1784
Langmuir 1995,11, 1784-1790
Adsorption of PbBr2 Complex on Mercury Electrodes Milivoj Lovrid” and Sebojka Komorsky-Lovrid Center for Marine Research Zagreb, “Rudjer Boikovit.” Institute, P.O. Box 1016, Zagreb 41001, Croatia Received November 14, 1994. In Final Form: February 3, 1995@ Adsorption of PbBrz complex to the surface of a mercury electrode was measured by pulse and dc polarography. Theoretical models were developed and the adsorption parameters were calculated from dc polarographic data. The adsorption of PbBrz occurs according to the surface complexationmechanism with strong lateral attractions in the adsorbed layer. The maximum surface concentration of adsorbed PbBrz is linearly correlated to the surface concentration of initially adsorbed bromide ions. The surface complexation constant is A3 = (7.5 T 1.5) x lo3M-l, Frumkin’s coefficient is approximatelyg = (4.1 ‘f 0.7) x 10l2 J cm2mol-2, and the maximum coordination factor is Cf4-l = 5.0 T 0.5. Each initially adsorbed bromide ion serves as a center of crystallization for a maximum of five molecules of PbBr2.
Introduction Some surface-active inorganic anions induce the adsorption of their complexes with metal ions onto mercury electrode~.l-~The adsorption of metal complexes with inorganic ligands is characterized by equilibria between the activities of free metal cations, free ligand anions, and their complex ions, both in the bulk of the solution and a t the surface of a mercury electrode. Usually, only one complex species is adsorbed. In majority of cases it is a neutral complex (e.g., PbIz, PbBrz, CdIz, Cd(N&, Zn(N& Zn(CNS)2,etc.),1-3,5,7-20 but there are also some negatively charged surface-active complexes: PbC13-,4,5BiC14-,21~22 CdBr3-,23and P b B r ~ c l - .The ~ ~ surface-active complex can be identified by comparing the dependence ofthe intensity of adsorption effects on the ligand concentration with the theoretical complex species distribution scheme calculated from the given s y ~ t e m . ~ , However, ~ ~ ~ , ~this ~ , procedure ~ ~ - ~ ~ offers no reliable information on the structure of the adsorbed complex s p e ~ i e s . ~Three , ~ ~ ,possible ~~ mechanisms of anion-induced adsorption are proposed. In the first one, the direct adsorption of the surface-active complex, without the participation of initially adsorbed ligand ions, is a s s ~ m e d . This ~ , ~ assumption has two consequences: the coordination number of the metal ion is Abstract published in Adoance A C S Abstracts, April 1, 1995. (1)Murray, R. W.; Gross, D. J. Anal. Chem. 1966,38,392. (2)O’Dom, G. W.; Murray, R. W. J . Electroanal. Chem. 1968,16, 327. (3)Anson, F. C.; Barclay, D. J. Anal. Chem. 1968,40,1791. (4)Caselli, M.; Papoff, P. J . Electroanal. Chem. 1969,23,41. (5)Barclay, D. J.; Anson, F. C. J . Electroanal. Chem. 1970,28,71. (6)LovriC, M.Anal. Chim. Acta 1989,218,7. (7)Tur’yan, Ya. I. J . Electroanal. Chem. 1992,338,1. (8)KlemenEiC, V.; FilipoviC, I. Croat. Chem. Acta 1969,31,29. (9)O’Dom, G. W.; Murray, R. W. Anal. Chem. 1967,39,51. (10)Lauer, G.; Osteryoung, R. A.Anal. Chem. 1969,41,1882. (11)Barclay, D. J.;Anson, F. C. J . Electrochem. SOC.1969,116,438. (12) Kowalski, Z.; Anson, F. C. J . Electrochem. SOC.1969,116,1208. (13)FilipoviC, I.; TkalEec, M.; Mayer, B.; Piljac, I. Croat. Chem.Acta 1969,4i,i45. (14)Sluyters-Rehbach, M.;Breukel, J. S. M. C.; Gijsbertsen, K. A.; Wijnhorst, C. A,; Sluyters, J. H. J . Electroanal. Chem. 1972,38, 17. (15)Herman. H. B.: McNeelv. R. C.: Surana. P.: Elliott. C. M.: Murray. R. W.Anal. Chem. 1974,46,“1258. (16)Tur’yan, Ya. I. Zh. Obshch. Khim. 1983,53,2314. (17)Montemayor, M.C.;FatasJ . Electroanal. Chem. 1988,246,271. (18)ZeliC, M.; LovriC, M. Electrochim. Acta 1990,35,1701. (19)Tur’yan, Ya. I. Elektrokhimiya 1990,26, 1182. (20)ZeliC, M.; Branica, M. J . Electroanal. Chem. 1991,309,227. (21) Komorsky-LovriC, 3.; LovriC, M.; Branica, M. J . Electroanal. Chem. 1988,241,329;1989,266,185. (22)Komorsky-LovriC, S.;Branica, M. J . Electroanal. Chem. 1993, 358,273. (23)ZeliC, M.; Branica, M. Anal. Chim. Acta 1992,262,129. (24)ZeliC, M.; Branica, M. Electroanalysis l992,4,623. (25)LovriC, M.; ZeliC, M. J . Electroanal. Chem. 1991,316,315. @
