Adsorption of cadmium on alumina and silica: analysis of the values of stability constants of surface complexes calculated for different parameters of triple layer model

COLLOIDS

AND ELSEVIER

Colloids and Surfaces A: Physicochemical and Engineering Aspects 117 (1996) 201 214

A

SURFACES

Adsorption of cadmium on alumina and silica: analysis of the values of stability constants of surface complexes calculated for different parameters of triple layer model M a r e k K o s m u l s k i a'b'l alnstitute of Catalysis and Physical Chemistry of Interfaces, Laboratory of Adsorption and Physical Chemistry of Interfaces, Polish Academy of Sciences, P1.M.C.Sklodowskiej 3, 20031 Lublin, Poland bForschungszentrum Karlsruhe, Institut for Nukleare Entsorgungstechnik, P.O. Box 3640, 76021 Karlsruhe, Germany Received 20 December 1995; accepted 16 May 1996 Abstract The calculated values of stability constants of surface complexes formed by heavy metal ions depend on the assumed model of the electric double layer and its parameters. Using various parameters of the triple-layer model (TLM) (which fit the titration data almost equally well), one obtains stability constants in a range as wide as two orders of magnitude. On the other hand, the equilibrium constants of the surface reactions = A 1 - O - N a + C d z+ =-=A1-OCd + + N a + ( l o g K = 7 . 4 at 15°C and l o g K = 7 . 1 at 35°C) and = - A 1 - O - N a + C d Z + + C I - + H + = - - - A 1 - O H C d C I + + N a + (log K = 15.7 at 15°C and 14.9 at 35°C) are not dependent on the TLM parameters. The surface complexes formed in these two reactions are used in a model which is able to explain cadmium adsorption from NaCI and NaC104 solutions up to a concentration of 1 mol dm -3. Only one surface complex, =-Si-OCd +, is used in a model which explains the adsorption of cadmium on silica from the same electrolytes, and the equilibrium constant of the surface reaction =-Si-O-Na + Cd 2+ =-=Si-OCd + + Na + (log K = - 0 . 9 at 15°C and - 1 . 0 at 35°C) is not dependent on the TLM parameters used in its calculation. The adsorption of cadmium at constant pH increases with temperature, but adsorption at a constant surface charge density is independent of temperature for both oxides.

Keywords: Aluminum oxide; Cadmium; Electric double layer; Silicon oxide; Specific adsorption; Surface complexation; Triple layer model 1. Introduction C a d m i u m is considered to be a dangerous pollutant and its migration in the environment is strongly affected by adsorption. The adsorption of heavy metal cations on oxides is often interpreted in terms of the surface complexation model (SCM). Various aspects of specific adsorption have been discussed in several reviews [ 1 - 7 ] , where a long list of the relevant literature can be found. 1 Mailing address: M. Kosmulski, Forschungszentrum Karlsruhe, INE, P.O. Box 3640, 76021 Karlsruhe, Germany. 0927-7757/96,/$15.00 © 1996 Elsevier Science B.V. All rights reserved P H S0927-7757 (96) 03706-5

The definitions of the stability constants of surface complexes contain exponential terms to account for the electrostatic potential ~, in the interracial region, e.g. -=AI-OH + C d 2+ = ---A1-OCd + + H +

(1)

K=AI_OCd+ = [ ~ A 1 - O C d + ] {H + } × [__-AI_OH]-I {Cd2+ } -1

x e x p [ - F(ffo --

2qJcd)/RT]

(2)

where (except in the last term) [ ] denotes the concentrations of the surface species and { }

202

M. Kosmulski/Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201 214

denotes the activities of ions in the bulk solution. The subscripts 0 and Cd in Eq. (2) refer to the surface plane and the plane in which the heavy metal ions are adsorbed, respectively. The heavy metal cations are usually assumed to adsorb in the surface plane, so ~cd = ~bo (e.g., see Refs. [5,8,9]). Furthermore, in the surface complexes considered in the present paper, heavy metal ions are assumed to adsorb in the surface plane unless another plane of adsorption is specified. The electric potential 0o in Eq. (2) cannot be measured directly but it can be calculated from the models of the electric double layer. The computer program FITEQL [ 1 0 ] was specially designed for such calculations. In reaction (1), one proton is released per one adsorbed cation. The proton stoichiometry can be determined from experimental data and it often differs from unity. The following reactions --AI-OH + C d 2+ -1- H 2 0 = - A 1 0 C d O H

+ 2H +

(3) - A 1 - O H + Cd 2 + = =A1-OHCd 2 +

(4)

correspond to the release of two and zero protons per one adsorbed cation, respectively. By combining reaction (1) with reactions (3) or (4), fractional values can be obtained. The adsorption of heavy metal cations on oxides is often measured in the presence of complexing anions. Complexation in the solution reduces the concentration of free metal cations, e.g. Cd 2+, in the solution and thus the concentration of the surface species formed in reactions (1), (3) and (4). However, the experimentally observed adsorption is often relatively insensitive to the presence of complexing anions (see Ref. [9] and references cited therein). This may be explained by the formation of surface complexes containing these anions, e.g. ---A1-OH + Cd 2+ + C1 = ---A1-OCdC1 + H +

(5)

=-A1 OH + C d 2+ 4- C1- = ---A1-OHCdC1 +

(6)

