Thallium bromide adsorption and two-dimensional crystallization on

Thallium Bromide Adsorption and Two-Dimensional Crystallization on Mercury Electrodes C. Michael Elliott’ and Royce W. Murray’ Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, N.C. 275 74

The surface excess of TI(I) on Hg Is dependent on [Br-1, rising gradually to an adsorption isotherm discontinuity foilowed by a plateau value of rTl, a second discontinuity, and plateau. The two discontinuities are described a second by the solution condition [Tl+][Br-] = constant, and are interpreted in terms of successive monolayer precipitations of TiBr controlled by surface solubility product constants. The thermodynamic AHo and ASo parameters are determined for the monolayer TiBr crystal. The adsorption of TI(I) in the pre-discontinuity isotherm region is not controlled by as in anion-induced adsorption. The adsorption reaction is given by (TiBr).oln The pre-discontinuity isotherm data fit a Frumkin isotherm with an attractive interaction parameter CY of sufficient site to predict the isotherm discontinuity.

rm

rsr

The adsorption of Pb2+ on Hg electrodes from aqueous halide solutions appears to be exceptional (1-5), exhibiting features not found for other adsorbing metal complexes (6). One property in particular is the appearance, in plots of r P b vs. solution [X-1, of large, discontinuous increases in r P b to an adsorption plateau value ( I ) . Observing that the r p b discontinuities occur for a solution condition [Pb2+][X-I2 = constant, the effect was interpreted in terms of two-dimensional monolayer precipitation of PbXz due to a surface solubility lower than that of “bulk” PbX2. Subsequent work showed that these unusual adsorption isotherms occur also for Tl+ in aqueous halide. For T1+ in bromide solution, two discontinuities occur in isotherm plots of rT1 vs. [Br-1. A preliminary report interpreted this as formation of a crystalline bilayer (7). We have examined the rT1 isotherm discontinuities in detail and describe here the physical properties of the adsorbed TlBr surface crystal. The portion of the adsorption isotherm preceding the discontinuities has also been investigated and found to be of the Frumkin type with an attractive interaction parameter. Measurements of rT1 are conducted with double potential step chronocoulometry at a hanging mercury drop electrode equilibrated with the solution of T1+ and Br-.

EXPERIMENTAL Chemicals. Water used for adsorption experiments was house distilled water passed through ion exchange and charcoal columns, distilled through a Corning all-glass still, and redistilled from basic 0.01 M KMn04 under pure 02. In several experiments where utmost purity was desired, this water was further subjected to a single distillation through a Pt pyrolysis column (8). All commercial samples of KN03 supporting electrolyte proved to have appalling levels of organic and insoluble impurities. The former evaded removal by multiple recrystallizations. Adequate purification was achieved by fusing the recrystallized material in a 500-ml round-bottom flask at 350 “C and aerating with pure 0 2 for 30 min. The melt was poured into an inch of cold distilled water, then recrystallized twice further. T1+solutions were prepared from reagent grade TIN03 (K & K). Current address, Department of Chemistry, Stanford University, Stanford, Calif.

Cell and Electrodes. The working electrode was a 0.02-0.03 cm2 hanging mercury drop (HMDE) dispensed from a Brinkmann microburet. The SCE reference electrode had a cracked glass junctioq to avoid chloride contamination. The cell was a 100-ml beaker cell thermo8Jated to 0.2 “C. Techni,que for rT1 measurement. The adsorption of T1+ was evaluated with double potential step chronocoulometry (DPSCC) (9, 1 0 ) on a HMDE equilibrated at Einit with the stirred solution for (typically) 1 min. Adsorption isotherms and the rTI discontinuities were determined by measuring rT1 in 1 M KNO3 at constant [TI+],gradually increasing [Br-1. Measurements at constant [Br-1, gradually increasing [Tl+],produce equivalent data. The DPSCC experiment involves a potential step from Ei,it to the T1+ reduction wave plateau (Efinal= -0.7 V) for some time T (ordinarily 100 msec) and returning to Einit for an equal time. Plots of charge vs. f(t) (9, I O ) for the forward and reverse steps afford values of Qads (nFArTI) and Q d ] (difference of double layer charge between Einit and Efinal).The DPSCC experiment was used in a computerized format ( 1 , I I ) . Theory of the experiment (9, 10) assumes immediate re-equilibration of the adsorbed layer in the reverse potential step. In experiments where rT1 is on the isotherm plateau, this assumption is violated, but errors in rT1 due to possible change in the double layer charge at Einitoccasioned by the adsorption are expected to be insignificant since on the plateau rT1 is so large that Qads >> Qdl. This problem has recently seen detailed discussion (12). r B r in K N O B Solution. Data for r B r at Einit in 1 M KN03 are needed to assess the role of anion induced adsorption (6) in the T1+ adsorption. A simple potentiostatic procedure was devised to measure rBr in which a slow drop time DME was potentiostatted at Einit in the solution of interest for 10 sec of drop life and then stepped to -1.0 V vs. SCE (FBI = 0). The charge A Q passed for this step was measured after it reached a constant value (-20 msec). This experiment was performed for a series of [Br-] at each given Einit. The AQ vs. RT In [Br-] data were differentiated (by least squares fitting to a moving four-point polynomial whose center point derivative was evaluated) to provide (dqsinit/dp),(where dp = dpK& N dpBr = d(RT In [Br-] since [K+] N constant) as a function of Einit and [Br-1. At the most negative Ei,it (-0.60 V), (dqElnit/dp)is zero within experimental error. These data were next numerically integrated from -0.60 V to Einit for each [Br-1, the integrals corresponding to r B r according to the relation (13).

(3) a&

&it

=(”) aE

fl

Data acquired in this fashion are given in Table I. If the potential step is made much earlier in DME drop life, both AQ and r B r decrease owing to adsorption nonequilibrium. For times exceeding 5 sec, r B r was essentially independent of step time down to [Br-] 1 mM for all Einitexamined.

-

Table I. Surface Excess Values of Bromide Ion in 1 M KNO, in pC/cm2 E vs. SCE

(Br-) rnM 0.40

4.52

8.28

15.18

... ... ... ... . . . . . . . . . . . . 0.6 . . . . . . . . . 0.7 0.9 . . . . . . . 0.9 1.4

0.6

0.8

1.0

1.6

1.6 2.6

1.7

2.6

3.9

2.6

4.2 5.6 7.4 9.7

3.8

5.7

0.81.11.4 1.0 1.5 1.8

3.9 5.7

-0.42 . . -0.38 -0.34 -0.30.. -0.26...

1.342.47

.