0743-746319512411-1784$09.00/0
not changed by the adsorption and the maximum surface concentration of the adsorbed complex is independent of the surface concentration of the adsorbed ligand. The second mechanism is based on the surface complexation concept: the adsorption is regarded as a formation of one or more additional coordination bonds between metal ion and ligands that are initially adsorbed on the m e r ~ u r y . ~ , ~ The main proof for the validity of this hypothesis is the experimentally obtained relationship between the surface concentration of the adsorbed ligand in the absence of metal ions (e.g., r C N S o and Tcl”) and the amount of metal complex adsorbed when the metal ion is added (rZn(CNSI3 and rPbC14, re~pectively).~ A base for the third mechanism is a concept of the competitive adsorption which applies to the adsorption of negatively charged complexes: if the charge of the mercury surface is conserved, the adsorption of one complex ion must be accompanied by the desorption of one ligand ion from the surface.6 Theoretical influences of the proposed mechanisms on dc polarographic waves of metal ions are reexamined in this paper. The model is applied to polarograms of lead ions in bromide media, and the parameters of the adsorption isotherm of the neutral PbBrz complex are determined. The previously published results18 apply to a single bromide concentration and here the relationship between the adsorption parameters and the surface concentration of the adsorbed bromide ions is investigated in order to distinguish the proper adsorption mechanism. The adsorption of lead ions was observed in ~hloride,4,5,14,24,26-28bromide,15,17,18,20,24,26,28-30 iodide,1,5,8,13,15,17,20,26,28-32and thiocyanata26B3 media. The dc polarograms of Pb(I1)in iodide8J3z31and bromidelamedia split into a diffusion controlled main wave and a n adsorptive postwave which indicates rather strong adsorption. In 0.117 M bromide solution, a t ionic strength I = 4 M, this adsorption follows Frumkin’s isotherm and the parameters arela rm= 1.35 x lop9mol/cm2,a = 3.9, (26)Barker, G.C.;Bolzan, J. A. Fresenius Z.Ana1. Chem. 1966,216, 215. (27)Timmer,B.; Sluyters-Rehbach,M.; Sluyters,J. H. J.Electroanal. Chem. 1968,18,93. (28)ZeliC, M.; Branica, M. Anal. Chim. Acta 1992,268,275. (29)Gross, D.J.; Murray, R. W. Anal. Chem. 1966,38,405. (30)Bond, A. M.; Hefter, G. J . Electroanal. Chem. 1971,31,477; 1973,42, 1; 1976,68,203. (31)Srinavasan, V. S.; Sundaram, A. K. Aust. J . Chem. 1962,15, 729,734. (32)Vargalyuk, V. F.; Loshkharev, Yu. M. Elektrokhimiya 1978,14, 1421. (33)Kalvoda, R.; Anstine, W.; Heyrovsky, M.Anal. Chim.Acta 1970, 50,93.
0 1995 American Chemical Society
Adsorption of PbBr2
Langmuir, Vol. 11, No. 5, 1995 1785
and P = 1.17 x lo4 M-l. A very high Tm value is in agreement with previously observed lead surface concentrations in bromide15 and chloride14media (9 x mol/cm2and 6 x mol/cm2,respectively), at potentials more positive than -0.2 V, which were attributed to the formation of adsorbed crystalline bilayers of PbBr215and PbC1214 on the mercury surface.
Experimental Section Analytical grade chemicals, Pb(N03)2, NaC104*H20, HClO4, and NaBr (all "Merck), and double distilled water were used. A digital multimode polarograph Autolab (Eco Chemie, Utrecht), an AT 286-16 personal computer with a printer, and the three-electrode system consisting of a n EG&G PARC Model 303A static mercury drop working electrode (SMDE, a medium drop with the constant area of 0.015 cm2 and formation time of 0.1 ~ , 3 ~ , 3a5 platinum wire as an auxiliary electrode, and Ag/ AgCY4 M NaCl reference electrode were used for sampled dc and pulse polarographic measurements. The drop time was 1s and the scan increment was 2.4 mV. The ionic strength and the acidity (pH 2) were adjusted by NaC104 and HC104, respectively. The solutions were deaerated by high-purity nitrogen and kept under a nitrogen blanket thereafter.