Reactions (5) and (6) illustrate two different proton stoichiometries at the same chloride-to-cadmium ratio in the surface complexes. Surface complexes with a chloride-to-cadmium ratio higher than one (with different proton stoichiometries) can be also considered. In order to predict the adsorption of cadmium from solutions containing chlorides, the equilibrium constants of relevant surface reactions should be determined. Only the total concentration of the metal ions at the surface can be determined experimentally, but it is not possible to measure the concentrations of particular surface species. In the fitting routine leading to the values of the equilibrium constants of the surface reactions, some arbitrary assumptions are unavoidable and these severely affect the results. First, the total concentration of surface hydroxyl groups Ns can be estimated rather than determined exactly by various methods which lead to values ranging from 1 to 20 groups per square nanometre [ 11 ]. If the site 'density is overestimated, the calculated equilibrium constants of the surface reactions are underestimated by the same factor and vice versa. This is clearly illustrated in Ref. [ 11 ], where the equilibrium constants of the same surface reaction have been calculated assuming different site densities. In addition to Ns, the following adjustable parameters are used by the TLM: C~ and C2, the inner and outer layer capacitances, respectively; and K +, K , Kcation and Kanion, the respective equilibrium constants corresponding to the formation of the following surface species: =-SOHJ, --SO-, =-SO-Na and =-SOH2-C1 (NaCl is an example of a background electrolyte). In FITEQL one can choose between the T L M and simpler models of the electric double layer which use fewer parameters. No direct spectroscopic evidence of surface complexes with alkali metal cations has been found. Therefore, the TLM is often criticized. It is not the aim of the present paper to discuss the validity of the assumptions for the TLM. The problems of the proper choice of TLM parameters have been discussed in detail in the literature [12,13]. The number of adjustable parameters in the T L M may be reduced by the following constraints

Such surface complexes may be interpreted as the adsorption of cadmium chloride complexes from the solution, e.g.

log K+ - log K

=A1-OH + CdC1 + = ---A1-OCdC1 + H +

log Kanion - - l o g Kcation = 2pHpzc

(5a)

= 2pHpzc

(7) (8)

M. Kosmulski/ Colloids Surfaces A. Physicochem. Eng. Aspects 117 (1996) 201-214

where PZC denotes the point of zero charge, which can be determined directly from the experimental data. When Eqs. (7) and (8) are applied, the actually fitted parameters are ApKa = - ( l o g K+ + log K_ )

203

0.0

-0.5

o o o o o Ct=0.8 F -z ooooo C t = l . l Fm-z;ApK,=2 azs,,azx ApK,=4~o

(9) +

ApKcompI = - ( l o g

Kanio n +

log Kcation)

(10)

The choice of the electric double layer model and of the values of parameters within the same model may lead to a difference, by an order of magnitude, in the equilibrium constant of the same surface reaction calculated from the same set of experimental data assuming the same site density [ 11]. Thus, the values of such equilibrium constants are useless unless the model parameters which were assumed to calculate them are available. This is specially important when the values from different sources are compared, e.g. in order to find a correlation of these constants with bulk hydrolysis constants [1] or with dielectric constants of the adsorbents [14]. Most authors try to solve this problem by an arbitrary choice of a unique set of electric double layer parameters. The other possibility is to characterize the adsorption of heavy metal ions by parameter(s) whose values are insensitive to the choice of T L M parameters. In Fig. 1, the equilibrium constants of surface complexes, which are responsible for cobalt adsorption on alumina, K =Al_OCo + =

[~A1-OCo + ] {H + } x[=A1-OH]

1{Co2+}-1

× exp(FOo/RT)

(11)

from Ref. [11] are plotted as a function of the binding constants of the background electrolyte cations KN, = [---A1-O Na] {H + }[-=A1-OH] ~{Na + }-a x e x p ( - F(0o - Oa)/RT)

(12)

where 0r is the potential in the layer of adsorbed counterions. All the data points obtained for the inner layer capacitance C~ of 0.8 F m -2 yield a straight line with a slope close to 1. This means that the ratio of the equilibrium constants defined by reactions (11) and (12) is approximately constant, i.e. independent of the set of ApKa, KNa and

0 .~- t.o I1

t~ O -1.5 -

-2.0

-9.0

-~.5

log

-~.0

-7.5

KN,

Fig. 1. Dependence between the stability constant of the -A1OCo + surface complex and the binding constant of background electrolyte cation calculated for various T L M parameters; data from Ref. [ 11 ].

Ns selected to calculate the K_=AI_OCo +. This ratio is equal to the equilibrium constant of the following surface reaction - - - A 1 0 - N a + C o 2+ = ~ A 1 0 C o + + N a +

(13)

The log K value of this reaction calculated for the data points with C, = 0.8 F m -2 equals 7.0. Also, the data corresponding to C , = 1.1 F m -2 and ApKa = 2 (Fig. 2) yield a straight line of slope close to 1. This set of data yields a log K of reaction (13) equal to 7.2. The slope of the straight line corresponding to C~ = 1.1 F m -2 and ApKa = 4 is equal to 0.7, so log K of reaction (13) calculated from these data depends on the Ns value, but in a range between 7 and 7.2. Thus, the equilibrium constant of reaction (13) is much less sensitive to the choice of the T L M parameters than that defined by Eq. (11) and seems to be very promising as a parameter characterizing the adsorption of heavy metal ions. The nearly constant value of log K of reaction (13) is not surprising, namely, the assumed T L M parameters have a similar effect on the equilibrium constants defined by Eqs. (11) and (12), and when the ratio is calculated these effects cancel out.

M. Kosmulski/ Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201-214

204 100 O. 1

80

Iani

i 0.1

~Q o,,

/' /

,oc.

,,;

M NoCIOI~/ /

so.

7/" o/ I

40-

,: [~:'J

0

D J~ I

20-

AA A

"m,,_m ~._~. " j

_ _ 0.1 1 ~...__-~_. 0.01

M NaCI

....

1

__

0.1 M NoCIO,

+ pH

h

~

io

Fig. 2. Cd(n) adsorption on alumina as a function of the pH and ionic strength at lY'C. The data used to calculate the model curves (reaction (1)) are given in Tables 1-3.

