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Evidence for the occurrence of specific adsorption of fluoride and bifluoride ions from aqueous KF+KHF2 solutions at constant ionic strength at the mercury-solution interface
ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne Printed in The Netherlands
l
EVIDENCE F O R T H E O C C U R R E N C E OF SPECIFIC A D S O R P T I O N OF F L U O R I D E A N D B I F L U O R I D E IONS F R O M A Q U E O U S K F + K H F 2 S O L U T I O N S AT C O N S T A N T I O N I C S T R E N G T H AT T H E M E R C U R Y SOLUTION INTERFACE
A. W. M. VERKROOST, M. SLUYTERS-REHBACH AND J. H. SLUYTERS
Laboratory of Analytical Chemistry, State University, Utrecht (The Netherlands) (Received July 10th, 1969)
INTRODUCTION
Since Grahame's work 1 numerous attempts have been made to explain the rise in the double-layer capacity of a mercury electrode in fluoride solutions occurring at positive potentials. Several possibilities were suggested by Mott and Watts-Tobin 2. The most important of these attribute the effect to: 1. Specific adsorption of the F - ion. 2. Specific adsorption of the O H - ion. 3. An electrochemical reaction. A common method 3 to detect specific adsorption of any anion and to assess the amount of it, is to evaluate the surface excesses of the cation and the anion from electrocapillary curves. Then, the excess of anions in the diffuse double layer is calculated assuming that the cation is not specifically adsorbed. The difference from the total anion surface excess gives the amount of specifically adsorbed anion. However, if the surface excess of the cation differs little from the amount predicted by the diffuse double-layer theory in the absence of any specific adsorption, serious errors are introduced at low concentrations and positive electrode charges. In the case of fluoride solutions, no significant specific anion adsorption can be detected in this way. Payne 4 tried to ascertain the adsorbability of the O H - ion, making capacity measurements in N a O H solutions at a positively polarised mercury electrode. No evidence was found that O H - adsorption is an important effect. From measurements in N a F solutions at different concentrations, and considering pH changes due to hydrolysis, he concluded that the F - ion is responsible for the anodic rise in the capacity and that this ion is involved in the dissolution reaction of mercury at more positive potentials. Armstrong et al.5 made impedance measurements in N a F and N H 4 F solutions of various pH, at potentials where this dissolution reaction occurs. They analysed the impedance after the Randles' method and found evidence that in fluoride solutions mercury dissolves as Hg(OH)2. F r o m this they inferred that specific adsorption of O H - ions, together with the dissolution reaction, are responsible for the high capacity values observed in their experiments. However, the effect that causes the capacity to increase in a potential region where a faradaic process occurs, is now well J. Electroanal. Chem., 24 (1970) 1-9
2
A . w . M . VERKROOST, M. SLUYTERS-REHBACH,J. H. SLUYTERS
understood as being quite different from the effects occurring at an ideal polarised electrode 6. F r o m Armstrong's work it can be seen that the earlier mentioned al~odic rise starts at a far less positive potential than the dissolution reaction. In view of these controversies, it seemed worthwhile to make another attempt to investigate the double-layer capacity of mercury in fluoride solutions. Thus far only solutions with p H > 5 were considered, because of the glass-attacking properties of HF. We have made a new approach in performing capacity measurements in fluoride solutions at lower pH, in an all-Perspex and -Teflon cell, thus excluding both the presence of O H - ions and contamination by silicofluoride, which has been invoked by Frumkin et al. 7 to explain the anodic rise. As will be shown, the special aspect of our study is the fact that at low pH, bifluoride ions exist in considerable amounts besides fluoride ions. Since we have worked with solutions of constant ionic strength, e.g. x M K F + ( p - x ) M KHF2, the situation is analogous to that in some recent studies of other systems of mixed electrolytes, such as K I + K F 8, K C I + K F 9, N H 4 N O 3 + N H 4 Fa° and N H 4 C 1 0 4 + N H 4 F 11, The elegant thermodynamic analyses procedure for such systems, developed by Dutkiewicz and Parsons 8, has the advantage of avoiding the diffuse-layer correction and thus minimising the error introduced by it. EXPERIMENTAL Solutions of x M K F + ( p - x ) M K H F 2 in the range 0 < x < p were prepared by adding small quantities of H F to a solution of p M KF. Values of p were 4, 1 and 0.1 respectively and for each series four different values o f x were taken. The composition of the various solutions is reported in Table 1. The p H was measured with a compensating millivoltmeter, using a platinum-hydrogen electrode and a saturated calomel electrode (SCE). All solutions were made up in twice-distilled water with p.a. reagents. DeaeraTABLE
1
COMPOSITION OF THE VARIOUS SOLUTIONS K 2=
Soln.