-0.22 0.7 -0.18 0.8 1.8 -0.10 1 . 5 -0.14

0.73

2.1

3.1

27.8

51.0

8.1 12.6 5.6 8.1 11.4 15.1 8.0 11.4 15.1 21.0

2.1 2.7 4.7 1.8 3.0 4.2 7.0 11.6 16.1 20.6 26.6 2 . 5 4.4 6.7 10.6 17.0 2 3 . 0 28.3 3 4 . 9 1.4

ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976

259

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I

5

0

w

20

15

IO

[Br-I, mM

Figure 1. TI(I) surface excess at Hgo as a function of [Br-] from 1.0 m M TI(I) solution HMDE pre-equilibrated 60 sec; 1 M KN03: hnn = -0.1 volt (0),-0.2 volt (A),-0.3 volt ( 0 ) €tina, ; = -0.7 volt vs. SCE. Arrow indicates bulk solution saturation with respect to TIBr,

This analysis of r B r is relatively unrefined and the uncertainties in Table I are moderate. Use of Equation 1 strictly requires constant total ionic strength; we maintained [KN03] constant to avoid changes in the competing NO, adsorption and so ionic strength varies by some 6% through the data. We believe the data are sufficiently precise, however, for the purposes at hand. Our r B r values are lower than the literature values available (14, 1 5 ) at the higher [Br-] reflecting the competing Nos- adsorption in our solutions. rTI

n

ISOTHERM DISCONTINUITIES A N D Ksurp

Crystalline Bilayer Model. Double potential step chronocoulometric measurements of rT1 as a function of [Br-] at given Einitand temperature produce isotherms like those shown in Figure 1. The isotherm discontinuities were interpreted in a preliminary report ( 7 )as reflecting surface solubility-controlled formation of two successive crystalline monolayers of TlBr. The most direct evidence for the involvement of the solubility of monolayer TlBr in the isotherm discontinuities comes by examining the combinations of [Tl+] and [Br-] at the discontinuities. For given supporting electrolyte, Einit and temperature, a discontinuity is very accurately described by the relation [Tl+][Br-] = constant over more than a 1OX range of concentration (Table 11). This is true whether the isotherm is measured as rT1 vs. [Br-] at constant [Tl+], or vice versa. The constant, which we term Ksurface product or Ksurp,has the form of a solubility product constant and has a value lower than that of “ordinary”

-5

-.k -;

-8 E, v o l t s v s S.C.E

-.9 - 1 ‘ 0

Figure 2. Linear sweep chronoamperograms of 1 mM [TI+] in 1 M KN03 at 25 OC at a series of [Br-1; sweep rate = 0.1 V/sec

bulk TlBr (measured polarographically as 16.5 x in 1 M KNOB). When the product of solution [TP] and [Br-] exceeds the Ksurp for a TlBr monolayer, surface phase formation occurs. r T I then rises to a plateau of magnitude entirely consistent with geometrical requirements for a monolayer section of a TlBr crystal of body centered cubic CsCl structure ( 7 ) .That the second isotherm discontinuity represents formation of a second crystalline layer (rather than structural modification of the first) is shown both geometrically ( 7 ) and by cyclic voltammetry in which T1+ of the first and second plateaus give separate and distinct adsorption waves (Figure 2). The parameter Ksurpcan be considered an equilibrium constant. We describe now several factors which affect Ksurp,including competitive coordination of T1+, solution temperature, extremes of [T1+]and [Br-1, and the potential (Ei,it) of the electrode on which the monolayer crystal forms. Competitive Coordination of T1+. Ksurpvaries with the supporting electrolyte concentration and anion due to the weak coordination of T1+ by the NO, and F- anions. Table I1 shows that if the [T1+] used in the calculation [Tl+]free[Br-]= Ksurpis corrected for this coordination, the surface solubility product is relatively invariant with electrolyte. Two other ligands were added to 1 M KNOBsolutions as competitive coordinators of T1+. The addition of EDTA gives rTI isotherms like those of Figure 1. Values of Ksurp derived from these isotherms are consistent with those of

Table 11. KsurpDerived from the Product [Tl+][Br-] at r T I Isotherm Discontinuitiesa Discontinuity

x 1066 K U p ‘ X 1O6C 1.0 M KNO, -0.3 1st 5.0-0.5 9.73 0.38 2.85 0.10 -0.3 2nd 5.0-0.5 13.43 0.49 3.94 0.14 -0.2 1st 5.0-0.5 10.7 0.85 3.15 0.25 4.62 2 0.13 -0.2 2nd 5.0-0.5 15.7 0.45 -0.3 1st 1.0 3.75 3.03 0.1 M KNO, -0.3 2nd 1.0 5.67 4.57 1.0 4.37 3.52 -0.2 1st 1.0 7.20 5.81 -0.2 2nd -0.3 1st 1.0 6.0 2.66 1.0 M KF 3.88 -0.3 2nd 1.0 8.75 -0.2 1st 1.0 6.30 2.84 -0.2 2nd 1.0 10.25 4.55 a Averaged data from Table I, reference 7 are included here for comparison purposes. bKsurp = [T1+] [Br-1. In 1 M KNO,, averages of duplicate experiments at each of four concentrations between 5.0-0.5 mM TIf. CKsurpcorrected for TI+ coordi-, nation by supporting electrolyte ion using constants (16)KTU\IO,= 2.4, K T F = 1.25. %it

Electrolyte

~

260

ANALYTICAL CHEMISTRY,

~

[Tl+],rnM

~~

VOL. 48, NO. 2, FEBRUARY 1976

Kw

* ** *

***

Table 111. Thermodynamic Parameter9 for Bulk and Monolayer TlBr Ejt

oc

-11

-11

ASoppt,,, cal/mol-deg

-21.2 f 0.26 -13 180 ? 70b -22.6 ? 0.3 -13 550 f 90 -14 730 f 630 -26.7 k 2.2 -0.1 -13 480 f 40 --22.9 f 0.1 -0.3 -13 530 f 33 -23.4 f 0.1 -0.2 ... -12 740 f 140 -20.9 f 0.5 Bulk a Values of AH" and A S obtained from Figure 3 slopes are for the dissolution reaFtion; signs are reversed in Table to represent precipitation reaction. b Standard deviation of sloges taken for T < 25OC except for 0.1 where only T < 20 C data was used. -0.3 -0.2

3 5-

32

AHDppt,,, cal/mol

tinuity

5c

-I4 3 '

Discon-

I 33

34 IVTx

35

a4

36

37

Figure 3. Temperature dependence of Ksurp in 1 M KN03 (solid lines) Ksurp measured at 1 m M [TIf] by varying [Br-] through isotherm discontinuity. SCE reference maintained at 25 "C.First discontinuity measured at hna = -0.1 volt (A),-0.2 volt ( O ) ,-0.3 volt (H):second discontinuity measured at €init = -0.2 volt (V),-0.3 volt (x). Ksp for bulk solution precipitation measured polarographically (- - 0 - -)