The Model A complex formation equilibrium in a large excess of ligand is assumed CM*
cMLl*
= CM,t*( 1
+ B)-l
= q(CL,t*YCM,t*(1
(1)
+ B)-'
which is determined by a given ligand concentration and electrode potential, fn+l= rLo/rMLn+l,ma is the ratio between r L o and maximum surface concentration of the adsorbed complex4and 6 = rML,+l/rMLn+l,max. It is assumed that the initial surface concentration of adsorbed ligand ions is set instantaneously. For the third mechanism, the adsorption of negatively charged complex MLn+l- is assumed. (c)The competitive adsorption:6 ML,+,-
z z (ML,Jads
A dc polarogram is calculated under additional assumptions that the redox reaction is reversible, that the product forms an amalgam, that the adsorption of MLzO (or ML3-) follows Frumkin's isotherm, and that a stationary, planar diffusion model applies to the sampled dc polarography on the static mercury drop electrode. The differential equations
rML,
= Pads,n
rML,,max
- rML,)-l
= rML,(rML,,~ax
+
Kn(CL,t*)nCM,t*(l Kn(CL,t*)n
t = 0, x
(1)
(4)
(L-)ads
(MLn+l-)ads (11) rML,+,
= An+l
r L o Kn(CL,t*)nCM,t*(l
+B +
An+lfnilK~(CL,t*)nCM,t*)-l fn+l;ln+icML,*
= e(1 - e)-'
acdat = D(a2cdax2)
(10)
I0:
c M , ~= c M , ~ * , cp
0:
C L , ~= CL,~*, CM
'0,x-m:
'M,t
2
0, 6 = 0
+
= C M , ~ ( ~ B)-l
+ 'M,t*, P'
-.
+
Pads,ncM,t*)-'
+
(9)
(3)
were Pads,n and rML,,m= are the adsorption constant and the maximum surface concentration of the adsorbed complex (MLnIads.
(b) The surface complexation:6 ML:
acM,Jat= D ( a 2 c M , J a x 2 )
have to be solved under the following initial and boundary conditions:
t Pads,nCML,*
*
rLo/rML,+l,max.
t 2 0, X (a)The direct adsorption: ML:
(L-)ads
(MLn+1-lads+ L- (111)
(2)
where = CML,*CM*-l(CL,t*)-J, B = x E l q ( C ~ , t * f , CM,t* and cL,t* are total bulk concentrations of metal and ligand ions, respectively, while CM* and CML,* are bulk concentrations of free metal ions Mn+and complex MLj(n-J),respectively, and KJ are stability constants. For the first and second mechanisms, it is further assumed that only the neutral complex species MLnois adsorbed.
+
(5)
(6)
where &+I = rMLn+l(rLCML,*)-l is the equilibrium constant of reaction 11, r L o is the ipitial surface concentration of the adsorbed ligand ions, in the absence of metal ions, (34)Bond, A.M.;Jones, R. D. Anal. Chim. Acta 1980,121,1. (35)Anderson, J. E.;Bond, A. M.; Jones, R. D.; OHalloran, R.J. J. Electroanal. Chem. 1981,130, 113.
D(aCM,/3x),=, = ilnFS + Tm d6ldt
D(&dax),,, = -ilnFS where S is the working electrode surface area, cp is the R TE, ~ 2 ~ amalgam concentration, E = nF(E - E ~ z ~ ~ Iand is the reversible half-wave potential of a simple redox reaction Mn++ ne P. The parameters 6, P, Tm, a, and b depend on the assumed mechanism. For the first mechanism (I): 6 = rML,/rML,,max, P = Pads,n, rm= rML,,", a = 2grML,,maw/RT, and b = Kn(cL,t*).n. For the second mechanism (11): e = rML,+l/rML,+l,max, p = f n + l L + l , rm= rLo/fn+l, a = 2 g T L o / f n + l R T , and b = Kn(qt*)". For the third mechanism (111): 6 = rML,+l/rML,+l,max, P = fn+@ex,n+l/CL,t *, rm= rLo/fn+l, a = 2grL0/fnflRT,and b = Kn+l(cL,t*)nT1. The other symbols have their usual meanings. Frumkin's isotherm is not inconsistent with the surface complexation and competitive adsorption concepts. Because of lateral attractions, the dissociation rate of the surface complex (MLn+l-)adsmay decrease as the surface coverage is increased, which results in An+l exp(a6) =
3 ~
LovriC and Komorsky-LouriC
1786 Langmuir, Vol. 11, No. 5, 1995
-
50
\
/
30
20
10
log(W/M)
iogllBil/Ml
Figure 1. Normal pulse polarography of 5 x M Pb(I1)in (I- 2)M NaC104 x M NaBr M HC104. Ionic strength I = 1 M (1)and 4 M (2, 3). Dependence of peak currents (A) and peak potentials (B) on the logarithm of bromide ions concentration. Curve 3 in part A is the NPP limiting current; t d = 1 s and t , = 50 ms.
+
0 -2
+
-1
--
,
5
L o g CBr / ( n o I ,'I
)
1
0
Figure 2. Theoretical distribution of PbBr2 complex species in the system (Z- x ) M NaC104 + x M NaBr, where Z = 1M (1)and 4 M (2). Stability constants: for I = 1M,log K1= 1.1, log K2 = 1.8, log K3 = 2.0, and log K4 = 1.5; for Z = 4 M,log K1 = 1.48, log KZ= 2.5, log K3 = 3.5, log K4 = 3.5, and log K5 = 2.7.43
Similar reasonings apply also to the third mechanism. The solution of eqs 9 and 10 was given p r e v i o ~ s l y . ' ~ , ~ ~
rML,+l(rLCML,*)-l.