(mol 1-1)
4
K~ = 5.5
[F-]
[HF2]
[HF]
[F-]
[HF2-]
[HF]
1
0.1
--
--
0.1
--
2 3 4
0.075 0.057 0.037
0.025 0.043 0.063
0.083 0.19 0.43
0.07 0.05 0.03
0.03 0.05 0.07
0.077 P=0.1 0.18 0.42
5 6 7 8
0.94 0.68 0.35 0.14
0.06 0.32 0.65 0.86
0.015 0.12 0.46 1.53
0.93 0.66 0.30 0.11
0.07 0.34 0.70 0.89
0"013/ 0.091 0.42 p = 1
9 10 11 12
3.64 2.83 1.70 0.88
0.36 1.17 2.30 3.12
0.025 0.10 0.34 0.89
3.63 2.81 1.62 0.77
0.37 1.19 2.38 3.23
0.019 / 0.077 | 0.27 ! 0.76 3
J. Electroanal. Chem., 24 (1970) 1-9
1.49
p = 4
SPECIFIC ADSORPTION OF FLUORIDEAND BIFLUORIDEIONS
3
tion was performed with tank nitrogen which had been passed through a vanadous sulfate solution. For the double-layer capacity measurements an all-Perspex cell was made, provided with a Teflon dropping mercury electrode, which was constructed following the method given by Raaen et al. ~2. The capillary was tested by making capacity measurements in NaF solutions at different concentrations. A good agreement with literature values ~ was found. A mercury pool was used as a counter electrode. The potential of the DME was measured with respect to a SCE, connected to the cell solution by means of a potassium fluoride salt bridge, contained in a Teflon siphon. The impedance of this cell, containing the solutions mentioned, was measured at 25°C, using an a.c. bridge as described previously t3. In the potential region studied the ohmic component remained constant, indicating that no faradaic reaction occurred. The measured capacities were independent of frequency. CALCULATIONOF THE CONCENTRATIONSOF FLUORIDESPECIES Since the pH of the solutions ranged between 2 and 9, the concentrations of H + and O H - are negligible with respect to that of K +, so that the predominant species present in the solution are K +, F - , H F and HF2. As far as we know, no evidence for the existence of higher H+-fluoride complexes has been reported in the literature. The ionic strength p is identical with the concentration of the potassium ion if complete dissociation of K F and K H F 2 is assumed. The equilibrium between the different species is governed by the equations: [HF] [H +] [ F - ]
K1
(1)
[HF] [V-] - / ( 2
(2)
[ F - ] + [ H F ; ] = [K +] + [H +] ~ p
(3)
[HF] + [ H F ; ] = s - [H +] ~ s
(4)
-
[HF~]
in which p is the amount of KF and s the amount of H F originally mixed in one litre of solution. The brackets denote the concentration of the corresponding species. Literature values 14 for the equilibrium constants are reported in the range 0.8 x 103 < K I < 1.6x 103 and 4 < K 2 < 5.5. In fact, eqns. (2), (3) and (4) are sufficient to calculate the concentrations of F - , HF and HF~ in our solutions. Equation (1) was used to check the data obtained with regard to their consistence with the pH measured, with satisfactory results. An uncertainty is introduced in the calculation because of the unknown activity coefficients which are implicated in the equilibrium constants, causing K1 and K 2 to be a function of the ionic strength. However, this will be reflected by the ranges given above. Moreover, K 2 contains only the quotient fF-/fHV~, which will vary little with changes in ionic strength. Therefore, we calculated two sets of values for [ F - ] = x , [ H F 2 ] = p - x and [HF] = ( 1 / K 2 ) [ ( p - x ) / x ], using the two limiting values 4 and 5.5 for K2 (see Table 1).
J. Electroanal. Chem.,24 (1970) 1-9
4
A . W . M . VERKROOST, M. SLUYTERS-REHBACH, J. H. SLUYTERS
THERMODYNAMIC ANALYSIS
In analogy with the procedure followed by Dutkiewicz and Parsons 8 we may write the electrocapillary equation for a pure mercury electrode in contact with an aqueous solution containing KF, K H F 2 and H F at constant temperature and pressure as : - d7 = q dE + + FHF : d~IKHF2-t- FHF dflltF q-/'F dflKF
(5)
where ? is the interfacial tension, q the charge per unit area on the mercury surface, E ÷ the potential of the mercury electrode with respect to a reference electrode reversible to the potassium ion in the working solution, F i the surface excess of species i relative to water and #j the chemical potential of the salt j. In approximation we may write d#~ = R T d (ln rnj)
(6)
where mj is the molal concentration of species j. From eqns. (1)-(4) we have mKF=X , mKnv2=P--X and rn.e= (1/K2)[(p--x)/x]. Consequently, - d T = q d E+ +
F- - - - - F H v ~ p-x
----Fn p-x
RTdlnx
(7)
The concentrations of ions of the same charge in the diffuse layer are in the proportion of the ratio of their bulk concentrations. Therefore, the diffuse layer contributions F~ ~-s and FHF 2 - s ~ to the total surface excesses are related by =
F~v ~
[F-] -
[HF~]
x -
(8)
p-x
With ri =
s+ rt
we obtain from eqns. (7) and (8) x 1 (~O-i~nx) ~+ =rl---- p - x
RT
F~F; _ p FHF p-x
(9)