1st 1st 1st 2nd 2nd

crystal is enormously different from bulk TlBr, as expected if the two materials have similar crystal structures. The observed enthalpy difference implies that the interaction between the adsorbed monolayer crystal and Hg exceeds that between a monolayer TlBr crystal and the surface of a bulk crystal. A partial analysis of the stabilization energy is obtained by considering the thermochemical cycle:

Tlg+

I -

+ Br,-

C,"

C?D

EDTA-free solutions provided the relation used to calculate Ksurpis

TlBr(2D1,

Ksurp= ([Tl+] - [EDTA]) [Br-] T h e other added ligand was so42-. Reliable values of K T ~ s o ~are - not available, so the effect of so42-on Ksurp was employed to evaluate this stability constant. With Einit = -0.3 volt and [Tl+]= 1 m M in 1 M KN03, Ksurpwas determined for solutions containing 0.05, 0.10, 0.20, 0.30, and for [S042-]= 0, 0.40 M Na2S04. Taking Ksurp= 9.6 X values of K T I S O ~of- 2.22, 2.40, 2.77, 2.59, and 2.50, respectively, were calculated from these data. These tests of Ksurpas an equilibrium constant were completely satisfactory. Clearly, insofar as competitive equilibria are concerned, the TlBr surface precipitation is subject to influence by such equilibria in a normal and predictable manner. ICsurpas f(T). The greater solubility of bulk TlBr as compared to monolayer TlBr crystals on Hg requires that the thermodynamic components which constitute K,, and Ksurpbe different. T o assess AHo and A S o , K,, and Ksurp were carefully measured as a function of temperature with results shown in Figure 3 and Table 111. At the higher temperatures, log K vs. 1/T plots are nonlinear to an extent depending on the value of chosen. This curvature is discussed in a later section. At lower temperatures, which correspond experimentally to lower [Br-] levels, the plots of Figure 3 are quite linear. A H o and A S o derived from the lower temperature data are given in Table I11 for the precipitation reaction direction. As far as we are aware, these are the first such thermodynamic parameters reported for monolayer crystals. The data in Table I11 show that precipitation to form a monolayer TlBr crystal involves a larger exothermic enthalpy and a larger entropy decrease than precipitation to form bulk TlBr. It follows that the controlling cause of the lowered monolayer TlBr solubility must be an enthalpy effect. Neither AHopptn or ASoPptn for the monolayer TlBr

AH*&

TIBr(3D),

I

AH"?,,- AH",,,

TIBr(ZD),d.

where U 3 D is the bulk TlBr lattice energy from the usual Born-Haber cycle, A H 0 2 ~and m 0 3 D are enthalpies of Table 111, and m a d s r the quantity sought, is the adsorption energy of the 2-D crystal plus any solvation processes. The lattice energy for the two dimensional crystal, U ~ Dis, for a standard state consisting of a single 110 plane (7) of TlBr located in a vacuum, and is obtained by calculating from ionic geometry and the bulk lattice energy the stabilization interactions in the single plane. The bulk lattice energy is 170 kcal/mol ( 1 7 ) , U ~ isDcalculated as -155 kcal/mol and A H 0 2 ~- A H 0 3 D < 1 kcal/mol. The stabilization energy is thus -16 kcal/mol. We can only speculate about the component factors of m a d s . Solvation of the solution side of the TlBr monolayer crystal is probably exothermic, as is the coulombic interaction between the electrode charge and anions of the crystal. A rough estimate of the latter factor suggests it to be relatively small. Herman et al. ( 1 ) found that PbF2 neither adsorbs nor forms surface crystals, in contrast to PbBrz and PbI2. Fluoride ion does not exhibit strong covalent interaction with mercury. We believe that the covalent term of AH& is perhaps its most important component. The entropy term for TlBr precipitation is large and positive, so the ionic ordering effect exceeds that of ionic desolvation. The entropy terms of Table 111, like enthalpy, were examined in terms of deposition of monolayer TlBr crystal on Hg surface as compared to deposition on bulk TlBr crystal surface. The deposition of monolayer TlBr on Hg is entropically the slightly less favorable event. The following might contribute toward this difference. (i) The double layer may be more ordered at a monolayer T1-on-Hg surface than on a Hg surface. (In view of the decrease in q m observed (vide infra) on the TlBr adsorption isotherm plateau, this explanation seems unlikely.) (ii) The vibrational freedom of T1+ and Br- in monolayer TlBr is less than that in bulk TlBr. (iii) There is creation of surface order in the


261

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l

l

I

I

I

I

I

t

-.8

-.4 0

8 -.E -.4 Log ([TJ'I x IO3)

4

0

.4 .8

Figure 4. Ksurpas a function of [TI'] (dashed curve). Numbers on curves represent first and second discontinuity. Solid curve is Ksurp correctedfor TlBr complex formation in solution

Hg phase by bonding of surface Hg atoms to the geometrically fixed array of Br- in the monolayer TlBr crystal. Speculating that the last of these may be the most important term would be entirely consistent with our thoughts on m a d s given above. Table I11 shows that the thermodynamic parameters for the second adsorption isotherm discontinuity also differ from those of bulk TlBr precipitation. The definition of Ksurpfor the second discontinuity includes the thermodynamic effects of the first discontinuity, so actual differences of the second crystal monolayer thermodynamic parameters from bulk AHopptn and ASoppt, values are fairly small, and numerically too uncertain to merit any attempt at analysis. KsUrpas f(l"Br). The range of [Tl+] useable in studying Ksurpis roughly 0.1-10 mM. The upper [Tl+] limit occurs because in the DPSCC experiment at high [T1+],the charge due to adsorbed TI+ becomes inordinately small compared to that from diffusing T1+.The lower [Tl+] limit occurs because a t low [Tl+] a longer stirring period is required to establish adsorption equilibrium near the isotherm discontinuity, and this apparently also transports sufficient adsorbable impurities to the electrode to make rT1 poorly reproducible. Ksurpis invariant with the [TI+]used in establishing the rT1 adsorption isotherm at the high [Tl+] limit, but at the low [Tl+] limit Ksurpincreases. This is shown in Figure 4 for Einit = -0.2 and -0.3 volt. The change in Ksurpis only partially erased by correcting for TlBr complex formation ( K T ~=B2.09) ~ (16) and must therefore reflect some surface phenomenon. The Ksurpincrease at a given Einit occurs at about the same [Tl+] and [Br-] for the two isotherm discontinuities. Significantly, increase occurs a t lower [Br-] for the more positive Einit.In the previous section we saw that Ksurpdeviated from strict equilibrium constant behavior at higher temperatures, becoming enlarged at the more positive Einit. There is one common factor in the onset of each of the above changes in Ksurp;this is increasing adsorption of bromide. At low [Tl+J, high [Br-] must be used (to exceed Ksurpand cause surface precipitation), leading to large r B r . r B r naturally increases at a more positive Einit. At higher temperatures, the increase in Ksurpnecessitates use of larger [Br-] with consequence of increased r B r . If one furthermore examines each circumstance under which Ksurpbecomes enlarged, it occurs whenever r B r exceeds a critical mol/cm2. Below this critical value, about 0.7-1 X value, Ksurpremains constant although r B r varies by more than an order of magnitude. 262