The choice of the number of surface reactions used in a model to describe the adsorption of heavy metal ions is rather arbitrary. In some systems (e.g., Ref. [11]) one obtains a satisfactory correlation between the experiment and the model with only one surface reaction analogous to reaction (1). On the other hand, as many as five various surface reactions analogous to reactions (1) and (3) (6) were used to interpret the adsorption of cadmium on goethite from 0.1 mol din-3 solutions of NaC1, NaNO3 and from a 1:1 mixture of these media [9]. Obviously, one can improve the fit between the model and the experimental adsorption data by addition of surface reactions to the model, but with many adjustable parameters, one can hardly determine a unique set of values, and many combinations of parameters can lead to very similar results. In the present study, the models with possibly few surface reactions are preferred. Eq. (2) and analogous definitions of the equilibrium constants for reactions (3)-(6) suggest that the adsorption equilibria may be affected by the ionic strength through the activity coefficients of the ions in the solution on the one hand, and the changes in the electrical potential on the other hand. Thus, adsorption experiments carried out

at different ionic strengths can be used to test different adsorption models more thoroughly than using adsorption data collected at one ionic strength. Adsorption data covering a broad range of ionic strengths are relatively rare and they have been recently summarized [7]. It follows from this comparison that the increase of the ionic strength causes a significant decrease of adsorption of s-metal ions (always), d-metal ions (only in the presence of complexing anions) on negatively charged surfaces. In contrast, the adsorption of multivalent cations on positively charged surfaces is relatively insensitive to the ionic strength. The similarity in the adsorption behaviour of different systems suggests that the same adsorption model can be used to interpret the adsorption of different metal ions on different oxides. In the present study, Cd(u) adsorption on silica and alumina was studied as a function of pH at NaC1 and NaCIO4 concentrations ranging from 0.001 to 1 mol dm 3; thus a broad range of ionic strengths was covered with complexing and noncomplexing anions. The initial cadmium concentration was lower than the concentration of available surface sites by three orders of magnitude in order to avoid the adsorption of polynuclear complexes and surface precipitation. Usually more than one surface complexation reaction is necessary to describe adsorption in the presence of complexing anions [8,9]. The experimental data are analyzed in order to find "universal" constants, independent of the assumed TLM parameters.

2. Experimental Chromatographic silica and alumina (predominantly the ), form) from Merck were washed with nitric acid solution and then with water to remove soluble impurities. The properties of the adsorbents and the solid-to-liquid ratios used in the adsorption experiments are given in Table 1. Adsorbent preparation and the method ofpotentiometric titration with adsorption measurement were described in detail elsewhere [15]; in this study a Beckman 5500B instrument was used for 7 radioactivity measurements. Analytical reagent grade chemicals from Aldrich and l l s m C d radioisotope

M. Kosmulski / Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201-214 Table 1 Properties of the adsorbents and conditions for the adsorption experiments Property

Silica

Alumina

Surface area (mZg ~) PHpzc Solid-to-liquid ratio ( g d m 3)

388 <5 10

130 9.(P, 8.4 b 20

" A t 15~C. b At 35~C.

from OPiDI (Poland) were used. The experiments were carried out at 15 and 35°C in a nitrogen atmosphere. The ionic strength (NaC1, NaC104) varied from 0.001 to 1 mol dm -3. The initial Cd(n) concentration was 10 -5 mol dm -3. In this concentration range and at a solid-to-liquid ratio given in Table 1, the course of the percentage uptake (pH) curves is only slightly sensitive to the initial concentration of specifically adsorbed cations [ 16].

3. Calculations The triple layer model (TLM) version of the SCM was chosen for the model calculations. In the first step, the T L M parameters were calculated from potentiometric titration data (0.01, 0.1 and 1 mol dm 3 NaCI) by means of FITEQL. In all the calculations, the pH meter display was assumed to correspond to the proton activity. The activities of the other ions in the solution were calculated from their concentrations using the Davies formula (this feature is provided by FITEQL). The /(anion values for chlorides and perchlorates were assumed to be equal for both oxides since the titration curves are not sensitive to the nature of the anion over the pH range of interest. The value of C2 = 0.2 F m 2 was selected after Ref. [ 11]. The silica and alumina data were treated in a somewhat different manner. Symmetrical binding of background electrolyte by alumina is assumed (Eq. (8)) in the present study. Another approach was used in Ref. [11], namely Kanion and Koation are fitted as independent parameters. Many different sets of model parameters produce almost identical cr0(pH ) curves. Only with C l ~ 0 . 9 F m - 2 is a reasonable agreement between experimental and calculated titration curves

205

observed, with the exception of Ns = 1 site nm 2 where Ca ~ 1 F m-2 gives better results. Thus, the choice of C I = 0 . 9 F m -2 was forced by the potentiometric data. This capacity is used in all calculations for alumina (Table 2) and it lies in the range found in Ref. [ 11 ]. The selected Ns, ApKa and Ap/(compI values given in Table 2 were used to compare adsorption models involving different surface reactions (Table 3). On the other hand, assuming any N s value between 1 and 20 sites nm 2 and any ApK a value between 0 and 4, one can reproduce the experimental ao(pH ) curves for alumina by fitting ApKcorapl. Twelve sets of TLM parameters: Ns = 1, 3, 9 and 20; ApKa = 0, 2 and 4 are used to calculate the parameters characterizing cadmium adsorption in a model involving reactions (1) and (6) (Tables 4 and 5). For silica, the concentrations of -=SOH] and ---SOH2 C1 surface species were assumed to be negligible over the pH range of interest, so only K_ and KNa were adjusted. For any C1 > 2 F m -2 and Ns > 6 sites nm-2, the other T L M parameters may be adjusted to reasonably reproduce the titration data. The selected values are given in Table 2. The set of T L M parameters for silica given in Table 2 is not unique. The effect of the assumed C a and N s values on the calculated stability constant of a cadmium surface complex is shown in Tables 6 and 7. The following logarithms of the formation constants were used at 15 and 35~'C: CdC1 +, 2.0; CdCI2, 2.6; CdC13, 2.4; CdC12-, 1.7; C d O H +, 3.9 [17]. Concentration of the other cadmium cornTable 2 Selected parameters of the T L M determined from potentiomentric titrations Parameter

Silica

Alumina

Ns(sites n m 2) C1 (F m 2) C2 (F m -a) log K _ log KNa 1/2 ApK a 1/2 ApKcompl

6 2 0.2 - 6.70 a, - 6.43 b 7.80 a, -- 7.27 b

3 0.9 0.2

a At 15°C. b At 35°C.