where Fi~ denotes the surface excess due to specific adsorption. Finally, since at constant p the activity of K ÷ is independent of x, the condition E ÷ constant may be replaced by Esc E constant, if EscE is the potential of the mercury electrode with respect to a saturated calomel electrode. Instead of (9) the corresponding equation for constant charge can be used in the form: 1 // 0~SCE~ ] R T \O--hnXJq = F~
x p-x
-- - - F H F ~ 1
P p-x
-- - - F H F
(10)
with ~scE = 7 + qEscE (10a) In order to obtain information about the influence of undissociated H F on the double layer, we measured double-layer capacities in 1 M HC104 and 0.1 M HC104, with H F added up to 1 M. In these acid media, H F will remain almost comJ. Electroanal. Chem., 24 (1970) 1-9
SPECIFIC ADSORPTION OF FLUORIDE AND BIFLUORIDE IONS
5
pletely undissociated. N o difference was found in the capacities from those in the pure HC104 solutions and it is therefore very probable that the neutral species HF is not adsorbed, in which case eqn. (10) takes the form: 1
RT \0 In x/q
F- ----nv~ p _ ~
RESULTS AND DISCUSSION
The double-layer capacity of the D M E in the solutions of Table 1 is shown as a function of potential in Figs. la, b and c. In each diagram the curves coincide at potentials more negative than - 500 mV v s . SCE. In the positive potential region, an appreciable lowering of the capacity with decreasing x (fluoride concentration) or increasing p - x (bifluoride concentration) is observed. This causes a more pronounced appearance of the hump. 0
30 1
ff
1 25
o_
20 +Q2
-0.2 -0.4 Potential (V vs. SCE) £
b 35 35
t
u 3C
h
3
9
k
i
10
I
d I
U
2~ 25 +0.2
-c;2
Potential (V vs. SCE)
-d4
+0.2
~) -0.2 Potential (V vs. SCE)
-d4
Fig. 1. Differential capacity curves for solutions of x M K F + ( p - x ) M KHF2. p: (a) 0.1, (b) 1, (c) 4. The numbers correspond with the solns, of Table 1. J. Electroanal. Chem., 24 (1970) 1 9
6
A.W.M.
VERKROOST, M. SLUYTERS-REHBACH, J. H. SLUYTERS
Valuesof q and y in the different K F + K H F 2 solutions were determined by back integration of the capacity-potential curves from E = - 6 0 0 m V v s . SCE. At this potential, each series of curves at constant ionic strength coincides. Values of q and 7 at - 6 0 0 m V v s . SCE were obtained with the E C M in pure fluoride solutions as sta{ting point, using the values 15 EECM= _ 473 mV v s . N C E and 7ECM= 42.57 /~J c m - 2. We assumed EEcM and YECMin the pure fluoride solutions to be independent of the ionic strength, which is true in the absence of specific adsorption at the potential of the ECM. In all series there was no significant shift in Ezc M with varying x. In Fig. 2a, b and c, ~scz is plotted as a function of log x for several integral values of q.
40.8 15
&-. "~40.6
13
4%8
-1:3
J
log x
40.2
\\\x
39.8 i
-0.75
40.C
c
~
-0.5
log x
-0.25
9
::
15
x
;
log X
Q3
0.6
Fig. 2. ~SCEas a function o f x and q for solns, o f x M K F + ( p - x ) M K H F 2 in water at 25°C. p: (a) 0,1, (b) 1, (c) 4. K z : (O) 5.5, ( × ) 4. The numbers correspond with the different values of q. J.
Electroanal. Chem., 24 (1970) 1-9
SPECIFIC ADSORPTION OF FLUORIDE AND BIFLUORIDE IONS
7
In 0.1 M solutions, ~scE increases slightly with the fluoride concentration x, but in 1 M and 4 M solutions, ~SCEdecreases with x. This means that the right-hand side of eqn. (11) is positive, indicating that the fluoride ion must be specifically adsorbed. As it is only natural to suspect the bifluoride ion to be specifically adsorbed too, it seems necessary to separate the right-hand side of eqn. (11) in the contributions of the fluoride and bifluoride ion. We tried to do this by assigning adsorption isotherms for these ions in solutions o f K F + KHF2, which should be found in agreement with experimental data. If/`~- could be neglected with respect to x / ( p - x) /-HF~, 1 or vice versa, no such adsorption isotherm can be found. This is illustrated by the fact that 1 (~scE ~ R r \ 9 In XJq calculated from Fig. 2a, b and c can have both positive and negative values, while /-3- and FIaF 1 ~ can be only zero or positive. Applicaton of the simple Henry adsorption isotherm at constant electrode charge to both the fluoride and bifluoride ion would deliver the equations: F3- = ex = fl(p-
(12)
(13)
or
x r3
1 (~(SCE)
- p_~ rh~
-
R T k~l~n x/q = ( ~ - f l ) x
(14)
This last relationship is certainly not obeyed in Fig. 2b. On the contrary, values of F1F- -- {x/(p-- x) } F1HF~ decrease with increasing x. Using a Langmuir type isotherm we have kx(1-0) = k - 1 0 1 k2(1--0) = k_202
(15)
where 01 and 02 are the fractional surface coverages due to the F - and the H F ~ ion, respectively and 0 = 01 + 02. From eqns. (14) and (15) it follows that 01 /-3_ x = K (16) 02 - a F~F~
p--x
where a is a factor which accounts for the difference in size of the F - and H F £ ion, and K = ( k l k _ 2 / k 2 k _ 1)O n e obtains /`3 /`HF 5
-
K
x
- / c - -
a p-- x
x
(17)
p-- x
from which it follows that /`1_
p-xr"
=
-
r3
(18)
The right-hand side of eqn. (18) predicts that J. Electroanal. Chem., 24 (1970) 1-9
8
A.W.M.