[TL'I, m M Figure 5. KsUrP for first discontinuity as a function of Einit

It seems then that the energetics of desorbing a previously adsorbed ion such as Br-, or the effect of intrusion of some adsorbed Br- into the monolayer TlBr crystal, can increase the solubility of monolayer TlBr. The effects of strong adsorption extend to foreign materials such as Triton X-100, which at 0.00005% concentration completely prevents formation of the TlBr surface crystal under any conditions. K,,,, as f(E).Aside from the changes in Ksurpabove a critical value of r B r a t high [Br-] or positive E i n i t , Ksurpexhibits potential dependency which is completely independent of rBr. Table I1 and Figure 4 show data for Ksurpat -0.2 and -0.3 volt for ranges of [Br-] where Ksurpexhibits "normal" equilibrium constant type behavior. The potential dependency is also examined in Figure 5 over a broader range of &,it. The monolayer TlBr crystal at 25 "C becomes monotonically more soluble as Einit is made more positive. The change in Ksurpaccelerates at the most positive potential until, a t Einit > -0.10 volts, Ksurp> K,, and no monolayer formation is observed. The potential dependence of Ksurpis understandable on a thermodynamic basis using the data of Table 111. As Einit becomes more positive, formation of the monolayer TlBr crystal becomes enthalpically more favored, but entropically less favored. The more exothermic A?Iopptn at positive Einit is consistent with stronger Br--Hgo bonding. The greater loss in entropy also can be accounted for by stronger Br--Hg" bonding with consequences of increased order in the Hg surface. At 25 "C, the entropy term becomes dominant at Einit -0.10 volt, the monolayer TlBr solubility no longer is smaller than that of bulk TlBr, and the rT1 isotherm discontinuity vanishes. The differing potential dependencies of AHopptn and ASopptn mean that it is possible to observe a different ordering of Ksurpwith potential at other temperatures. At T > 25 "C, the trend in Ksurpof Figure 5 is simply accentuated. A t T < 25 "C, Ksurpchanges less and less rapidly a t positive potentials and, at T = 0 "C, actually reverses its potential dependency between -0.2 and -0.1 volt. Thus a t T = 0 "C, Ksurp(-O.l) < Ksurp(-0.3) < Ksurp(-0.2). This is simply the consequence of having two opposing thermodynamic parameters with different dependency on Einit. In an earlier report ( I ) , we observed that Ksurpfor PbXz surface crystals decreases at more positive potentials, which (at 25 "C) is opposite to the potential dependency found for TIBr. In view of the forenoted observation at T = 0 "C for TlBr, it is probable that the difference between PbX2 and TlBr at 25 "C is simply again a matter of opposing AHopptnand ASopptn terms. At -0.2 and -0.3 volt at all temperatures and [Br-1, the


-

Flgure 6. rrl vs. [Br-] isotherms at Elnit= -0.1 volt as a function of

Figure 7.

temperature (numbers on curves are OC). Curves normalized to [Br-] axis of &it = -0.3 isotherm (dashed curve)

Measured by varying [TI'] at constant [Br-1. [Br-] = 10 rnM, dashed line, data points not shown, KpUrp # ([Br-1): 35 mM(A): 45 m M ( A ) ; 55 rnM(V): 65mM(0);75mM(O):85rnM(@)

shape of the isotherm and rT1 which correspond to the two adsorption isotherm plateaus are essentially constant (rT1 = 7.2 and 14.8 X mol/cm2). At -0.1 volt, a slight dependency of the plateau rT1 can be discerned. Figure 6 shows a series of rT1 vs. [Br-] isotherms at -0.1 volt all normalized to the -0.3 volt isotherm at corresponding temperature. At the lowest temperatures, the -0.1 volt plateau rT1 exceeds that observed a t higher temperature and more negative potential. There is an apparent compacting of the monolayer TlBr crystal. While the reason for this is unknown, it can be argued that it is yet another reflection of strong Br--Hgo bonding at more positive Einit. Linear Sweep Chronoamperometry. An array of chronoamperograms of solutions at various points along a r T I vs. [Br-] isotherm is shown in Figure 2. Two sharp adsorption peaks are evident, appearing sequentially as [Br-] is raised, the more negative peak appearing first. Each peak begins to appear a t a [Br-] in the vicinity of an adsorption isotherm discontinuity. While the rT1 vs. [Br-] isotherm rises abruptly to a full-blown plateau, however, the chronoamperometric adsorption peak grows more gradually with increasing [Br-1, requiring a 20-30% excess over Ksurp to achieve its full magnitude. This is due to reduction of some diffusing T1+ on the leading edge of the reduction wave; the lowering of [T1+]in the absence of excess [Br-] tends to displace the monolayer precipitation equilibrium. The two adsorption peaks can be observed more clearly at fast sweep rates and in solutions of low [Tl+]and sufficiently high [Br-] to exceed Ksurp.Under these conditions, the diffusing T1+ wave becomes, relatively, small. The two peaks can be integrated to produce the same plateau rT1 as observed by DPSCC. Shapes of pre-peak adsorption waves have been described for linear sweep chronoamperometry by Wopschall and Shain (18) for product adsorptions obeying the Langmuir isotherm. The adsorption peaks are generally symmetrical in shape, and have a potential, relative to the diffusion wave potential, governed by the free energy of adsorption. The TlBr adsorption peaks, in contrast, are distinctly nonsymmetrical, the fall of current on the cathodic side being much more abrupt than the rise on the anodic side. Epeakfor the TlBr adsorption peaks shifts with potential sweep rate even down to fairly slow (50 mV/sec) rates. The depletion of the monolayer TlBr surface crystal in this experiment seems not entirely Nernstian. Extrapolation of a plot of Epeak vs. sweep rate to zero sweep rate yields -0.480 volt and -0.537 volt vs. SCE for the two peaks. The diffusing T1+ E1/2 in 1 M KNOBis -0.47 volt. The free en-

rTI

as a function of [TI+] [Br-]

ergy of adsorption of the second monolayer of a TlBr crystal bilayer, as judged from Epeakvs. E1/2, is less than that of the first monolayer, as intuitively expected. It is not obvious to us, however, how a thus-derived adsorption free energy should be interpreted for this case of monolayer phase formation. This completes our discussion of data relating to the rT1 adsorption isotherm discontinuities. We turn now to the portion of the rT1 adsorption isotherm which precedes the surface crystallization event.