-1.5
4
4 . i/,uA
Results and Discussion A redox reaction of Pb2+/Pb(Hg)in acidic perchlorate 3. and bromide media is fast and reversible37(k,= 3.3 C ~ / S ~ ~ and k , = 0.2 C ~ / respectively). S , ~ ~ In dc polarography, the 2. limiting currents are inversely proportional to the square roots of drop lifetimes (for 0.5 < t d < 2 s) independently 1' ofbromide c o n c e n t r a t i ~ n s . At~the ~ ~ SMDE, ~ ~ ~ ~ ~the ~ ~effect ~ of the drop formation and the spherical effect are both neghgible if t d 2 1s.34,35 In 1M NaC104 M HC104, .os E/V the relationship between the logarithm of the ratio i/(& - i) and the potential is a straight line with a slope of 30 Figure 3. Sampled dc polarogram of 6 x M Pb(I1)in 0.4 F 2 mV. If [Br-I = 0.5 M and [Pb2+1= M, this slope M NaBr + 0.6 M NaC104 + lov2M HC104. Drop lifetime t d = is 27 F 2 mV. 1 s and step increment AE = 2.4 mV. Polarogram consists of Identification of the surface-active complex species was discret current-potential points which are interconnected for achieved by the normal pulse polarography (NPP) of 5 x graphical presentation. M Pb(I1) in two media: ( I - x ) M NaC104 x M NaBr M HC104,where I = 1and 4. Theory predicts that suggests that the most probable surface active species is the heights of the characteristic NPP maxima (i&, which the PbBrp complex. appear as a consequence of reactant a d s o r p t i ~ n , are ~~-~~ Limiting currents of pulse polarograms (curve 3 in proportional to the fractions of the total metal in the form Figure 1A) are diminished by the adsorption indicating of the surface active complex.25 The parabolic relationthat the equilibrium with the bulk of the solution is not ships between the NPP peak currents of Pb(I1) and the attained during a drop lifetime.25,41142 logarithm of bromide ions concentration, which are shown Figure 1B shows the linear relationships between the in Figure lA, exhibit summits for log([Br-l/M) = -0.4 potentials of the NPP maxima and the logarithm of Brand -0.95, if the ionic strength is Z = 1 M and 4 M, concentration, with slopes of -70 and -77 mV, for I = 1 respectively. This is in the agreement with the theoretical and 4 M, respectively. According to the theory,25these distributions of PbBrp complex species, shown in Figure slopes are equal to -2.3p*RTlnF, where p* = p if the 2, which were calculated using the stability constants adsorption of the complex MLp followsthe first mechanism, recommended for these ionic strengths43and reach suma n d p p* ( p + 1)if it follows the second mechanism. mits for the same log([Br-]/MI values. This identity The slopes in Figure 1B correspond top* = 2.4 and 2.6, (36)PiZeta, I.; LovriC, M.;ZeliC, M.; Branica, M. J . Electroanal. Chem. for I = 1and 4 M, respectively, which indicates that the 1991.318. 25. adsorption of PbBrp probably follows the second mecha(37)Sharpe,T.F.In Encyclopedia ofElectrochemistry ofthe Elements; nism. Bard, A. J., Ed.; Dekker: New York, 1973;Vol. I, p 235. (38)Barker, G. C.; Faircloth, R. L.; Gardner,A.W.Nature 1968,181, The possibility of visualizing the distribution of a 247 particular ionic species, such as the one in Figure lA, (39)Barker, G.C.; In Transactions of the Symposium on Electrode offers a n insight into ionic equilibrium in the solution and Processes; Yeager, E. B., Ed.; Wiley: New York, 1961;p 325. (40)Flanagan, J. B.; Takahashi, K.; Anson, F. C. J . Electroanal. may be very useful for metal speciation measurements. 1977,85,257. Chem. 1977,81,261; M Pb(I1) in 0.4 M A sampled dc polarogram of 6 x (41)Puy, J.; Mas, F.; Diaz-Cruz, J. M.; Esteban, M.; Casassas, E. Anal. Chim. Acta 1992,268,261; J . Electroanal. Chem. 1992,328,271. NaBr + 0.6 M NaC104 + M HC104is shown in Figure (42) Mas, F.; Puy, J.;Diaz-Cruz, J. M.; Esteban, M.; Casassas, E. J . 3. It consists of a diffusion controlled main wave (il)and Electroanal. Chem. 1992,326,299;Anal. Chim. Acta 1993,273,297. very steep adsorptive postwave (id. Two waves are Martell, A. E. Critical Stability Constants; Plenum (43)Smith,R.M.; Press: New York, 1976;Vol. 4,p 118. separated by a sharp minimum (Aimdmin). According to
+
+
+
Adsorption of P b B r z
Langmuir, Vol. 11, No. 5, 1995 1787
0.7
t
p9
0.60.5.