VERKROOST, M. SLUYTERS-REHBACH, J. H. SLUYTERS
RT \~ In x/q should always increase with increasing fluoride concentration, a condition which is in distinct disagreement with Fig. 2b. For the more complicated adsorption isotherms it is often not possible to write F~- and F~F~ as an explicit function of x which is necessary to calculate F~- {x/(p-x)} F~v~ for different values of x. Moreover, the probable influence of one ion on the other in the adsorption t process would provide an extra relation between F 1- and/'HF]" W e have tried some of the more complicated isotherms; however, for the reasons mentioned above the isotherm assignment seems to be unfeasible. Therefore, we must confine ourselves to consider the values of 1
RT \0 In XJq
'
as far as they are positive, as minimum values of F 1 (cf. eqn. (11)). In Table 2 these values are tabulated for various values of q and x, noted in terms of/~C cm-2. TABLE 2
p/mol 1-1
q/C cm -2
x(K2=5.5}
F /@ ~SCE~. ~ -
-
-
-
R T i~ ln xJq
0.1 0.1 0.1 0.1
13 15 13 15
0.04 0.04 0.08 0.08
1 1 1 1
9 11 13
0.2 0.2 0.2
15 9 11 13 15 9 11 13 15 9 11 13 15
0.2 0.8 0.8 0.8 0.8 1 1 1 1 3 3 3 3
1 1 1 1 4 4 4 4 4 4 4 4
/ , u c
cm
-2
0.7 0.7 4.2 4 - 3 -4.8 -6.8 --8.2
2 1 -0.8 -1.7 --0.8 -1.7 -3.9 --5.4 --3.7 -7.6 -9.8 -14
It can be concluded, therefore, that at sufficiently positive electrode charges the fluoride ion is specifically adsorbed to a significant extent. Most probably the bifluoride ion is specifically adsorbed also. The nature of the adsorption, or of the interaction between the two ions seems to be rather complicated, since it is not possible to describe the experimental results with simple isotherms. J. Electroanal. Chem., 24 (1970) 1-9
SPECIFIC ADSORPTION OF FLUORIDE AND BIFLUORIDE IONS
9
ACKNOWLEDGEMENTS
This investigation was supported in part by the Netherlands Foundation for Chemical Research (S.O.N.) with financial aid from the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.). The cooperation of Mr. Chr. Lanning and Mr. C. van der Lee in the construction of the electrode and the cell is gratefully acknowledged. SUMMARY
The double-layer capacity of a DME electrode in mixed solutions of fluoride and bifluoride solutions has been studied in order to investigate the nature of the anodic rise. The analysis procedure of Dutkiewicz and Parsons was used to demonstrate the specific adsorption of both the fluoride and bifluoride ion at positive electrode charges. Only minimum amounts of specifically adsorbed fluoride ions can be obtained from experiment, some of which are tabulated for various solution compositions and electrode charges. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
D. C. GRAHAME, J. Am. Chem. Soc., 76 (1954) 4819. N. F. MOTT AND R. J. WATTS-TOBIN, Electrochim. Acta, 4 (1961) 79. D. C. GRAHAMEAND B. A. SOBERBERG,J. Chem. Phys., 22 (1954) 449. R. PAYNE, J. Electroanal. Chem., 7 (1964) 343. R. D. ARMSTRONG, W. P. RACI~AND H. R. THIRSK, J. Electroanal. Chem., 14 (1967) 143. P. DELAHAY, J. Phys. Chem., 70 (1966) 2067, 2373. B. B. D~A~ASKIN,N. V. NIKOLAEVA-FEDOROVlCHAND A. N. FRUMKIN, Dokl. Akad. Nauk SSSR, 121 (1958~ 129. E. DUTKIEWlCZ AND R. PARSONS, J. Eleetroanal. Chem., I1 (1966) 100. R. PAVNE, Trans. Faraday Soe., 64 (1968) 1638. R. PAYNE, J. Phys. Chem., 69 (1965) 4113. R. PAYNE, J. Phys. Chem., 70 (1966) 204. H. P. RA~N, R. J. Fox AND V. E. WALKER, Report of Oak Ridge National Laboratory, ORNL-3344 uc-4-Chemistry TID-4500 (18th ed.). M. SLUYTERS-REHBACHAND J. H. SLUYTERS, Rec. Tray. Chim., 82 (1963) 535. L.G. SILLf?N,Stability constants o f Metal-lon Complexes, The Chemical Society, London, 1964, p. 256. E. DUTKIEWICZ, private communication.
