ADSORPTION AT THE ELECTRICAL DOUBLE LAYER
2601
The Electrical Double Layer with Simultaneous Anion and Cation Specific Adsorption: Thallium(1) Nitrate
by Gilles G. Susbielles, Paul Delahay,’ and Emanuel Solon Department of Chemistry, New York University, New York, New York 10003, and Coates Chemical Laboratory, Louisiana State University, Baton Rouge, Louisiana 70803 (Received March 7 , 1966)
Interfacial tension and differential capacity of the double layer were measured at 25” for mercury in TINOSat six concentrations from 0.025 to 0.2 M and from 0.2 to -0.25 v vs. sce (practically no T1 deposition). The following quantities were computed and interpreted: charge on the electrode, relative surface excesses of T1+ and ?rTo~-, amounts of specifically adsorbed T1+ and NOS-, and potential in the outer plane and in the cation and anion inner planes. The two Frumkin isotherms for simultaneous adsorption of TI+ and NOS- are quite self-consistent and indicate strong ion pairing of specifically adsorbed ions of opposite sign.
Introduction It was recently shown2 that the structure of the electrical double layer with cation specific adsorption (TlF) could be interpreted much in the same way as for anion specific adsorption. The latter case is fairly well understood from extensive previous work. Simultaneous specific adsorption of anion and cation is examined here for Tln’o~,as no detailed study of this case has been made to our knowledge. This salt was selected because it is quite soluble (about 0.4 M maximum concentration at 25”) and weak complexation (pK1 = 0.33 for at4 25”) is easily corrected for. Nitrate is quite strongly adsorbed specifically, but not overwhelmingly so in comparison with T1+, and thus is suitable. Electrocapillary curves for TIN03 in presence of K N 0 3 and HN03 were reported by Frumkin5 with the aim of demonstrating, conclusively and for the first time, significant specific adsorption of an inorganic cation on mercury. However, simultaneous specific adsorption of TI+ and NO3- was not examined in detail in that work. Experimental Section Thallium nitrate (Baker) was recrystallized twice and insoluble impurities (presumably oxides) were eliminated by filtration over a fritted glass disk. Purified activated charcoal was added to solutions which were then stirred for 12 hr. Solutions, after filtration,
were titrated for thallium(1) by iodate. The same solutions were utilized in measurements of electrocapillary curves and capacities. The following cell was used at 25 h 0.1O HglTlN03(~) ITlNO,(c) (TlN03(0.1 M ) 1 NH4P1’O3(4.2M)/sce(KCl) Two compartments with T1?S03at the coneentration c were utilized to minimize the effect of transfer from the compartment with (0.1 M ) . The nonthermodynamic junction potentials do not matter as they are constant. (See the procedure of Grahame and Soderberge6) The potential for the T1X03(c)I TlNo~(0.1 M ) junction was computed from the transference number of T1+ (t+ = 0.51) in This datum was estimated from the ionic mobilities of TI+ (1) To whom correspondence should be addressed at New York University. (2) P. Delahay and G. G. Susbielles, J . Phys. Chem., 70, 647 (1966). (3) For a review, see, e.g., P. Delahay, “Double Layer and Electrode Kinetics,” Interscience Division, John Wiley and Sons, Inc., New York, N. Y., 1965, pp 53-121. (4) J. Bjerrum, G. Schwarzenbach, and L. G. Sillbn, “Stability Constants,” Part 11, The Chemical Society, London, 1958, p 56. (5) A. N. Frumkin, “Transactions of the Symposium on Electrode Processes,” E. Yeager, Ed., John Wiley and Sons, Inc., New York, N. Y., 1961, pp 1-12. (6) D. C. Grahame and B. A. Soderberg, J. Chem. Phys., 22, 499 (1954).
Volume 70, Number 8 August 1966
2602
400
G. SUSBIELLES, P. DELAHAY, AND E.
SOLON
-
0.025
360
o 0.05 A 0.075 I 0.1s 0 0.2
I
1
I
0.1
0
-
I -0.1
E
( volts vs
I
- 0.2
S.C.E.1
Figure 1. Electrocapillary curves for TlNOa a t different concentrations ( M ) at 25". See ref 9 for complete data.
01 0.1
I
I
0
- 0.1 E'(v0ltS vs S.C.E. )
1
I
- 0.2
Figure 3. Charge on the electrode against potential for the solutions of Figure 1. See ref 9 for complete data.
of electrocapillary curves and differential capacities as in previous work2 on TlF, except that capillaries were not coated with Desicote.