-042.-
t 0
ow L I
/,
: , !Pbfi/lO'M 1 2 3 4 5 6 7 8 9 1 0 ~
,
.04
1
l o g f [ B r ~ l 0/ MI
,
,
1 2 3
[Pb"] / 10.' M ,
,
,
4 5 6 7 8 9 10
Figure 4. dc polarography of lead in 0.4 M NaBr + 3.6 M NaC104 + M HC101. Dependences of characteristic currents (A) and potentials (B) on the concentration of lead ions. The heights of the main wave (il), the postwave (iz), and the limiting current (ilim), are defined in Figure 3. Half-wave and the postwave (Ey& and potentials of the main wave (Euz)~ the potentials of maximum E,, and minimum Emin.t d = 1 s, AE = 2.4 mV.
the theory,& this minimum is a consequence ofvery strong adsorption of the reactant, and the steep postwave indicates lateral attractions in the adsorbed layer. It has been shown previously that the adsorption of PbBrz complex can be described by the Frumkin isotherm.18The postwave exhibits a broad maximum which probably belongs to the class of maxima of the third kind.45 However, the limiting current (ili,) is well defined. Other characteristic points, marked in Figure 3, are formal halfwave potentials of the two waves, ( E v z ) and ~ ( E ~ z )and z, the potentials of the maximum (Emax) and the minimum (Emin). Residual and capacitive currents can be neglected, except for the maximum, partly because of high metal concentration, and partly due to favorable properties of the sampled dc polarography on SMDE. Additional information on this system can be found in the previous communication.l8 The form of the polarogram depends on concentrations of both bromide and lead ions. For the constant bromide concentration from the range 0.1 5 [Br-l/M I0.9, the splitting of the polarogram into two waves under the influence of the increasing Pb(I1) concentration is shown in Figure 4A. The corresponding changes of the characteristic potentials are shown in Figure 4B. These relationships confirm the correct assignation of the waves and indicate the influence of strong lateral attractions on the postwave.1s,44,46~47 The influence of bromide ions is shown in Figure 5. Limiting currents are independent of Br- concentration, but the heights of the main wave (il) depend on [Br-I parabolicly, with the maximum for [Br-I = 0.4 M, in the agreement with the above conclusion about PbBrz being the surface-active complex. Differences between potentials of maxima and minima (Emax - Emin) are always between 2 and 6 mV, and the relationships between the other characteristic potentials can be seen in Figure 5B. The steepest postwaves (the smallest differences between Eminand (El/&)appear in 0.4 M NaBr, when the main waves are the highest. (44)LovriC, M.J . Electroanal. Chem. 1983,153, 1; 1984,175,33. (45) Frumkin, A. N.; Fedorovich, N. V.; Damaskin, B. B.; Stenina, E. V.; Krylov, V. S. J.Electroanal. Chem. 1974,50,103. (46)Laviron, E. In Electroanalytical Chemistry; Bard, A. J., Ed.; Dekker: New York, 1983;Vol. 12,p 53. (47)Laviron, E. J . Electroanal. Chem. 1974,52,395; 1976,62,245; 1979,105,25.
Figure 5. dc polarography of lead in (1 - x ) M NaC104 + x M NaBr M HC104. (A) Dependence of the main wave relative heights (il/il]m) on the bromide concentration. [Pb2+l/ M =6 x (l), 8x (21, and 1 x (3). (B)Dependence of the half-wave potentials of the main wave ( E I ~and z ) the ~ postwave (El& and of the potential of the minimum E,,, on the bromide concentration. [Pb2+l= 8 x M, t d = 1 s, AE = 2.4 mV.