1 0.01 a, 0.06 b

M. Kosmulski / Colloids Surfaces A. Physieochem. Eng. Aspects 117 (1996) 201-214

206

Table 3 The stability constant of cadmium surface complexes with alumina in models involving 1-3 surface complexation reactions a Fig. no.

T (°C)

Reaction

One reaction 2 15 3 35 Two reactions 15 5 35 15 35 15

Log K

1, ~bca = ~bo 1, t~ca = ~'o

- 1.13 0.64

-

~'o ~b0 ~bo ~b0

-- 1.51 -- 1.17 -- 1.50 - 1.17 --0.51

6 6 5 5 15

l, ~bca= ~bo 1, ~bcd= ~b0

- 1.51 --2.03

1, ~'Cd= 1, ~CO = 1, ~Pcd= 1, ~bCd= 14

Three reactions 6 15 7 15

Reaction

Log K

Reaction

Log K

SOSb/DF c

2.33 1.97 6.83 6.75 --2.15 -- 1.63 -- 1.16

5 1, ~bca= ~9,~

-2.40 -6.10

1.53 1.09 1.55 1.10 1.83 6 6

3.80 6.87

1.21 0.98

a TLM parameters from Table 2 were used in the calculations. b SOS: sum of weighted squares of residuals. c DF: degrees of freedom. Table 4 The calculated stability constants of cadmium surface complexes with alumina at 15'C N~ (Sites nm 2)

1/2 ApK a

1/2 ApKcompI

Log K ~ alocd +

Log K ~ Atoacacl ~

SOS/DF

l 1 1 3 3 3 9 9 9 20 20 20

0 1 2 0 1 "~ 0 1 2 0 1 2

0.90 0.66 0.63 0.40 0.00 -0.05 -0.12 - 0.52 -0.58 0.49 - 0.89 -0.95

0.31 -0.82 - 1.12 1.08 1.51 - 1.73 - 1.68 - 2.09 2.21 - 2.08 - 2.48 -2.57

8.06 7.57 7.27 7.25 6.83 6.64 6.62 6.22 6.10 6.22 5.82 5.73

1.83 1.73 2.02 1.54 1.53 1.51 1.47 1.46 1.43 1.46 1.46 1.44

plexes

is n e g l i g i b l e

concentration

over

the pH

and

cadmium

range of interest.

The stability constants

of the cadmium

surface

i o n s in t h e s u r f a c e p l a n e o r in t h e // p l a n e w a s considered. The choice of the log K values of the surface

reactions

was

based

c o m p l e x e s w e r e c a l c u l a t e d b y m e a n s o f t h e FITEQL p r o g r a m [-10], t a k i n g i n t o a c c o u n t t h e a d s o r p t i o n d a t a f o r 0.01, 0.1 a n d 1 m o l d m 3 N a C 1 a n d 0.1 a n d 1 tool dm -3 NaC104 simultaneously. The TLM

SOS/DF (sum of weighted degrees of freedom),

m a k e s it p o s s i b l e t o c a l c u l a t e t h e e l e c t r i c p o t e n t i a l s

4. Results and discussion

4'o a n d ~'e- T h e f o r m a t i o n o f c a d m i u m s u r f a c e complexes with different proton stoichiometries, and

chloride-to-cadmium

ratios,

with

particular

The Cd(II) adsorption

on

squares

on alumina

NaC1 and NaCIO 4 concentrations

a

minimum

of residuals/

at different

as a function of

M. Kosmulski / Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201-214

207

Table 5 T h e calculated stability c o n s t a n t s of c a d m i u m surface c o m p l e x e s with a l u m i n a at 3 5 ° C Ns (Sites n m

1/2 A p K a

1/2 ApKcompl

L o g K ~ AIOCd+

L o g K =_AIOUCaCl•

SOS/DF

z)

1

0

1.08

0.02

7.97

1.34

1

1

0.70

- 0.46

7.48

1.30

1

2

0.66

-0.73

7.16

1.70

3

0

0.46

-0.75

7.16

1.10

3

1

0.06

- 1.17

6.75

1.09

0.00

3

2

- 1.38

6.55

1.10

9

0

-0.07

- 1.33

6.53

1.04

9

1

-0.46

- 1.74

6.13

1.03

9

2

-0.53

1.87

6.02

1.01

20

0

-0.43

- 1.72

6.12

1.03

20

1

-0.83

-2.12

5.72

1.02

20

2

- 0.90

- 2.22

5.63

1.01

Table 6 The calculated stability c o n s t a n t s of c a d m i u m surface complexes with silica at 1 5 ° C Ns (Sites n m

C1 ( F m - 2 )

Log K

L o g Keation

L o g K-=siocd+

SOS/DF

L o g K Eq. (19)

2)