J. Electroanal. Chem., 24 (1970) 1-9
l
EVIDENCE F O R T H E O C C U R R E N C E OF SPECIFIC A D S O R P T I O N OF F L U O R I D E A N D B I F L U O R I D E IONS F R O M A Q U E O U S K F + K H F 2 S O L U T I O N S AT C O N S T A N T I O N I C S T R E N G T H AT T H E M E R C U R Y SOLUTION INTERFACE
A. W. M. VERKROOST, M. SLUYTERS-REHBACH AND J. H. SLUYTERS
Laboratory of Analytical Chemistry, State University, Utrecht (The Netherlands) (Received July 10th, 1969)
INTRODUCTION
Since Grahame's work 1 numerous attempts have been made to explain the rise in the double-layer capacity of a mercury electrode in fluoride solutions occurring at positive potentials. Several possibilities were suggested by Mott and Watts-Tobin 2. The most important of these attribute the effect to: 1. Specific adsorption of the F - ion. 2. Specific adsorption of the O H - ion. 3. An electrochemical reaction. A common method 3 to detect specific adsorption of any anion and to assess the amount of it, is to evaluate the surface excesses of the cation and the anion from electrocapillary curves. Then, the excess of anions in the diffuse double layer is calculated assuming that the cation is not specifically adsorbed. The difference from the total anion surface excess gives the amount of specifically adsorbed anion. However, if the surface excess of the cation differs little from the amount predicted by the diffuse double-layer theory in the absence of any specific adsorption, serious errors are introduced at low concentrations and positive electrode charges. In the case of fluoride solutions, no significant specific anion adsorption can be detected in this way. Payne 4 tried to ascertain the adsorbability of the O H - ion, making capacity measurements in N a O H solutions at a positively polarised mercury electrode. No evidence was found that O H - adsorption is an important effect. From measurements in N a F solutions at different concentrations, and considering pH changes due to hydrolysis, he concluded that the F - ion is responsible for the anodic rise in the capacity and that this ion is involved in the dissolution reaction of mercury at more positive potentials. Armstrong et al.5 made impedance measurements in N a F and N H 4 F solutions of various pH, at potentials where this dissolution reaction occurs. They analysed the impedance after the Randles' method and found evidence that in fluoride solutions mercury dissolves as Hg(OH)2. F r o m this they inferred that specific adsorption of O H - ions, together with the dissolution reaction, are responsible for the high capacity values observed in their experiments. However, the effect that causes the capacity to increase in a potential region where a faradaic process occurs, is now well J. Electroanal. Chem., 24 (1970) 1-9
2
A . w . M . VERKROOST, M. SLUYTERS-REHBACH,J. H. SLUYTERS
understood as being quite different from the effects occurring at an ideal polarised electrode 6. F r o m Armstrong's work it can be seen that the earlier mentioned al~odic rise starts at a far less positive potential than the dissolution reaction. In view of these controversies, it seemed worthwhile to make another attempt to investigate the double-layer capacity of mercury in fluoride solutions. Thus far only solutions with p H > 5 were considered, because of the glass-attacking properties of HF. We have made a new approach in performing capacity measurements in fluoride solutions at lower pH, in an all-Perspex and -Teflon cell, thus excluding both the presence of O H - ions and contamination by silicofluoride, which has been invoked by Frumkin et al. 7 to explain the anodic rise. As will be shown, the special aspect of our study is the fact that at low pH, bifluoride ions exist in considerable amounts besides fluoride ions. Since we have worked with solutions of constant ionic strength, e.g. x M K F + ( p - x ) M KHF2, the situation is analogous to that in some recent studies of other systems of mixed electrolytes, such as K I + K F 8, K C I + K F 9, N H 4 N O 3 + N H 4 Fa° and N H 4 C 1 0 4 + N H 4 F 11, The elegant thermodynamic analyses procedure for such systems, developed by Dutkiewicz and Parsons 8, has the advantage of avoiding the diffuse-layer correction and thus minimising the error introduced by it. EXPERIMENTAL Solutions of x M K F + ( p - x ) M K H F 2 in the range 0 < x < p were prepared by adding small quantities of H F to a solution of p M KF. Values of p were 4, 1 and 0.1 respectively and for each series four different values o f x were taken. The composition of the various solutions is reported in Table 1. The p H was measured with a compensating millivoltmeter, using a platinum-hydrogen electrode and a saturated calomel electrode (SCE). All solutions were made up in twice-distilled water with p.a. reagents. DeaeraTABLE
1
COMPOSITION OF THE VARIOUS SOLUTIONS K 2=
Soln.