+
Two series of experiments were performed. The concentrations of bromide ions were changed from 0.1 M to 1M in both series, but in the first one the ionic strength was adjusted to I = 1M by NaC104, and in the second series it was not. Polarograms of 6 x M, 8 x M, and 1 x M Pb(I1) were recorded in each bromide solution of both series. Each recording was repeated six times. In a particular bromide solution, for a particular Pb(I1) concentration, the reproducibility of characteristic potentials and currents was excellent: F1 mV and %5%, respectively. An average polarogram was represented by a set of average characteristic currents and potentials: i d i l i m , idiiim, Aimax/min/ilim, (EI/Z)I - (EI/z)z, Emax -Emin, Emax - (E1/2)2,and E m i n - (E1/2)2. Instead of simulating whole current-potential curves which are influenced by random errors, as we did previously,18 the average polarograms were simulated by forcing the model to fit the values of these characteristic currents and potentials. Some results of these experiments are shown in Figure 5. One can notice that they cannot be organized in smooth and coherent functions but are randomly scattered about freely assumed mean values (the tin lines). So, although the reproducibility of single polarogram was satisfactory, the dispersion of experimental results obtained from different bromide solutions decreased the precision of the determination of average adsorption parameters. The results obtained from the first series of experiments (I= 1M) were simulated assuming that PbBrz complex is adsorbed directly, according to the first mechanism. This was done for two reasons: firstly, because the actual surface concentrations of bromide ions were unknown, and secondly, in order to verify whether the results of simulations corroborate the basic hypothesis of this mechanism, or not. The simulation procedure was very precise: to fit exactly a certain set of experimentally obtained characteristic currents and potentials, a particular set of precisely determined parameters (p,Tmand g) was needed. Because of the dispersion of experimental data, the values of adsorption parameters obtained by the simulation are also scattered significantly about the mean values. However, by the combination of the mean values of adsorption parameters, no particular experimentally obtained polarogram, but only an imaginative average polarogram, can be simulated. So we decided to present the results of simulations in the form of Table 1. Analyzing the results in Table 1, one can notice that the
1788 Langmuir, Vol. 11, No. 5, 1995
Lourib and Komorsky-Lowrib Table 1 [Pb2+l= 6 x ~~
[Br-l/M
,m03 M-1
10-9 mol/cm2
g/1012 J cm2/mo12
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.70 1.70 2.05 2.05 1.70 1.60 1.60 1.50 1.30 1.70
0.80 1.07 1.15 1.14 1.22 1.19 1.26 1.30 1.40 1.54
5.50 4.98 4.69 4.84 4.52 4.71 4.42 4.43 4.34 3.78
rPbBrz,max,
M EN -0.400 -0.412 -0.426 -0.433 -0.434 -0.440 -0.441 -0.442 -0.441 -0.447
rBr,Eo 10-10
moVcm2
f3
ad103 M-I
1.87 2.17 2.34 2.50 2.66 2.75 2.86 2.98 3.08 3.24
0.234 0.203 0.203 0.219 0.218 0.231 0.227 0.229 0.220 0.210
7.27 8.38 10.07 9.35 7.80 6.92 7.05 6.54 5.91 8.08
1.90 2.14 2.30 2.48 2.62 2.71 2.81 2.92 3.00 3.18
0.156 0.178 0.230 0.225 0.202 0.226 0.207 0.223 0.224 0.212
9.63 9.08 7.09 7.14 7.94 6.64 6.78 5.83 5.36 6.60
1.87 2.11 2.29 2.47 2.60 2.69 2.80 2.90 2.98 3.14
0.144 0.185 0.183 0.190 0.198 0.177 0.207 0.228 0.229 0.196
9.04 7.56 7.64 8.68 7.56 9.04 5.79 5.26 4.80 7.13
[Pb2+]= 8 x 10-4 M
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.50 1.62 1.63 1.61 1.60 1.50 1.40 1.30 1.20 1.40
1.22 1.20 1.00 1.10 1.30 1.20 1.36 1.31 1.34 1.50
4.26 4.34 5.20 4.92 4.15 4.54 4.10 4.26 4.16 3.72 [Pb2+l= 1 x
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1.30 1.40 1.40 1.65 1.50 1.60 1.20 1.20 1.10 1.40
1.30 1.14 1.25 1.30 1.31 1.52 1.35 1.27 1.30 1.60
4.00 4.67 4.56 4.15 4.02 3.71 4.04 4.29 4.19 3.33
adsorption constant Pads,2 does n_ot depend on bromide concentration. Its mean value is Pads,2 = (1.5 F 0.2) x lo3 M-l. On the contrary, the maximum surface concentration of (PbBrz),d, clearly increases with increasing Br- concentration. The mean values of rpbBrz,mm can be described by the approximative equation rpbBr2,max = (1 0.5[Br-1) x mol/cm2. To analyze this dependence more exactly, it was assumed that the presence of C104- ions does not change significantly the surface concentration of Br- ions. If it is true, then r B 2 can be calculated from data published by Lawrence et aL4* These data are compiled in Figure 6. For each polarogram of the first series, a particular characteristic potential E = ( ( E I I z ) ~ (E1/2)2)/2 was calculated and the corresponding surface concentration of Br- ions was readout from Figure 6. These data are reported in the fifth and sixth columns of Table 1. The values of rpbBr2,max obtained by the simulation are plotted against the values of r B r , E o in Figure 7, and the significant correlation is obtained. This relationship clearly proves that the adsorption of PbBrz contradicts the basic hypothesis of the first mechanism: the independence of the maximum surface concentration of the surface-active complex from the surface concentration of the ligand. So the adsorption of PbBrp must be analyzed according to the second mechanism. This conclusion was confirmed by the fact that the ratiofi = rBr,Eo/rpbBr2,ma did not depend on bromide concentration. The values of this ratio are
+
+
(48) Lawrence, J.;Parsons, R.; Payne, R. J.EEectroanal. Chem. 1968, 16, 193.