2

2.5

- 6.17

- 7.38

- 8.00

0.52

- 0.62

3

2.5

- 6.25

- 7.61

- 8.35

0.66

- 0.74

3

2.2

- 6.37

- 7.52

- 8.26

0.68

- 0.74

6

2.2

- 6.60

- 7.85

- 8.71

0.92

- 0.86

6

2

- 6.70

- 7.80

- 8.64

0.95

0.84

9

2.2

- 6.75

- 8.07

- 8.93

1.01

- 0.86

9

2

- 6.85

- 7.99

- 8.86

1.04

- 0.87

9

1.8

- 6.99

- 7.90

- 8.75

1.07

- 0.85

20

2.2

- 7.08

- 8.42

- 9.32

1.11

- 0.90

20

2

-7.16

-8.34

-9.26

1.14

-0.92

20

1.8

- 7.30

- 8.26

-9.16

1.17

0.90

Table 7 T h e c a l c u l a t e d s t a b i l i t y c o n s t a n t s o f c a d m i u m s u r f a c e c o m p l e x e s w i t h silica a t 3 5 ° C Ns (Sites n m

C1 ( F m - 2 )

Log K_

L o g Kcation

L o g K =-SiOCd+

SOS/DF

L o g K Eq. (19)

3

2.5

- 5.97

- 7.11

- 7.94

0.98

- 0.83

3

2.2

- 6.10

- 7.00

- 7.85

0.94

- 0.85

6

2.2

- 6.31

- 7.36

- 8.32

0.83

- 0.96

6

2

-6.43

-7.27

-8.23

0.82

-0.96

9

2.2

- 6.46

- 7.56

- 8.55

0,83

- 0.99

9

2)

2

- 6.58

- 7.47

- 8.46

0,82

- 0.99

20

2.2

- 6.78

- 7.92

- 8.94

0,83

- 1.02

20

2

-6.89

-7.83

-8.86

0,83

- 1.03

M. Kosmulski/ Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201 214

208

the pH is shown in Figs. 2 and 3. The extent of the experimental error in these and in subsequent figures is represented by the size of the graphical symbols. In 1 mol d m s NaCI, CdC1 ° and CdCI3 are the predominant ionic forms of cadmium in the solution, but the adsorption increases with the pH, as is usually observed for cations. Cadmium adsorption at a constant pH and background electrolyte concentration increases when the temperature increases. This trend is also typical for cation adsorption, while the adsorption of anions usually decreases with the temperature [6]. These results are not obvious: the positive surface charge of alumina and the occurrence of cadmium in anionic rather than cationic forms may suggest that the adsorption of cadmium from 1 tool dm -3 NaC1 would show features characteristic for anions. The s-shaped curves in Figs. 2 and 3 can be linearized when log (% uptake/(100% - % uptake)) is plotted as a function of pH. The slope of these Kurbatov plots [2] for the data presented in Figs. 2 and 3 is about 1 except for l m o l d m s NaCI, where it is about 0.8 (Fig. 4). This result shows that one proton is released per one adsorbed cadmium ion in the absence of chlorides, i.e. 100 u

/'/I ~ u

,'/, I

80-

/o

~

m.~

L..'/-

o

O

//;/"i,,j

8o-

~/ / ~ ;~7 / ;'~. 0 ~a~'/.~ / ~

¢,) 40-

,

/

~,'/~l 0 A ~,,/I ~" /

20AI]~

.V~'IY II t.,"

l l ~ l

4

'

.

.

i , / '

ffP~J// A

o

-/

/

.

ITrm o l A,'~,AA0,01

M NaCI

ooooo 1 mnnmmm 0.1

M NaCl04

~ - ...... .

.

_ _

1 O, 1 0.01

M NaCI

1

0.1

M NaCIO

5

pH Fig. 3. Cd(n) adsorption on alumina as a function of the pH and ionic strength at 35"C. The data used to calculate the model curves (reaction (1)) are given in Tables 1 3.

° ~-'

1000

i

fTI'T~ 0.1

CL

/~0.01 tO0

ooooo

/ M NaCI

1

nuamuu 0.1 M NaCl04

0

~-

0

1 ~• !

.T_..

,!

o.t~ (1)

,,

/

~ n A

00 mp~O 0 000 °~ 0

4:

-~a_o.ot 1! z-

B~o.oot 10

pH Fig. 4. Kurbatov plots for the data points taken from Fig. 3. The slope of the line equals 1 and corresponds to a release of one proton per one adsorbed ion.

reaction (1) rather than reactions (3) or (4) is responsible for cadmium adsorption on alumina. A detailed discussion of proton stoichiometry in the adsorption of multivalent cations can be found in the literature [2,5]. An analogous reaction was found to describe the adsorption of many heavy metal ions on goethite [5] and cobalt adsorption on alumina [11]. Both cadmium and cobalt [11] adsorption data show nearly theoretical slopes corresponding to a release of one proton per one adsorbed heavy metal ion when 20% < % uptake < 80%. Outside this region, the theoretical dependence of adsorption on the pH is much steeper as compared with the experimental data. Also, several sets of data reported in [5] show such deviations. The curves shown in Figs. 2 and 3 were calculated for the selected TLM parameters (Table 2) using an adsorption model with a single reaction (1) with cadmium adsorbed in the surface plane (Table 3). This simple model overemphasizes the effect of chlorides on pHso (the pH value at which 50% of cadmium is adsorbed) and the model curve corresponding to 1 mol dm -3 NaC1 is much steeper than that following from the experimental data. However, it gives a much better fit than any other model involving only a single

M. Kosmulski / Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201-214

reaction. For example, in a single-reaction model with reaction (1) but with cadmium adsorbed in the /~ plane, the effect of NaC1 on pHso is much more overestimated compared with the curves shown in Figs. 2 and 3. Hayes and Leckie [-18] have shown that a model assuming the adsorption of heavy metal ions on goethite in the surface plane gives a much more realistic dependence of adsorption on the ionic strength than a model with

209

tO0

£oo. ~J 8 0

,////

o

o

/o

- -

l

6o

q'cd = q'~.

