence of anomalous
a
____-____
(21) E. M. Hanna, A. D. Pethybridge, and J. E. Prue, J . Phys. Clien?., 75, 291 (1971). (22) T. Erdey-Grfiz, L. MajthCnyi, and E. Kugler, Acta Chim. Acad. Sci. Himg., 37, 393 (1963). (23) C. G . Swain and D. F. Evans, J . Amer. Cl7em. Soc., 88, 383 (1966).
Table VI. Single Ion Activity Coefficients of Potassium and Fluoride Ions in Solutions of Potassium Fluoride. Standard Values of pF (-log U F -). Temperature, 25 "C
a
D
m
Ca
0.01 0.05 0.1 0.2 0.5 1.o 2.0 3.0 4.0
0.009970 0.04983 0.09961 0.1990 0.4961 0.9868 1.951 2.888 3.794
Y+ = ')'Kc
pFb
= YF -
0.903 0.820 0.715 0.721 0.670 0.645 0.658 0.705 0.779
2.044 1.381 1.111 0.837 0.415 0.190 -0.119 -0.325 -0.494
Unit: moles per liter at 25 "C. -log aF-, where a is activity on the scale of molality,
activity behavior exists t o warrant the selection of potassium fluoride over sodium fluoride as a standard for fluoride ion activity. IONIC ACTIVITIES IN SOLUTIONS OF KF
In our earlier paper (9), we proposed a convention for deriving ionic activities in solutions of unassociated chloride salts, separating the mean activity coefficient into its ionic components on the basis of hydration numbers of the ions. The activity coefficients of the alkali chlorides were shown to be consistent with the presumption that the chloride ion is not hydrated. If both cation and anion are hydrated, the equations involve the hydration numbers of both ionic species. In the case of potassium fluoride they take the following form: log
YK+ =
log Y+
+ 0.00782 (h,
log
YF-
=
log 7 ,
+ 0.00782 (h- -
- /?-)WIG
(6)
and ~+)WI@
(7)
Inasmuch as the hydration number of fluoride ion (h- = 1.87) is virtually identical with that of potassium ion (h+ = 1.9), Y K C = YF- = The values are summarized in Table VI. It is recommended that reference solutions of potassium fluoride be chosen for the standardization of fluoride ionselective electrodes and that these solutions be aaigned the values of pF, that is -log U F - , listed in the last column of the table. RECEIVED for review July 6, 1971. Accepted August 9, 1971. Work supported in part by the National Science Foundation under Grant G P 14538.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1865