THE PRE-DISCONTINUITY rT1 ADSORPTION ISOTHERM In a rT1 vs. [Br-] isotherm such as Figure 1,a significant T l + surface excess is observed in the pre-discontinuity region where [Tl+][Br-] < Ksurp.The isotherm discontinuities clearly lie outside the boundaries of the anion-induced adsorption model of Anson and Barclay (6). It was of interest whether this is also true of T1+ adsorption in the prediscontinuity region. I t was also of interest whether any connection could be discerned between properties of the pre-discontinuity adsorption and the monolayer TlBr precipitation a t the isotherm discontinuity. Classical anion-induced adsorption refers to a reaction MX,(soln)

+ pX(ads)

-

MX(,cp)(ads)

(2)

where the metal complex adsorption is controlled and limited by the population r x of adsorbed free ligand (6, 19). Tests for such control center on evaluation of the r M isotherm as a function of rx. (I'x is observed from solutions of X in the absence of metal.) This is explored for TlBr in the following section. rT1 vs. [Tl+][Br-] and &,it. A series of detailed rT1 vs. [Tl+] pre-discontinuity isotherms for six [Br-] ranging from 35-85 m M was determined at -0.2 volt. This is a high [Br-] range in which (vide supra) Ksurp= f([Br-I). Data were taken at these [Br-] so that the isotherm was extended to higher levels of rT1. It was discovered that these prediscontinuity isotherms could be placed on a common diagram if rT1 were plotted vs. the product [T1+][Br-1. Overlay of the data of the six isotherms in the pre-discontinuity region, shown in Figure 7, is striking. An isotherm at lower (10 mM) [Br-] where Ksurp # f ([Br-1) also exactly overlays the other rT1 data at low r T ] . Over the [Br-] concerned, r B r varies from 0.8 to 2.6 X mol/cm2 (Table I). In order to further examine rT1 vs. r B r , rT1 was measured for a series of solutions in which [Br-] was changed,


263

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~~

I\

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[ Br-]a, mM

E I N-, Figure 8.