©

The coincidence between experimental and model curves in Figs. 2 and 3 is quite satisfactory when the data corresponding to 1 mol dm 3 NaC1 are neglected in the comparison. For this limited set of data, the effect of electrolyte on cadmium adsorption is negligible. Many earlier studies of the ionic strength effects on the specific adsorption of cations on positively charged surfaces were limited to electrolyte concentrations up to 0.1 mol dm -3, and negligible effects of electrolytes on pHso even in the presence of complexing anions were reported. It should be emphasized that conclusions of this kind may depend on the range of electrolyte concentrations covered. The lower value of the slope of the Kurbatov plot in the presence of 1 mol dm 3 NaC1 (Fig. 4) can be explained in terms of an adsorption model using reaction (1) and another reaction in which cadmium is adsorbed without proton release. Since a low value of the slope of the Kurbatov plots is observed only in the presence of chlorides, reaction (6), corresponding to the adsorption of the cadmium chloride complex without proton release may be a good choice. As a matter of fact, the model assuming that cadmium adsorption in the systems considered is due to reactions (1) and (6) gives a smaller SOS/DF than any other model involving only two surface reactions. However, only a slightly larger SOS/DF is obtained with a combination of reactions (1) and (5) (Table 3). In both models, the calculated equilibrium constants of reaction (1) are practically identical. The model curves calculated for a combination of reactions (1) and (6) are presented in Fig. 5. Compared with Fig. 3, the curve corresponding to 1 mol dm 3 NaC1 is less steep, according to the experimental trend, and the pHso on this theoretical curve corresponds to the experimental value. The model

~J

40

/k/n

,/

//o Q

//

20

I I I I I 10.1 /k~kA/kO.01 M NaCI

/

oolMI, O 1 ",.Rig.. O. 1 M NoCIO

AA ~

10

pH Fig. 5. Cd(n) adsorption on alumina as a function of the pH and ionic strength at 35°C. The data used to calculate the model curves (reactions (1) and (6)) are given in Tables 1 3.

curves in Fig. 5 predict cadmium adsorption from 0.01 and 0.1 m o l d m -3 NaC1 to be higher than from 0.1 mol dm -3 NaC104 at low pH values. This corresponds to the experimental trend. An increase of cadmium adsorption on goethite in the presence of chlorides at low pH values has been also reported (Ref. [9] and references cited therein). Several other models involving two reactions responsible for cadmium adsorption give a SOS/DF value lower than a model with reaction (1) alone. For example, one can consider the formation of surface complexes =A1OCd + C1-

(14)

-A1OCd +-C104

(15)

with cadmium in the surface plane and the anion in the/~ plane. The SOS/DF value for such a model (Table 3) is considerably lower than in a model involving only reaction (1). A higher formation constant for the former complex is in line with the affinity of cadmium to chlorides. Even lower SOS/DF values may be obtained with models involving three surface reactions. Two examples are given in Table 3 and in Figs. 6 and 7. Table 3 shows that the calculated stability con-

210

M. Kosmulski/ Colloids Surjhces A. Physicochem. Eng. Aspects 117 (1996) 201-214 100

IIIII10.1

"///~

/+~(~ q

enoo 1 "h/'m ~3 80- nnmmmn O.1 M NaCIO+//i V ¢d

"7"(3 l

-

-

/f+A /o

60-

iI

,o/

e..) 40-

'o/

<3.) E]

20-

""

1

~_a .,..'/'/'/'/'/'/'/'/'/~#" 0

_ _ 0.1 . . . . . . . . 0.01 _

_

_ _

o

÷

4

pH

M NaCI

1

0.1

~

M NaCIO

~

1o

Fig. 6. Cd01) adsorption on alumina as a function of the pH and ionic strength at 15°C. The data used to calculate the model curves (reactions (l), (5) and (6)) are given in Tables 1-3.

L 0.1 /%VVV~O.01 M NaOl I

oo~

~3 80

l a n a i O.1 M NaClO+

°+::l,.,

,," ,,',~'~//i,,,xl l O ' ~ ' ~ ~x ,' / ,! 70

,,'/11

" -

£/o

}t/o

=+0

+, + i/+ ++/o/

"°

¢.,.) 4 0 -

2o

7'2

1

-f,,"/¢'/

........ 0.01

o

4

-

,4

~

+

~

M NoCI

11 M No0,o ~ lo

pH Fig. 7. Cd0]) adsorption on alumina as a function of the pH and ionic strength at I5°C. The data used to calculate the model curves (reactions (1) with Cd adsorbed in the surface plane, (1) with Cd adsorbed in the fl plane and (6)) are given in Tables 1-3.

stants of surface complexes decrease when a new reaction is added to the model. Thus, a comparison of stability constants of