1 0.2
0.1
0
- 0I
- 0.2
E ( v o l t s vs S.C.E.)
Figure 2. Differential capacity against potential for the solutions of Figure 1. See ref 9 for complete data.
and NOa- at infinite dilution.' The following electrolyte activity coefficients were computed by interpolation on the basis of the values listed by Robinson and Stokes? 0.838 (0.025 M), 0.779 (0.05 M), 0.736 (0.075 M), 0.702 (0.1 M), 0.649 (0.15 M), and 0.606 (0.2 M). The concentrations of T1+ and NO3-, needed in the application of the Gouy-Chapman theory, were computed4 from pK1 = 0.33. This correction was minor except for the more concentrated solutions. The same equipment was used in the determination The Journal of Phyeical Chemistry
Results and Thermodynamic Analysis The electrocapillary curves of Figure 1 were used to compute the two constants needed in the integration of the capacity-potential curves of Figure 2, and the same procedure was applied as in our T1F study2 to smooth out electrocapillary curves. Complete data are available.Q The final values of the curve p~ on the electrode are plotted in Figure 3 against the potential E. No arbitrary attempt was made to correct for the crossover of the curves for 0.05 and 0.075 M in Figure 3. The resulting error should be quite minor. We shall generally use p~ rather than E , but conversion is immediate by means of Figure 3. The relative excess r T 1 + of T1+ was computed by graphic differentiation of the plot of interfacial tension against the chemical potential of T11\TO3 at constant potential against a hypothetical reference electrodea that is reversible to NO3-. Errors were minimized by repeating differentiation twice. Values of r N O s ~
~
~
~~
(7) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworth and Co. Ltd., London, 1959, p 463. (8) See ref 7, pp 181 (eq 8.4a), 496. (9) Deposited as Document 8991 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. 20540. A copy may be secured by writing the Document number and remitting $1.25 for photoprints or $1.25 for 3 5 m m microiilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress.
ADSORPTION AT THE ELECTRICAL DOUBLELAYER
2603
20
15
0.075
01
E
c!
u
10
I5
5
0
q, (pC.crn-*l
Figure 5. Same plot as Figure 4 but for the relative surface excess of NOa-. 5
adsorption (KNOs, see ref 6). Thus, the surface excess of each ion is enhanced by specific adsorption of the ion of opposite sign. 0
I
15
I
10
NonthermodynamicAnalysis
I
5 q,, (pC.crn-*)
0
Figure 4. Relative surface excess of TI+ against the charge on the electrode for T1NOa at different concentrations ( M ) .
were obtained by difference from the charge on the electrode. It is thus assumed that T1+ and NO3- are the sole ionic species in solution; H+ and OH- can be neglected for the prevailing TlN03 concentrations even with slight hydrolysis. Deposition of T1 could be neglected since the concentration of T1 in mercury near the surface, as calculated from the Nernst equation, was at the most 1.5 X M in the worst case and was much lower in most cases. The analysis of the electrode as an ideal polarized mercury electrode thus was valid with good approximation. Results of the thermodynamic analysis are shown in Figures 4 and 5 about which the following comments are made. (a) r T 1 ' increases markedly as QM becomes less positive. (b) Values of rT1+, at a given QM, are higher than those for TlF, Le., than in the absence of anion specific adsorption.2 (c) r N O s - increases with qM at the more positive q M values as one would expect, but they also increase with decreasing QM for the higher concentrations. This effect is due to increasing specific adsorption of T1+ as QM decreases. Values of r N O s - in the region of marked T1+ specific adsorption are higher than in the absence of marked cation specific
Method of Calculation. Grahame's analysis6)lo is not applicable since it presupposes that only one ionic species is specifically adsorbed. A method, based on simple electrostatic relationships and the Gouy-Chapman theory was applied. The corresponding model is shown in Figure 6, about which it is noted that the inner plane for T1* is closer to the electrode than that for NO3-. One has 41+ -
41-
=
(4T/E)(QM
+ q1+)(a-
- a+)
(2)
where 4 represents the potential, E is the dielectric constant, z is the distance from the electrode, and q is the charge per unit area (qzd8 is the charge in the diffuse double layer). It is noted that 41+ and 41are average potentials (macropotentials), $.e., potentials calculated without consideration of the discreteness of charge. A single value of e, which is not that for the bulk of the solution, is introduced in these equations, as discussed below. Equations of this type were used by a number of authors3 and particularly by Devanathan" and Levine, Bell, and Calvert12 for single-ion adsorption. (10) See ref 3, pp 60-63. (11) M. A. V. Devanathan, Trans. Faraday Soc., 50, 373 (1954). (12) S. Levine, G. M. Bell, and D. Calvert, Can. J. Chem., 40, 518 (1962).
volume 70, Number 8 August 1966
G. SUSBIELLES, P. DELAHAY, AND E. SOLON
2604
qM
s:
4;
q2-8
M '
$+
4-
4z
Figure 6. Model of the compact double layer.