-0.396 -0.417 -0.431 -0.436 -0.439 -0.444 -0.447 -0.448 -0.450 -0.454
M
-0.399 -0.421 -0.433 -0.438 -0.441 -0.447 -0.449 -0.451 -0.453 -0.458
listed in the seventh column of the Table 1. Their mean value is f3 = 0.21 T 0.02. The relationship between the adsorption constant Pads$ of the first mechanism and the surface complexation constant 23 of the second mechanism is simple: P&,2 = f&. The values of 23 are listed in the last column of the Table 1. Their mean value is 23 = (7.4 T 2.5) x lo3M-l. The dependence of Frumkin's coefficient g on the bulk concentration of bromide ions is shown in Figure 8. The decreasing of the mean values of the coefficientg with the increasing of Br- concentration can be approximated byg = (5 - 1.3[Br-l) x 10l2J cm2/mo12. However, the mean values of Frumkin's factor a = !&rPbBrz,max/RT increases with the increasing of Br- concentration: si = 4.2 0.4[Br-], in agreement with increasing of rpbBr2,max. If the extreme values of g , calculated for [Br-I = 0.1 and 1M, are omitted, the results of simulations can be interpreted as being independent of [Br-I, with an average value g = (4.4 F 0.4) x 10l2J cm2/ mol2. The precision of the measurements does not allow distinguishing between these two possibilities. These results indicate that the adsorption of PbBrz complex should be simulated according to the second mechanism if the correct adsorption parameters are to be calculated. Since the values of r B r o were measured in the solutions of various ionic strengths,43the experiments of the second series were performed under similar conditions. The results of simulations of the polarograms of this series are reported in Table 2. According to the second mechanism, the adsorption of PbBrz is defined by three
+
Adsorption of PbBr,
Langmuir, Vol. 11, No. 5, 1995 1789
+ t
y+ + +
+ 0.5
1
.
[ B i l /M Figure 8. Dependence of Frumkin's coefficient g on bulk concentration of bromide ions. All data are as in Figure 5. Table 2
[Pb2+]= 6 x
M
g/10l2J -0.4
-0.5
E/V
Figure 6. Dependence of surface concentration of bromide ions on electrode potential and bulk concentration of bromide
ions, as compiled from ref 48. CBr-IN = 0.01 (1),0.02 (2),0.03 (3), 0.04 (4), 0.05 ( 5 ) ,0.06 (6), 0.07 (7),0.08(8),0.09 (9),0.1(lo), 0.2 ( l l ) , 0.3 (121, 0.4 (13),0.5 (141, 0.6 (151, 0.7 (161, 0.8 (17), 0.9 (181, and l ( 1 9 ) .
[Br-l/M
f3
A3/103M-l
0.2 0.3 0.4 0.5 0.6 0.7 0.9 1
0.191 0.199 0.220 0.218 0.220 0.210 0.232 0.211
8.91 8.50 8.00 7.80 7.27 8.02 5.60 8.10
cm2/mol2 E N 4.80 4.47 4.80 4.35 4.40 4.12 4.51 3.78
[Pb2+]= 8 x
+
+
.r
0.179 0.172 0.183 0.217 0.186 0.183 0.213 0.205 0.209
+
I t
I
*
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 1
2
8.38 9.30 8.20 7.00 8.60 8.20 6.10 5.85 6.70
5.09 4.26 4.10 4.74 3.84 3.65 4.10 3.87 3.66
-0.419 -0.421 -0.436 -0.432 -0.435 -0.440 -0.444 -0.446
2.12 2.37 2.48 2.67 2.79 2.87 3.06 3.25
M
-0.406 -0.422 -0.429 -0.442 -0.439 -0.441 -0.445 -0.448 -0.454
1.83 2.10 2.32 2.44 2.61 2.73 2.83 3.02 3.18
[Pb2+]= 1 x
2.5
3
Figure 7. Dependence of maximum surface concentration of adsorbed lead complex on thejnitial surface concentration of bromide ions at the potential E = ((EI/Z)I+(E~2)2)/2.All data
are as in Figure 5.