a given surface species calculated from models involving different numbers of surface reactions may be misleading. There are, however, exceptions from this rule: the equilibrium constant of reaction (1) calculated for a model involving reaction (1) and reaction (5) or (6) is equal to that calculated for a model involving all three reactions. Also, the equilibrium constants of reaction (6) calculated from a model involving reactions (1)(~kCd = ~o ) and (6) on the one hand, and a model involving reactions (1) (~Cd = ~ko); (1) (~Cd = ~p) and (6) on the other hand are practially equal (Table 3). Fig. 6 shows similar trends as Fig. 5, namely, the calculated adsorption from 0.1 mol dm -3 NaC1 at low pH values is more pronounced than from NaC104 solutions. On the other hand, in Fig. 7 the calculated adsorption from 1 mol dm 3 NaC104 at low pH values is clearly overestimated, but in terms of SOS/DE, the model curves in Fig. 7 are better fitted than those in Fig. 6 or any other set of model curves shown in this paper. This result shows that a model leading to the lowest SOS/DF value must not be accepted uncritically. It is shown in Fig. 1 that the equilibrium constant of reaction (13) is slightly sensitive to the choice of the T L M parameters. Also, with a model of cadmium adsorption with two surface reactions (1) and (6) it is possible to find parameters characterizing cadmium adsorption which are independent of the TLM assumptions. Tables 4 and 5 summarize the equilibrium constants of these reactions, which are calculated using different T L M parameters. These results show many features similar to those reported in Ref. [ 11 ]. The calculated equilibrium constants and the corresponding SOS/DF values decrease when N s increases while the other T L M parameters are kept constant. This suggests that a high Ns is more appropriate for the adsorption modelling of heavy metal ions on alumina. While the particular equilibrium constants (reactions (1) and (6)) vary by two orders of magnitude, their ratio is constant for a given temperature. Therefore, the calculated ratio [=A1OCd + ]/[=A1OHCdC1 + ] at a given ionic strength and pH value is independent of the assumed T L M parameters. Fig. 8 shows the calculated log K of reactions (1) and (6) as a function of Kcation. Except for the data corresponding to 1 sitenm -2, for which the SOS/DF was considerably higher than for the other data, the

M. Kosmulski/Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201 214

211

0- -- - -

O

/ -1-

42!

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o

itlltl ~

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2

/

4

-3 -IO

log

-3

-8

_t 9

L||||l

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20

2

28

log KNa

KNa

(c)

(a) 8.5

O

8.0

7-

7.5 +

+

U ~7.0

r~

o ,< II

II

6-

o

/

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~00000

IIIlil

ApK,=0

©

/

2

29 l o g KNa

5

_

(b)

-to

[illll 29 log

2 28

Ksa

(d)

Fig. 8. The equilibrium constants of (a, c) reaction (1) and (b, d) reaction (6) at (a, b) 15°C and (c, d) 35°C calculated al different TLM parameters as a function of the binding constant of the cations of the background electrolyte. The lines correspond to constant values of the equilibrium constants of reactions (16) and (17). data points yield a straight line whose slope is close to 1. This m e a n s that the e q u i l i b r i u m constants of the following surface reactions ---AI O - N a + C d

2+==A1-OCd ++Na +

(log K = 7.4 at 15°C a n d 7.1 at 35°C) ---A1-O-Na + Cd 2 + + C1- + H +

(16)

= ---A10HCdC1 + + Na +

(17)

(log K = 15.7 at 15°C and 14.95 at 35°C) are i n d e p e n d e n t of the T L M parameters. The above values of the e q u i l i b r i u m constants corr e s p o n d to the lines plotted in Fig. 8. W h e n the values of the e q u i l i b r i u m c o n s t a n t s of

M. Kosmulski / Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201-214

212

a reaction are given at different temperatures, the standard enthalpy of this reaction may be calculated as AH~°d~= RT2d In Kads/dT. On the other hand, when the value of the equilibrium constant characterizing the adsorption is not available, the enthalpy of adsorption can be estimated directly from adsorption isotherms at different temperatures using the approach presented in Ref. [-6]. Fig. 9 shows the adsorption of cadmium on alumina at various NaC1 concentrations as a function of the surface charge density. In such coordinates, the adsorption is practically independent of the temperature, so the overall enthalpy of cadmium adsorption on alumina at constant ao equals zero. It is particularly interesting that this enthalpy is slightly sensitive to the presence of complexing anions. The standard enthalpies of reactions ( 1 ) and (6) calculated from the temperature dependence of the equilibrium constants (Table 3 and 4), assuming that Ns and ApK a do not depend on the temperature, are equal to 30 kJ mo1-1 and - 9 kJ mo1-1, respectively and they are slightly sensitive to the choice of the T L M parameters. The adsorption of cadmium on silica can be explained satisfactorily in terms of a model

involving only one surface reaction =-Si-O-H + Cd 2+ = - S i - O C d + + H +

The equilibrium constants of this reaction calculated for different TLM parameters are given in Tables 6 and 7. Fig. 10 shows that the model curves properly reflect the experimentally observed trends. The last columns of Tables 6 and 7 show that the equilibrium constant of the reaction =-Si O - N a + C d 2+ = ~ S i - O C d + + N a +

100

CALCULATED ......

0 o o

~) 80-

~::]

_

80-

A

O~

___

A@

[]

A

• A

20-

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AA

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.

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/(

o/o

•

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,

20.

/ °°/

•O •

o.io

1

O)

z~

A zl

M NaCI

M NaCl

1111110,1 1 M NoCI nmqNnm 0.1 o o o o o I M NaClO.~

0) 0

I

0.Ol

60-

40-

oi

MEASURED

A

80-

d' .

0.01

__ o,

,,,,a

0 0.00

(19)

calculated as a ratio of the equilibrium constant of reaction (18) and Kcatio. (compare Eq. (12)) is relatively insensitive to the TLM parameters. The adsorption of Cd(II) on silica shows several features which are also observed for alumina. Adsorption at a constant pH and electrolyte concentration increases with the temperature (Fig. 1 l) while adsorption at a constant ao does not depend on the temperature. Thus, the enthalpy of adsorption at constant a o equals zero and the standard enthalpy of reaction (18) calculated from the temperature dependence of its equilibrium constants, assuming that Ns and Ct do not depend on the temperature, equals 33 kJ mol 1 and it is independent of the TLM parameters used in the calcu-

i00

0

(18)

O

o.15

o/Cm

i

0.20

-2

Fig. 9. Cd(u) adsorption on alumina as a function of the surface charge density at 15°C (empty symbols) and 35°C (filled symbols).