r T I as a function of complex ([TIBr]soln = 1.67 X

rarX

10'0

TV

Fnlta t

v5

SCE

constant concentration of TlBr

MJand constant

rsr

~~~

Table IV. Hg Drop Extrusion Double Layer Charges at E = -0.20 volt us. SCE [TI+] = 0 mM 9 m , pC/cm2

[TI+] = 1.0 mM 9m2 p C / c m *

0.0 9.6 10.8 2.0 10.2 11.6 4.0 10.7 9.6 6.0 10.9 10.5 7.0 11.0 11.1 8.0 11.3 11.3 9.0 11.3 11.5 10.0 10.9 10.9' 11.0 11.7 11.3 10.8 9.8 12.0 13.0 11.0 9.4 15.0 11.6 7.1 ... 5.2+ 16.0 18.0 12.3 5.6 a Arrows denote positions of first and second discontinuities, respectively.

mol/cm2 = 1.9 f 0.3(*): 2.7 & 0.3(A);3.3 f 0.3 ( 0 ) 3.8 ; f 0.3

(0); 4.7 f 0.3(x)

but r B r was maintained constant by manipulating the chosen Einit, using Table I. Also, the product [Tl+][Br-] was maintained constant by manipulating [Tl+]. Because of errors in an early version of Table I, the r& in this experiment was constant only to within -10%. Nonetheless, the results (Figure 8) demonstrate that several rT1 vs. E curves overlay exactly regardless of the extant value of r B r . The data show that rT1 is not controlled by the population of adsorbed bromide, and also show that rT1 = F ( E i n i t ) a t constant [Tl+][Br-1. Attempts to establish any type of correlation between r B r and rT1, including plots of r T I vs. r B r (curved), have been unsuccessful. The only factor which suggests a relation a t all is that in every case examined r B r is 1 rT1. However, in the face of the foregoing results, we conclude this is only fortuitous, and that the anion-induced adsorption model is inappropriate for the TlBr adsorption even in the pre-discontinuity region. Effect of Adsorption on qm. Determining the influence of adsorption on the charge qm of the electrical double layer a t &it allows inferences on the charge of the adsorbing metal complex. One straightforward method of q m measurement is the drop extrusion experiment (20), in which a HMDE potentiostated a t Einit is abruptly extruded. The charge passed as a result of the electrode area change is measured for bromide solutions with and without T1+ present. Representative data are given in Table IV, and show that q m is apparently unaffected by the adsorption prior to the isotherm discontinuity, and depressed thereafter. DPSCC experiments were conducted on similarly extruded drops to measure rT1 to ascertain whether adsorption equilibrium had been reached. At concentrations well onto the first adsorption isotherm plateau, the measured rT1 was 80-90% of its equilibrium value. On the second plateau, rT1 was 60-90% of its equilibrium value. Thus, Table IV may underestimate the degree to which formation of the TlBr monolayer crystal (at arrows) depresses q,. Nonetheless, the observed depression of q m is an order of magnitude less than the charge corresponding to r T ] on the first (70 pC/cm2) and second (140 fiC/cm2) plateaus. This implies that the monolayer thallium species on the electrode surface is neutral (e.g., TlBr), which is consistent with our interpretation of Ksurp.We presume that the observed depression of q m reflects displacement of adsorbed Br- and NO, by the surface crystal. 264

ANALYTICAL CHEMISTRY, VOL. 48, NO.

Table V. &dl from DPSCC Reverse Potential Step in Pre-Discontinuity Region of rT1Isotherm.a Einit = -0.2 v [ Br-] = 35 mM

0.00 0.50 1.00 2.00 3.00 4.00 5.00 6.00 7.00 7.50

0.48 1.47 1.60 2.37 3.74 4.93 6.45 9.30 12.93 17.80

[ Br-] = 7 5 m M

19.62 18.67 19.01 18.66 18.99 19.00 18.95 18.86

18.75 18.75

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.25

0.77 1.69 2.71 4.11 5.66 8.11 11.19 16.31 22.28 26.14

21.71 22.33 22.65 22.48 22.20 22.40 22.94 22.64 22.68 22.67

Data for q m a t Einitcan also be derived from DPSCC Qdl results using a drop extrusion value for q m a t E f i n a l ( r B r = 0). In the pre-discontinuity region of the rT1 isotherm, this and the drop extrusion approach when compared gave equivalent values of q m a t Einit.Some Qdl data for the prediscontinuity region of rT1 vs. [Tl+] isotherms (used in preparing Figure 7 ) are given in Table V. In the pre-discontinuity region of the r T ] isotherm, Tables IV and V demonstrate that adsorption of Tl+ is not accompanied by a large change in qm. There are three possible interpretations of this result. First, the adsorption of TlBr; could be accompanied by desorption of an equivalent amount of Br-. Since we have shown that rT1 is unaffected by r B r regardless of the relative levels of each, we regard this interpretation as unreasonable. Second, since qm = 41 + q 2 - s , where q1 is charge due to specifically adsorbed ions and q 2 - s is diffuse layer charge, one could suppose adsorption of a charged thallium species without affecting r B r but altering q 2 - s an equivalent amount. We discard this interpretation also, since coincidence would be unduly strained for Qdl to remain invariant over the large range of rT1 displayed in Table V. Last, and the interpretation we favor, q m is invariant with r T ] if the adsorbing species is neutral and does not displace adsorbed bromide. The Adsorbed Complex. The foregoing results that in the pre-discontinuity region rT1 is not controlled by r B r and q m # f(rT1) indicate that the adsorption reaction can be written

2, FEBRUARY 1976

1.01

I

I

I

I

I

0'3

2

IT9*I [Br-1 / ( [TL'I IB r - I )e = , 9 5

'''0

Figure 9. Fractional surface coverage 6' of adsorbed TlBr for isotherms at €init = -0.15 volt (Curve A), -0.20 volt (Curve 4, and -0.25 volt (Curve C), normalized to C O = O . ~ ~

Figure 10. Shape of theoretical Frumkin isotherm as a function of attractive interaction parameter against C B = O . ~

For Curves A and C, [Br-] = 50 mM. Curve 8 is composite of Figure 8 data. _ _ - -indicates KSpfor Curve A and Ksurp(at low [Br-1) for Curves B and C. - is theoretical Frumkin isotherm calculated from least square fit of data (D) to Eauation 5

TlBr(so1n)

In [O/C(l - O)] = 2a0

(3)

where K T ~ = B 2.09. ~ If the complex TlBr is the adsorbing species rT1 should depend directly on the product [Tl+][Br-] as is observed in Figure 7. The essential difference of course between the TlBr adsorption and the anion-induced adsorptiop model (6) is that the quantity of the TlBr adsorption is not controlled by (Br-),ds sites, but occurs directly on the Hg surface. Presumably, the Hg-Br bond remains an important ingredient in causing the adsorption. The increasing strength of this bond with increasingly positive Elnitwould serve as rationale for the potential-dependency of TlBr adsorption demonstrated in Figure 8. Why TlBr adsorption should occur without the participation of adsorbed free ligand shown by CdI2 and other anion-induced adsorbers is far from obvious. The natural suspicion that this pre-discontinuity behavior is in some way related to the existence of the monolayer precipitate-forming discontinuity is strengthened somewhat by examination of the TlBr adsorption isotherm. considered next. Assignment of the TlBr Adsorption Isotherm. The generally upward-bending shape of pre-discontinuity isotherms (Figure 7 ) suggests that there may be interactions between the adsorbed TlBr complexes. The Frumkin isotherm allows for such interactions and was chosen for comparison to pre-discontinuity isotherms. The isotherm equation (13,21) is B 1-0

+ In (3

(5)