(mol 1-1)
4
K~ = 5.5
[F-]
[HF2]
[HF]
[F-]
[HF2-]
[HF]
1
0.1
--
--
0.1
--
2 3 4
0.075 0.057 0.037
0.025 0.043 0.063
0.083 0.19 0.43
0.07 0.05 0.03
0.03 0.05 0.07
0.077 P=0.1 0.18 0.42
5 6 7 8
0.94 0.68 0.35 0.14
0.06 0.32 0.65 0.86
0.015 0.12 0.46 1.53
0.93 0.66 0.30 0.11
0.07 0.34 0.70 0.89
0"013/ 0.091 0.42 p = 1
9 10 11 12
3.64 2.83 1.70 0.88
0.36 1.17 2.30 3.12
0.025 0.10 0.34 0.89
3.63 2.81 1.62 0.77
0.37 1.19 2.38 3.23
0.019 / 0.077 | 0.27 ! 0.76 3
J. Electroanal. Chem., 24 (1970) 1-9
1.49
p = 4
SPECIFIC ADSORPTION OF FLUORIDEAND BIFLUORIDEIONS
3
tion was performed with tank nitrogen which had been passed through a vanadous sulfate solution. For the double-layer capacity measurements an all-Perspex cell was made, provided with a Teflon dropping mercury electrode, which was constructed following the method given by Raaen et al. ~2. The capillary was tested by making capacity measurements in NaF solutions at different concentrations. A good agreement with literature values ~ was found. A mercury pool was used as a counter electrode. The potential of the DME was measured with respect to a SCE, connected to the cell solution by means of a potassium fluoride salt bridge, contained in a Teflon siphon. The impedance of this cell, containing the solutions mentioned, was measured at 25°C, using an a.c. bridge as described previously t3. In the potential region studied the ohmic component remained constant, indicating that no faradaic reaction occurred. The measured capacities were independent of frequency. CALCULATIONOF THE CONCENTRATIONSOF FLUORIDESPECIES Since the pH of the solutions ranged between 2 and 9, the concentrations of H + and O H - are negligible with respect to that of K +, so that the predominant species present in the solution are K +, F - , H F and HF2. As far as we know, no evidence for the existence of higher H+-fluoride complexes has been reported in the literature. The ionic strength p is identical with the concentration of the potassium ion if complete dissociation of K F and K H F 2 is assumed. The equilibrium between the different species is governed by the equations: [HF] [H +] [ F - ]
K1
(1)
[HF] [V-] - / ( 2
(2)
[ F - ] + [ H F ; ] = [K +] + [H +] ~ p
(3)
[HF] + [ H F ; ] = s - [H +] ~ s
(4)
-
[HF~]
in which p is the amount of KF and s the amount of H F originally mixed in one litre of solution. The brackets denote the concentration of the corresponding species. Literature values 14 for the equilibrium constants are reported in the range 0.8 x 103 < K I < 1.6x 103 and 4 < K 2 < 5.5. In fact, eqns. (2), (3) and (4) are sufficient to calculate the concentrations of F - , HF and HF~ in our solutions. Equation (1) was used to check the data obtained with regard to their consistence with the pH measured, with satisfactory results. An uncertainty is introduced in the calculation because of the unknown activity coefficients which are implicated in the equilibrium constants, causing K1 and K 2 to be a function of the ionic strength. However, this will be reflected by the ranges given above. Moreover, K 2 contains only the quotient fF-/fHV~, which will vary little with changes in ionic strength. Therefore, we calculated two sets of values for [ F - ] = x , [ H F 2 ] = p - x and [HF] = ( 1 / K 2 ) [ ( p - x ) / x ], using the two limiting values 4 and 5.5 for K2 (see Table 1).
J. Electroanal. Chem.,24 (1970) 1-9
4
A . W . M . VERKROOST, M. SLUYTERS-REHBACH, J. H. SLUYTERS
THERMODYNAMIC ANALYSIS
In analogy with the procedure followed by Dutkiewicz and Parsons 8 we may write the electrocapillary equation for a pure mercury electrode in contact with an aqueous solution containing KF, K H F 2 and H F at constant temperature and pressure as : - d7 = q dE + + FHF : d~IKHF2-t- FHF dflltF q-/'F dflKF
(5)
where ? is the interfacial tension, q the charge per unit area on the mercury surface, E ÷ the potential of the mercury electrode with respect to a reference electrode reversible to the potassium ion in the working solution, F i the surface excess of species i relative to water and #j the chemical potential of the salt j. In approximation we may write d#~ = R T d (ln rnj)
(6)
where mj is the molal concentration of species j. From eqns. (1)-(4) we have mKF=X , mKnv2=P--X and rn.e= (1/K2)[(p--x)/x]. Consequently, - d T = q d E+ +
F- - - - - F H v ~ p-x
----Fn p-x
RTdlnx
(7)
The concentrations of ions of the same charge in the diffuse layer are in the proportion of the ratio of their bulk concentrations. Therefore, the diffuse layer contributions F~ ~-s and FHF 2 - s ~ to the total surface excesses are related by =
F~v ~
[F-] -
[HF~]
x -
(8)
p-x
With ri =
s+ rt
we obtain from eqns. (7) and (8) x 1 (~O-i~nx) ~+ =rl---- p - x
RT
F~F; _ p FHF p-x
(9)