0

5

pH Fig. 10. Cd(tI) adsorption on silica as a function of the pH and the ionic strength at 35°C. The model curves correspond to reaction (18).

M. Kosmulski/Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201-214 100

80-

( ~ : ) 0 . 1 M NoCI IIII110.1 M LiCI Jm ~ " B_ /MNAA/N0.1 M CsCI o / II ~ / II L open symbols 15 C / ~ / DO full symbols 35°C /,~ " / F . I ~ "L

213

discrepancy may be due to surface heterogeneity; also, Ct may vary from one alkali metal cation to another.

5. Conclusions 60-

40-

20-

~ z x

, 8

9

pH Fig. 11. Cd(n) adsorption on silica from 0.1 mol dm 3 solutions of alkali chlorides as a function of pH. The model curves (reaction (18)) are identical for Li, Na and Cs.

lations. Comparison of Figs. 10 and 5 confirms the trend found in Ref. [7] that the presence of complexing anions and a negative surface charge lead to a significant shift of pHs0 toward higher pH values. Fig. 11 shows that cadmium adsorption on silica from CsC1 solution is considerably lower than from NaC1 and LiCE It is well known that the negative surface charge density and the adsorption of alkali metal cations on silica increase from Li to Cs. This property of silica is unique a m o n g oxides and it may be interpreted in terms of the T L M as a difference in Kcation , namely KLi < KNa < Kcs. As a matter of fact, the values of a o of silica in 0.1 mol LiC1 and CsC1 may be reproduced using the selected T L M parameters from Table 2 except for Kcation, which is fitted by means of FITEQL and, for example, at 35°C, log K c s = - 7 . 0 2 and log KLi=-7.54. However, cadmium adsorption calculated from Eq.(18) with the above T L M parameters is slightly sensitive to the Kcation value and identical model curves were obtained for different alkali chlorides (Fig. ll). Thus, the observed difference between CsCI on the one hand, and NaC1 and LiC1 on the other hand cannot be explained in terms of the present model. This

(1) An SCM involving two or three surface reactions may be used to predict the adsorption of heavy metal ions on oxides from solutions containing complexing and non-complexing anions over a wide range of ionic strengths. (2) Cadmium adsorbs in the form of cations, while the adsorption of anionic cadmium chloride complexes is negligible even when the surface is positively charged and anionic complexes are predominant in the solution. A similar trend has been previously found for cadmium and mercury adsorption on goethite. (3) The calculated stability constants of surface complexes decrease when a new reaction is added to the model. (4) The stability constants of surface complexes depend on the T L M parameters used to calculate them. However, the equilibrium constants of the following surface reactions: - A 1 - O - N a + Cd 2 + = = A 1 0 C d + + N a + (log K = 7.4 at 15'~C and 7.1 at 35°C) and - A 1 - O - N a + C d 2+ + C 1 - + H + = -A1-OHCdC1 + + Na + (log K = 15.7 at 15°C and 14.9 at 35°C) are independent of the parameters of TLM. (5) The calculated standard enthalpies of surface complexation reactions are insensitive to the T L M parameters.

Acknowledgments A grant from the Alexander von Humboldt Foundation is gratefully acknowledged. Dr. HansThomas Weger is acknowledged for correcting the English.

References [1] P.W. Schindler, in M.A. Anderson and A.J. Rubin (Eds.), Adsorption of Inorganics at Solid Liquid Interfaces, Ann Arbor, 1981, Chapter 1.

214

M. Kosmulski/Colloids Surfaces A: Physicochem. Eng. Aspects 117 (1996) 201 214

[-2] D.G. Kinniburgh and M.L. Jackson, in M.A. Anderson and A.J. Rubin (Eds.), Adsorption of Inorganics at SolidLiquid Interfaces, Ann Arbor, 1981, p. 91. [3] J. Lyklema, Croat. Chem. Acta, 60 (1987) 371. [4] P.W. Schindler and W. Stumm, in W. Stumm (Ed.), Aquatic Surface Chemistry, Wiley, 1987, p. 83. [5] D.A. Dzombak and F.M. Morel, Surface Complexation Modeling: Hydrous Ferric Oxide, Wiley, New York, 1990. [6] M.L. Machesky, in D.C. Melchior and R.L. Bassett (Eds.), Chemical Modeling in Aqueous Systems, II, ACS Symp. Set. 416, Americal Chemical Society, Washington, DC, 1990, p. 282. [7] M. Kosmulski, Wiad. Chem., 49 (1995) 21 (in Polisht. [8] C. Tiffreau, J. Liitzenkirchen and P. Behra, J. Colloid Interface Sci., 172 (1995) 82. [9] L. Gunneriusson, J. Colloid Interface Sci., 163 (1994} 484.

[10] A. Herbelin and J. Westall, FITEQLver. 3.1., Oregon State University, Corvallis, Oregon, 1994. I l l ] L.E. Katz and K.F. Hayes, J. Colloid Interface Sci., 170 (1995) 477. [12] K.F. Hayes, G. Redden, W. Ela and J.O. Leckie, J. Colloid Interface Sci., 142 (1991) 448. [13] L.K. Koopal, W.H. van Riemsdijk and M.G. Roffey, J. Colloid Interface Sci, 118 (1987) 117. E14] D.A. Sverjensky, Nature, 364 (1993) 776. [-15] M. Kosmulski, J. Colloid Interface Sci., 135 (1990) 590. El6] M. Kosmulski, Ber. Bunsenges. Phys. Chem., 98 (1994) 1062. [ 17] R.M. Smith and A.E. Martell, Critical Stability Constants, Vol. 4 6, Plenum, New York, 1976, 1982, 1986. [18] K.F. Hayes and J.O. Leckie, J. Colloid Interface Sci., 115 (1987) 564.