with linear least squares fitting to the experimental data. Values of 0 were calculated using rT1 on the first (monolayer) isotherm plateau as rmax. The concentration of [T1BrIsoln,calculated from Equation 3, was used as C and ranged from 0.02 to 0.33 mM. The data employed were all in the pre-discontinuity region of the isotherms, and were taken at three Elnlt;-0.15 V, -0.20 V (data of Figure 71, and -0.25 V. A t 50 m M [Br-1, the -0.15 V data are a t an E,,,, sufficiently positive that a sharp discontinuity cannot be seen, being an extreme (Ksurp2 Ksp) of the effects displayed in Figure 5. Clear discontinuities follow the data a t -0.2 and -0.25 V. The fit of the data to Equation 4 proved to be excellent a t all three E,,,t. Results for CY and @ are given in Table VI. The data are plotted in Figure 9 in comparison to theoretical Frumkin isotherms calculated for the Table VI cy and (3 values. The horizontal axis is given as concentration normalized to the concentration C a t which % = 0.95 for convenience in displaying the comparison. The shapes of the theoretical isotherms a t -0.2 and -0.25 V are remarkable and require comment on the behavior of the Frumkin relationship as a function of the interactive parameter cy. Figure 10 is a normalized plot of Equation 4 for a ranging from 0 to 3 and is similar to a figure presented and discussed in a review (22) by Frumkin and Damaskin. As a increases from zero, the theoretical isotherm deviates increasingly in an upward-bending way from a Langmuirian shape until, a t a critical value of CY = 2.00, the isotherm achieves a vertical (dO/dC = a) slope. For a > 2.00, this is followed by a folding back and isotherm regions where dO/dC < 0. Clearly, no real adsorption system can be expected to exhibit a dO/dC < 0 region, and the S-shaped region of the isotherm connotes an unstable

The reaction as written is also consistent with the isotherms of Figure 7. Over the range of [T1+]and [Br-] studied, the solution concentration of the complex TlBr is given closely by

3C = -exp (-2aB)

a . Concentration axis normalized

tions. If a = 0, Equation 4 reduces to the Langmuir equation. Equation 4 was applied using the rearranged form

TlBr(ads)

[TIBrIsoin= K T I B[TI+] ~ Pr-1

= 0.5

(4)

where 3 = exp (-1G"/HT), AGO is the standard free energy of adsorption, C is solution concentration (replacing acand a characterizes intertivity for simplicity), O = I'/I',,,, actions between adsorbed particles. If the interaction parameter a is positive, the particle-particle interactions are attractive; a negative a corresponds to repulsive interac-

Table VI. Frumkin Isotherm Data for TIBr. See Figure 9. 150-

therm

Euut

a

A

-0.15 -0.20 -0.25

1.65 i 0.02 2.05 t 0.16 2.78 = 0 . 2 0

B C

In

P

8.68 + 0.02 8.34 = 0.04 7.98 I 0.04


265

condition of the adsorbed layer. The attractive forces between particles have become so great that a sudden coalescence, or ordering, or phase transition takes place. Analogous behavior exists for gaseous equations of state allowing for attractive interactions. For example, for real gases below Tcrit, van der Waal’s equation predicts similar Sshaped pressure-volume behavior in the region where the gas condenses. The isotherms of Figure 9 demonstrate that a relationship does exist between TlBr adsorption in the pre-discontinuity isotherm region and the TlBr monolayer precipitation. Figure 9 shows that an unstable region of the Frumkin isotherm can be predicted by isotherm data taken over pre-discontinuity regions of the isotherm. Furthermore, for the data at -0.15 V, no instability is predicted by the data, and no clear discontinuity is observed a t this Einit. The nature of the isotherm instability obviously is the exceeding of a critical attractive interaction between adsorbed TlBr units. We see this macroscopically as a monolayer precipitation of TlBr measurable by the behavior of Ksurp.In principle, the value of Ksurpis predicted by the point of theoretical isotherm fold-back. Comparison of the dashed lines of Figure 9 (drawn for Ksurpa t low [Br-] where Ksurp# F([Br-]) with the fold-back point of the isotherm shows that the prediction has only approximate quantitative perfection. The results of Table VI for a and fl are also of interest. The dependency of the interaction parameter a on potential is sharp and larger than other dependencies (13, 22) of which we are aware. The TlBr-T1Br attractive interaction diminishes markedly a t more positive potentials. The value of In @,on the other hand, increases as Einitbecomes more positive. The standard free energy of adsorption as measured by In /3 changes from -4.72 kcal/mol a t -0.25 V to -5.14 kcal/mol a t -0.15 volt. This change in the adsorption energy can be understood in terms of increasingly strong interaction of bromide in the adsorbed TlBr unit with HgO a t positive Einit.This is consistent with previous discussion of in the TlBr monolayer crystal, and of the potential-dependency of pre-discontinuity TlBr adsorption shown in Figures 1 and 8. It may also be that the decreasing TlBr-TlBr attractive interaction a t positive Einitis, in part, a consequence of a competing Br--Hgo interaction. The results of Figure 9 invite another interpretation of Ksurpin which it is not considered as a surface solubility product constant. In this view, the constancy of the product [Tl+][Br-] a t the adsorption isotherm discontinuity simply reflects a critical [TlBr],,~, whose adsorption controls the stability or instability of the adsorbed layer. The product of coalescence of an unstable adsorbed layer is not necessarily a monolayer crystal. The numerical value of Ksurpbears no relation to that of K,, but is merely a numerical consequence of some combination of K T ~ and B ~ the isotherm parameters cy and /3 for the given Einit. While this line of reasoning has some interesting consequences, we believe that interpretation of Ksurpas a surface solubility product constant is a more correct viewpoint. The above view of Ksurpaccounts less well for certain facts: (i) the existence of two isotherm discontinuities with idenincrements, (ii) discontinuities appear only when tical rmax Ksurpis numerically less than the known K,, of bulk TlBr, (iii) AH;,,, and values for monolayer and bulk precipitation are numerically similar, and (iv) the value of rmaxfor rT1 is very large and implies exceptionally close packing of adsorbed species. All of these facts are consistent with, and support, interpretation of Ksurpas a surface solubility product constant. We view the Frumkin isotherm behavior of the pre-discontinuity TlBr adsorption and the 266

ANALYTICAL CHEMISTRY, VOL. 48, NO.

2, FEBRUARY 1976

limited surface solubility of TlBr as defined by Ksurp,as separate manifestations of common underlying phenomena. The attractive TlBr-TlBr pre-discontinuity interactions imply a non-uniform, clustered distribution of adsorbed TlBr. In the limit, this clustering would provide TlBr “seed nuclei” of size sufficient for spontaneous growth in two dimensions. Formation of seed nuclei of sufficient size is a necessary and normal course of events for any precipitation event. Several other recent reports of metal complex adsorptions exhibiting attractive interaction-Frumkin behavior have appeared in the work of Anson et al. (23-25). In one (25), of Cr(NCS)i-, a near-discontinuity appears in the adsorption isotherm. An understanding of this unusual adsorption does not appear to involve a surface solubility effect.

OTHER MONOLAYER PHASES ON ELECTRODES Preliminary investigations have been made of T1+ solutions containing C1- and I-. The Tl+-Cl- system is characterized by weak initial adsorption followed by a single isotherm discontinuity rising to a plateau value of rT1. With Tl+-I-, there is strong initial adsorption increasing continuously to an initial plateau followed by a discontinuity leading to a second r T 1 plateau. There are similarities in these adsorptions to the TlBr case. The solubility of TlCl and T1I are respectively much higher and lower than TlBr, and the convenience of the concentration ranges used in the TlBr study is lost in these other cases unless solution temperature is adjusted. Thus far, the chloride, bromide, and iodide of both T1+ and Pb2+ ( I , 2) have been shown by DPSCC to exhibit solubility-related adsorption isotherm discontinuities. In anodic electrocrystallization studies of Tl(Hg)x in chloride solutions, Armstrong et al. (26), reported discontinuities in capacitance-potential curves and correctly assumed these to represent monolayer phase formation. The role of a surface solubility Ksurp< K,, was not recognized in these earlier studies. The criteria for DPSCC identification of yet further examples of a limited Ksurpwould seem to include as necessary but not sufficient conditions: (i) limited solution solubility of the metal complex and (ii) ability of the complex’s ligand to form adsorptive bonds with HgO.