where Fi~ denotes the surface excess due to specific adsorption. Finally, since at constant p the activity of K ÷ is independent of x, the condition E ÷ constant may be replaced by Esc E constant, if EscE is the potential of the mercury electrode with respect to a saturated calomel electrode. Instead of (9) the corresponding equation for constant charge can be used in the form: 1 // 0~SCE~ ] R T \O--hnXJq = F~
x p-x
-- - - F H F ~ 1
P p-x
-- - - F H F
(10)
with ~scE = 7 + qEscE (10a) In order to obtain information about the influence of undissociated H F on the double layer, we measured double-layer capacities in 1 M HC104 and 0.1 M HC104, with H F added up to 1 M. In these acid media, H F will remain almost comJ. Electroanal. Chem., 24 (1970) 1-9
SPECIFIC ADSORPTION OF FLUORIDE AND BIFLUORIDE IONS
5
pletely undissociated. N o difference was found in the capacities from those in the pure HC104 solutions and it is therefore very probable that the neutral species HF is not adsorbed, in which case eqn. (10) takes the form: 1
RT \0 In x/q
F- ----nv~ p _ ~
RESULTS AND DISCUSSION
The double-layer capacity of the D M E in the solutions of Table 1 is shown as a function of potential in Figs. la, b and c. In each diagram the curves coincide at potentials more negative than - 500 mV v s . SCE. In the positive potential region, an appreciable lowering of the capacity with decreasing x (fluoride concentration) or increasing p - x (bifluoride concentration) is observed. This causes a more pronounced appearance of the hump. 0
30 1
ff
1 25
o_
20 +Q2
-0.2 -0.4 Potential (V vs. SCE) £
b 35 35
t
u 3C
h
3
9
k
i
10
I
d I
U
2~ 25 +0.2
-c;2
Potential (V vs. SCE)
-d4
+0.2
~) -0.2 Potential (V vs. SCE)
-d4
Fig. 1. Differential capacity curves for solutions of x M K F + ( p - x ) M KHF2. p: (a) 0.1, (b) 1, (c) 4. The numbers correspond with the solns, of Table 1. J. Electroanal. Chem., 24 (1970) 1 9
6
A.W.M.
VERKROOST, M. SLUYTERS-REHBACH, J. H. SLUYTERS
Valuesof q and y in the different K F + K H F 2 solutions were determined by back integration of the capacity-potential curves from E = - 6 0 0 m V v s . SCE. At this potential, each series of curves at constant ionic strength coincides. Values of q and 7 at - 6 0 0 m V v s . SCE were obtained with the E C M in pure fluoride solutions as sta{ting point, using the values 15 EECM= _ 473 mV v s . N C E and 7ECM= 42.57 /~J c m - 2. We assumed EEcM and YECMin the pure fluoride solutions to be independent of the ionic strength, which is true in the absence of specific adsorption at the potential of the ECM. In all series there was no significant shift in Ezc M with varying x. In Fig. 2a, b and c, ~scz is plotted as a function of log x for several integral values of q.
40.8 15
&-. "~40.6
13
4%8
-1:3
J
log x
40.2
\\\x
39.8 i
-0.75
40.C
c
~
-0.5
log x
-0.25
9
::
15
x
;
log X
Q3
0.6
Fig. 2. ~SCEas a function o f x and q for solns, o f x M K F + ( p - x ) M K H F 2 in water at 25°C. p: (a) 0,1, (b) 1, (c) 4. K z : (O) 5.5, ( × ) 4. The numbers correspond with the different values of q. J.
Electroanal. Chem., 24 (1970) 1-9
SPECIFIC ADSORPTION OF FLUORIDE AND BIFLUORIDE IONS
7
In 0.1 M solutions, ~scE increases slightly with the fluoride concentration x, but in 1 M and 4 M solutions, ~SCEdecreases with x. This means that the right-hand side of eqn. (11) is positive, indicating that the fluoride ion must be specifically adsorbed. As it is only natural to suspect the bifluoride ion to be specifically adsorbed too, it seems necessary to separate the right-hand side of eqn. (11) in the contributions of the fluoride and bifluoride ion. We tried to do this by assigning adsorption isotherms for these ions in solutions o f K F + KHF2, which should be found in agreement with experimental data. If/`~- could be neglected with respect to x / ( p - x) /-HF~, 1 or vice versa, no such adsorption isotherm can be found. This is illustrated by the fact that 1 (~scE ~ R r \ 9 In XJq calculated from Fig. 2a, b and c can have both positive and negative values, while /-3- and FIaF 1 ~ can be only zero or positive. Applicaton of the simple Henry adsorption isotherm at constant electrode charge to both the fluoride and bifluoride ion would deliver the equations: F3- = ex = fl(p-
(12)
(13)
or
x r3
1 (~(SCE)
- p_~ rh~
-
R T k~l~n x/q = ( ~ - f l ) x
(14)
This last relationship is certainly not obeyed in Fig. 2b. On the contrary, values of F1F- -- {x/(p-- x) } F1HF~ decrease with increasing x. Using a Langmuir type isotherm we have kx(1-0) = k - 1 0 1 k2(1--0) = k_202
(15)
where 01 and 02 are the fractional surface coverages due to the F - and the H F ~ ion, respectively and 0 = 01 + 02. From eqns. (14) and (15) it follows that 01 /-3_ x = K (16) 02 - a F~F~
p--x
where a is a factor which accounts for the difference in size of the F - and H F £ ion, and K = ( k l k _ 2 / k 2 k _ 1)O n e obtains /`3 /`HF 5
-
K
x
- / c - -
a p-- x
x
(17)
p-- x
from which it follows that /`1_
p-xr"
=
-
r3
(18)
The right-hand side of eqn. (18) predicts that J. Electroanal. Chem., 24 (1970) 1-9
8
A.W.M.