From the Gouy-Chapman theory one has3 qZ-* = -2A sinh (Fdz/2RT)
FrTI+ = -FrNOI-
q1+
-l- A[exp(-Fdz/2RT)
= ql-
(4)
- 11
(5)
- A[exp(-Fd2/2RT) - 11 (6) (7)
There, & is the average potential in the outer plane of closest approach, c8 is the bulk concentration of TINOS, E* is the dielectric constant in the diffuse double layer, and R, T, and F have their usual meaning. We use here for E' the bulk value for water without consideration of saturation and the presence of the electrolyte. The resulting error is quite negligible as was pointed out by Grahame13and was more conclusively shown by Macdonald. l4 One finally has qb!
+ + + pz-s q1+
q1-
= 0
(8)
One of the foregoing equation is not independent and the system reduces to six equations with the six unknowns, +I+, $I-, 6, q1+, PI-, and p ~ - ~ .These quantities can be computed provided that $I+, XI-, and E are known (see below). The procedure is as follows. The values of qZ+, ql+, and ql- from eq 4 to 6 are introduced into eq 8, and the resulting equation in (bz is solved by iteration. Since (bz is now known, pz-s is given by eq 4 and pl+ and ql- by eq 5 and 6. Finally, +I+ and d1- are computed from two of the three eq 1 to 3. Selection of XI+, zl-,and e. This selection is really the crux of the problem since XI+, XI-, and e are known a priori. One could leave these quantities unknown and add restrictive conditions derived from a more detailed model, particularly one taking into account the discreteness of charge. Such a procedure would be more elaborate than the one adopted here, but it would The Journal of Physical Chemistry
lead to a more accurate description of adsorption with a sufficiently realistic model. The following more empirical approach was adopted. Values of z1+ and zl- were taken from previous work in which specific adsorption of only T1+ or KO3prevailed for all practical purposes. The value zl+= 2 A was selected as it fitted with previous work2 on specific adsorption of TI+ in TIF. Lower values of z1+ led to amounts of specifically adsorbed Nos- which were lower than those of T1+ for qm values a t which such a conclusion was manifestly absurd. Moreover, a value of z1+ appreciably lower than 2 A is unlikely since the ionic crystal radius of TI+ is approximately 1.4 A. The distance xl- = 3.15 A was adopted from an analysis of Payne's recent results15 for nitrate adsorption on the basis of the treatment of Levine, et al.,12 for low concentrations ($0.05 M ) . A selfconsistent interpretation followed for this value of zl-. This particular zl-can be interpreted by different models for specific adsorption of NOo- according to the orientation of the hydrated or partially hydrated NO3- ion. It must be stressed that values of XI+ and zl-departing slightly from the above ones might have been equally satisfactory. In fact we ascertained that ql+ and ql- varied only by a few per cent 3.5 from the range 1.8 xl+ 2.2 A and 3 XIA. The potentials were somewhat more sensitive. Calculations were carried out for E in eq 1 to 3 equal to 6, 8, and 9.6 (9.6 rather than 10 for no other reason than to simplify the'arithmetics somewhat). It turned out that calculated values of ql+ and ql- were not very sensitive to E but that calculated t$s strongly depended on E. The more consistent results corresponded to 6 < E < 7. It is noted that the constant E = 6 was chosen by Macdonald and Barlow16in a detailed treatment of the double layer for NaF. Thus, we may regard the value E = 6-7 as an average dielectric con52. The simplification stant in the region 0 < z resulting from the use of an average constant is considerable but is certainly open to criticism. An indirect check of the proper selection of XI+, XI-, and E was provided by the determination of the isotherms for T1+ and NOs- specific adsorption (see below). Amounts of Specifically Adsorbed 1'1+ and NO,-. The amount of specifically adsorbed T1+, calculated for E = 6, is plotted as q1+ against q M a t constant c8 in Figure 7 and against log a at constant q M in Figure