ACKNOWLEDGMENT Helpful discussions with R. P. Buck are gratefully acknowledged.

LITERATURE CITED (1) H. B. Herman, R. L. McNeely, P. Surana, C. M. Elliott, and R. W. Murray, Anal. Chem.. 46, 1258 (1974). (2) M. Sluyters-Rehbach. J. S. M. C. Breuksel, K. A. Gijsbertsen, C. A. Wijnhorst, and J. H. Sluyters, J. Nectroanal. Chem., 38, 17 (1972). (3) A. M. Bond and G. Hefter, J. Electroanal. Chem., 42, 1 (1973). (4) D. J. Gross and R. W. Murray, Anal. Chem., 38, 405 (1966). (5) M. Sluyters-Rehbach, S. Gonzalez, and J. H. Siuyters, J. Electroanal. Chem., 51, 405 (1974). (6) F. C. Anson and D. J. Barclay, Anal. Chem.,40, 1791 (1968). (7) C. M. Elliott and R. W. Murray, J. Am. Chem. SOC.,96, 3321 (1974). (8) B. E. Conway, H. Angerstein-Kozlowska, W. B. A. Sharp, and E. E. Criddle, Anal. Chem., 45, 1331 (1973). (9) J. H. Christie, R. A. Osteryoung. and F. C. Anson, J. €/ectroana/.Chem., 13, 236 (1967). (10) F. C. Anson. J. H. Christie, and R. A. Osteryoung, . - J. Electroanal. Chem., 13, 343 (1967). ( 11) G. Lauer, R. Abel, and F. C. Anson, Anal. Chem., 39, 765 (1967). (12) C. M. Elliott and R. W. Murray, Anal. Chem., 47, 908 (1975). (13) P. Delahay, “Double Layer and Electrode Kinetics”, Interscience, New York. 1965. (14) J. Lawrence, R. Parsons, and R. Payne, J. Electroanal. Chem., 16, 193 (1968). (15) A. R. Sears and P. A. Lyons, J. Electroanal. Chem.. 42, 69 (1973). (16) “Stability Constants of Metal Ion Complexes”, The Chemical Society, London, Spec. Publ., No. 7, 1958.

(17) D. A. Johnson, "Some Thermodynamic Aspects of Inorganic Chemistry", Cambridge University Press, 1968. (18) R . W. Wopschall and I. Shain, Anal. Chem., 39, 1514 (1967). (19) D. J. Barclay and F. C. Anson, J. Elecfroanal. Chem., 28, 71 (1970). (20) F. C. Anson. Anal. Chem., 38, 54 (1966). (21) A. Frumkin, Z. Phys., 35, 792 (1926). (22) A. Frumkin, and B. Damaskin, "Modern Aspects of Electrochemistry", Vol. 3, J. Bockris and B. Conway, Ed., Butterworths and Co., London, 1964. (23) F. C. Anson and R. S.Rodgers, J. Nectroanal. Chem., 47, 287 (1973). (24) S.N. Frank and F. C. Anson, J. Necfroanal. Chem., 5.4, 55 (1974).

(25) M. J. Weaver and F. C. Anson, J. Elecfroanal. Chem.. 60, 19 (1975). (26) R. D. Armstrong, W. P. Race, and H. R. Thirsk, J. Necfroanal. Chem., 23,351 (1969).

RECEIVEDfor review July 3, 1975. Accepted November 3, 1975. We acknowledge support of this research by the Materials Research Center, National Science Foundation U.N.C., under Grant GH-33623 and by National Science Foundation Grant GP-38633X.

Stepwise Titration of Some Anion Mixtures and Determination of Kspof Silver Precipitates with Silver Ion Selective Electrode Eric E. Chao and K. L. Cheng" Depadment of Chemistry, University of Missouri-Kansas City, Kansas City, Mo. 64 110

Anion mixtures, such as sulfide, arsenite, and arsenate can be stepwise titrated in alkaline media with silver solution using the silver ion selective electrode as an indicator electrode. Various mixtures of 15 anions in different combinations have been successfully determined by stepwise titration. A simple method for determining the equilibrium constants such as Ksp using an ion selective electrode has been developed. Equilibrium constants results for 15 silver compounds are reported. Most results agree well with the literature values and some are new data. Silver or arsenite can be determined gravimetrically or volumetrically based on the formation of AgSAs03 precipitate.

There are many methods for determining cations. However, fewer methods are available for determining anions. The commercially available silver ion selective electrode responds to both free silver ion and sulfide ion. The silver ion activity depends upon the sulfide or other ligand ion activity as it is controlled by the solubility product or equilibrium constants of silver sulfide or silver complexes. The solubility product of silver sulfide has been reported to be 1.48 X ( I ) . The Nernstian response of silver ion activity from 0.1 M to A4 has been reported by using a silver ion selective electrode ( 2 ) . Its use to determine the anions which form stable complexes or precipitates with silver ions may be advantageous. Further, it offers a simple method to determine their solubility product constant (Ksp)and stability constants ( K f ) . The use of a divalent ion selective electrode as an indicator electrode in the stepwise titration of triethylenetetraminehexaacetic acid has been reported (3).

The present paper reports the application of the siiver ion selective electrode as an indicator electrode to titrate sulfide, arsenite, and arsenate. A stepwise method of titrating many anion mixtures has also been developed. We also report here the K,, and the Kf values of 15 silver compounds. Some of them are reported for the first time. Many equilibrium constants which appeared in the literature vary widely. It should be worthwhile to reevaluate them with currently available ion selective electrodes.

EXPERIMENTAL Apparatus. The Orion model 94-16 silver sulfide ion selective

electrode and the Orion model 90-02 double junction reference

Table I. Gravimetric Determination of Silver as Silver Arsenitea N o . of experirnents

pH of precipitation

Silver taken, nig

.

Silver arsenite precipitate, nig

Sil\ e r b f o u n d . rng

Relative error, 9

-0.37 74.3 53.9 +0.19 149.4 108.3 +o. 1 9 224.3 3 11.0 162.6 4 11.0 299.7 217.2 +0.37 5 11.0 374.5 271.4 +0.33 447.6 6 11.0 324.4 -0.06 7 10.0 +0.46 108.1 149.8 108.6 8 8.0 108.1 150.4 109.0 +0.83 9 6.0 108.1 149.3 108.2 +0.09 a Amount of arsenite added: 1.0040 mmol. The precipitates were dried under vacuum for 17 hr. b Silver was calculated based o n the gravimetric factor 0.7248 assuming the precipitate was in the form of Ag,AsO,. 1 2

11.0

11.0

54.1 108.1 162.3 216.4 270.5 324.6

electrode were used for the silver ion activity measurements. All the pH and emf readings were taken from a Corning model 10 pH meter with expanded scale. Infrared spectra were taken from a Perkin-Elmer 621 grating infrared spectrophotometer and the CsI cell and Nujol oil were used. Reagents. The primary standard arsenic trioxide from the Thorn Smith Co. was used for the preparation of 0.1 M arsenite solution; a weighed amount of arsenic trioxide was first dissolved in a minimum amount of 0.1 M NaOH solution, then made up to volume. More diluted arsenite solutions were prepared by appropriate dilutions. The silver ion solutions were prepared from anhydrous silver nitrate. All chemicals used were reagent grade. The water used in the experiment was doubly deionized. Procedure. Determination of Arsenite. The silver ion selective electrode, the double junction reference electrode, and the combination pH electrode were immersed into a sample solution which contained arsenite ion and was adjusted to pH 11.0 with sodium hydroxide. The titration was initiated by adding the silver nitrate solution from a buret with constant stirring. The emf changes were recorded in each interval addition of 1 ml or 0.50 ml of the silver nitrate solution. Near the equivalence point, 0.25 ml or 0.10 ml of silver nitrate solution was added each time. The ratio of silver to arsenite was 3 to 1. The pH was constantly checked and adjusted to 11.0 with a dilute NaOH solution or a dilute "03 solution. Stepwise Titration of Sulfide, Arsenite, and Arsentate. The procedure for titrating a mixture of sulfide, arsenite, and arsenate as well as for titrating other mixtures was the same as the one described above. The resulting titration curves show three breaks for the titration of mixture of all three anions; the first break correANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976

267

Thallium bromide adsorption and two-dimensional crystallization on

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