VERKROOST, M. SLUYTERS-REHBACH, J. H. SLUYTERS
RT \~ In x/q should always increase with increasing fluoride concentration, a condition which is in distinct disagreement with Fig. 2b. For the more complicated adsorption isotherms it is often not possible to write F~- and F~F~ as an explicit function of x which is necessary to calculate F~- {x/(p-x)} F~v~ for different values of x. Moreover, the probable influence of one ion on the other in the adsorption t process would provide an extra relation between F 1- and/'HF]" W e have tried some of the more complicated isotherms; however, for the reasons mentioned above the isotherm assignment seems to be unfeasible. Therefore, we must confine ourselves to consider the values of 1
RT \0 In XJq
'
as far as they are positive, as minimum values of F 1 (cf. eqn. (11)). In Table 2 these values are tabulated for various values of q and x, noted in terms of/~C cm-2. TABLE 2
p/mol 1-1
q/C cm -2
x(K2=5.5}
F /@ ~SCE~. ~ -
-
-
-
R T i~ ln xJq
0.1 0.1 0.1 0.1
13 15 13 15
0.04 0.04 0.08 0.08
1 1 1 1
9 11 13
0.2 0.2 0.2
15 9 11 13 15 9 11 13 15 9 11 13 15
0.2 0.8 0.8 0.8 0.8 1 1 1 1 3 3 3 3
1 1 1 1 4 4 4 4 4 4 4 4
/ , u c
cm
-2
0.7 0.7 4.2 4 - 3 -4.8 -6.8 --8.2
2 1 -0.8 -1.7 --0.8 -1.7 -3.9 --5.4 --3.7 -7.6 -9.8 -14
It can be concluded, therefore, that at sufficiently positive electrode charges the fluoride ion is specifically adsorbed to a significant extent. Most probably the bifluoride ion is specifically adsorbed also. The nature of the adsorption, or of the interaction between the two ions seems to be rather complicated, since it is not possible to describe the experimental results with simple isotherms. J. Electroanal. Chem., 24 (1970) 1-9
SPECIFIC ADSORPTION OF FLUORIDE AND BIFLUORIDE IONS
9
ACKNOWLEDGEMENTS
This investigation was supported in part by the Netherlands Foundation for Chemical Research (S.O.N.) with financial aid from the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.). The cooperation of Mr. Chr. Lanning and Mr. C. van der Lee in the construction of the electrode and the cell is gratefully acknowledged. SUMMARY
The double-layer capacity of a DME electrode in mixed solutions of fluoride and bifluoride solutions has been studied in order to investigate the nature of the anodic rise. The analysis procedure of Dutkiewicz and Parsons was used to demonstrate the specific adsorption of both the fluoride and bifluoride ion at positive electrode charges. Only minimum amounts of specifically adsorbed fluoride ions can be obtained from experiment, some of which are tabulated for various solution compositions and electrode charges. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
D. C. GRAHAME, J. Am. Chem. Soc., 76 (1954) 4819. N. F. MOTT AND R. J. WATTS-TOBIN, Electrochim. Acta, 4 (1961) 79. D. C. GRAHAMEAND B. A. SOBERBERG,J. Chem. Phys., 22 (1954) 449. R. PAYNE, J. Electroanal. Chem., 7 (1964) 343. R. D. ARMSTRONG, W. P. RACI~AND H. R. THIRSK, J. Electroanal. Chem., 14 (1967) 143. P. DELAHAY, J. Phys. Chem., 70 (1966) 2067, 2373. B. B. D~A~ASKIN,N. V. NIKOLAEVA-FEDOROVlCHAND A. N. FRUMKIN, Dokl. Akad. Nauk SSSR, 121 (1958~ 129. E. DUTKIEWlCZ AND R. PARSONS, J. Eleetroanal. Chem., I1 (1966) 100. R. PAVNE, Trans. Faraday Soe., 64 (1968) 1638. R. PAYNE, J. Phys. Chem., 69 (1965) 4113. R. PAYNE, J. Phys. Chem., 70 (1966) 204. H. P. RA~N, R. J. Fox AND V. E. WALKER, Report of Oak Ridge National Laboratory, ORNL-3344 uc-4-Chemistry TID-4500 (18th ed.). M. SLUYTERS-REHBACHAND J. H. SLUYTERS, Rec. Tray. Chim., 82 (1963) 535. L.G. SILLf?N,Stability constants o f Metal-lon Complexes, The Chemical Society, London, 1964, p. 256. E. DUTKIEWICZ, private communication.
J. Electroanal. Chem., 24 (1970) 1-9