independent variables: 1 3 , f3, and g. The main characteristic of these simulations is the absence of rpbBrz,mm. Instead, the values of r B r o reported in ref 48 and shown in Figure 6 were used. One can notice that these r B r o values depend significantly on the potential. So, the simulation procedure was adapted to include the change of r B r o from drop to drop. To give the reader a possibility to roughly estimate a n actual surface concentration of Br- ions in the vicinity of characteristic potentials of the polarograg, the values of r B r , E o which correspond to the potential E = ((E1/2)1+(Ey2)~)/2 are listed in Table 2. The simulations of polarograms corresponding to [Br-] = 1M show that the change of r B r o with the electrode potential has no significant influence on the adsorption parameters
[Br-IN 0.1 0.3 0.4 0.5 0.7 0.8 0.9 1
f3
A3/103 M-l
0.187 0.149 0.212 0.171 0.178 0.196 0.168 0.190
6.95 9.30 6.50 8.75 7.30 6.12 7.74 7.40
g/10l2 J cm2/mo12 5.38 3.56 4.63 3.48 3.44 3.67 3.12 3.24
rBr,Eo/
EN -0.409 -0.435 -0.442 -0.444 -0.446 -0.450 -0.450 -0.456
mol/cm2 1.81 2.28 2.44 2.59 2.82 2.91 3.00 3.16
and g (compare Tables 1and 2). This means that the listed rBr,Eo values can be considered as the average surface concentrations of bromide ions in the potential range in which the polarogram develops. This fact justifies the calculations of f3 and 1 3 values listed in Table 1. The results in Table 2 show that both the ratio f3 and the surface complexation constant 1 3 do not depend on bromide coqcentration. Their mean values are f3 = 0.20 F 0.02 and A3 = (7.5 F 1.5) x lo3M-l, similarly as in the first series of experiments. The results for the coefficient g and Frumkin's factor af:= .&rBr,Eo/faT are also similar
f3, A3,
LovriC and Komorsky-LovriC
1790 Langmuir, Vol. 11, No. 5, 1995 to those which are shown in Figure 8: g = (4.8 - 1.3[Br-I) x 1012 J cm2/mo12,but g = (4.1 T 0.7) x 10l2J cm2/mol2 if the extreme values are neglected, and tis = 4.2 0.4[Br-l. For comparison, the surface complexation constant was determined by the simulation of dc polarograms and pulse M Pb(I1) and 5 x M Pb(II), polarograms of 1 x respectively, in bromide solutions of various ionic strengths, using previously developed algorithm^.^^ At this concentration of lead ions, the dc polarogram is a single wave (the postwave, see Figure 41, irrespective of the bromide concentration, and the adsorption of PbBrz can be approximated by the linear isotherm. The mean value of the calculated constants A3 = (8 F 2) x lo3 M-l is in agreement with the results of other simulations. These simulations suggest that the adsorption of PbBrz complex occurs as the Eurface complexation, with the maximum coordination Cf3)-l= 5.0 T 0.5. This coordination applies to the conditions of totally covered surface, when the adsorption process has characteristics of surface c r y ~ t a l l i z a t i o n as , ~ ~confirmed by very high values of Frumkin’s coeff~cient.~~ Each initially adsorbed bromide ion serves as a center of crystallization for, in average, five molecules of PbBrz. All of them do not have to be in direct contact with the electrode surface but can be situated in the space around adsorbed bromide ion. This can explain the maximum surface concentration of (PbBrz)ads which is higher than the geometrically estimated limiting monolayer concentration of bromide ions (1.1x moY cmZ).lJ5This concept implies that the lowering the surface coverage means the decreasing of an average number of PbBrz molecules which are bound to a single, adsorbed bromide ion. This is also a modification of the original concept3r5because the bonds between one (Br-)ads and several PbBrz molecules cannot be all the coordination bonds. Important is that PbBrz can be attached only to initially adsorbed bromide ions and not anywhere else a t the surface. This can explain the observed linear relationship between rPbBrz,max and rBr,Eo.
+
(49)Sadkovski, A. J . Electroanul. Chem. 1979,97,283; 1979,105, 1.
The mean values of rpbBrz,max and g, calculated by this simulations, are in the agreement with our previous results,18but the adsorption constant Pads,z is about 6 times lower. This difference can be explained by the influence of the increasing ionic strength (I = 4 M previously,18) similarly as demonstrated for the adsorption of BiC14-,22 but it needs further investigation. A very high value, Pads,Z = 3.1 x IO4 M-l, was calculated from the change of dc polarographic half-wave potentials, assuming that the adsorption of PbBrz obeys the Langmuir i ~ 0 t h e r m . lThis ~ Pads,Z probably corresponds to the product ,&I= P&,Z exp(a0)of Frumkin’s isotherm, which may appear constant if neither bromide nor lead ion concentrations are changed. Compared to anion-induced adsorptions of other metal ions, the adsorption of PbBrz appears equally as strong a s the adsorption of PbC13- (Pads,3 = 1.5 x lo3 M-’L4 stronger than the adsorptions of In13 and CdBr3- (Pads,3 = 3.94 x lo2 M-l and &s,J = 5.6 x lo2M-l, respectively)17 and much weaker than the adsorption of CdIz (Pads,Z = 1.38 x lo5 M-l l7 and A3 = 6 x lo5 M-l l6J9). One can notice here a n interesting coincidence that the ratio between two independently measuredl6J7Jgadsorption constants of CdIz is similar to the ratio f3 calculated in this paper: Pads,&3 = 0.23. Another criterion of the strength of the adsorption is the constant of the linear isotherm. It is defined as KH = Pads,nrML,,max, or KH = An+JLo. For the adsorption of PbBrz, it depends on both the concentration of bromide ions and the electrode potential, but to the first approximation rpbBr2,mm = (1.25 7 0.15) x moYcm2,if 0.2 M < [Br-I < 0.8 M. So, KH = (1.9 7 0.5) x cm. According to this criterion, the adsorption of PbBrz is weaker than the adsorption of BiC14- complex (KH= 8 x cmZ2).However, this criterion is not realistic. The effective adsorption constant of PbBrp increases with the increasing of the surface coverage because of lateral attractions between adsorbed molecules. So, its influence on dc polarograms is significantly higher than the influence of BiC14- adsorption. LA9408984
