Modeling surface acidity of two powdered activated carbons: Comparison of diprotic and monoprotic surface representations

MODELING SURFACE ACIDITY OF TWO POWDERED ACTIVATED CARBONS: COMPARISON OF DIPROTIC AND MONOPROTIC SURFACE REPRESENTATIONS B. E. REED” and M. R. Department

of Civil Engineering. (Received

20 November

~ATSUM~I.O

West Virginia University. Morgantown. 1990; accepred

in revtwd fortn

WV 26506, U.S.A.

26 Februury

1991)

Abstract-Powdered activated carbon (PAC) can behave as a weak acid in solution. Historically. the amphoteric nature of hydrous solids has been modeled as a single weak diprotic acid. To determine if the single diprotic representation was the most appropriate description of the PAC surface, two commercially available PACs underwent acidimetric-alkalimetric and NaNO, titrations. The surface complex formation (SCF) model, a variation of a soluble equilibriuni chemical model. was used to simulate experimental titration curves using several surface representations. A three-monoprotic site model was chosen to represent the amphoteric nature of both PACs studied, based on the following criteria: the goodness of fit of model results; the coherence of the representations to previously published results; and the agreement of surface site representations at different ionic strengths for the same PAC. Surface acidity parameters (pH,,,, , acidity coefficients and number of surface sites) and surface speciation diagrams are presented. Key Words--Activated carbon, acid-base behavior, acidity constants. complex formation model.

1. INTRODUCTION Interest in the use of hydrous solids for removai of heavy metals from various wastewater streams is increasing. Batchelor and Dennis[l] used metal oxides in the treatment of domestic wastewater while Matsumoto, etai.[2] reported that the addition of a powdered activated carbon (PAC) to biological suspended growth (BSG) treatment processes was effective in mitigating the toxic effects of soluble heavy metals. Adsorption of heavy metals from solution by PAC is believed to be responsible for improved BSG process performance. Metal adsorption

is a strong

function

of solution

pH. Stumm and Morgan131 have identified the pH as one of the more important parameters in determining metal adsorption by hydrous solids. Thus, an accurate description of the acid-base characteristics of hydrous solids is essential in modeling the metal sorption phenomenon. In the past, the surface acidity of metal oxides has been modeled as a single weak diprotic acid[l,4]. This approach was later applied to activated carbons[5-71. While the surfaces of metal oxides are fairly well defined. activated carbon surfaces contain numerous functional groups capable of binding and releasing protons(8,9]. Thus the single weak diprotic site representation may not adequately describe PAC surfaces, and other descriptions such as multiple site representations should be investigated. The purpose of this research was to determine the

‘To whom correspondence

should be addressed.

zero point of charge. surface

most appropriate surface-site representation for two commercially available powdered activated carbons. Acidimetric-alkalimetric titrations were performed on the two PACs and the surface complex formation (SCF) model was used to simulate the experimental titration curves, using surface acidity parameters determined from graphical and statistical methods. The mathematical solution of the SCF model was developed by modifying the solution equilibrium model entitled MINEQL[lO]. Results from this study will be used as a starting point for future work involving modeling heavy metal adsorption onto powdered activated carbon.

2. BACKGROUND

The basic premise of the surface complex formation model is the use of mass action laws to describe ion interactions with the hydrous solid surface. The surface of the hydrous solid acquires a surface charge, due to various surface groups or sites, and an electric double layer (EDL) develops around the charged particle. The total free energy of interaction is defined by the sum of the free energy of the chemical interaction at the solid surface and an electrostatic component. 2.1.1 Diprotic Surface Site Model. In the past, it has been assumed that all surface sites are capable of binding and releasing protons equally, thereby the solid can be modeled as a single weak diprotic acid. With this assumption, the surface functional groups can be represented by the following surface reac-

1192

B. E. REED and

tions:

M. R. MATSUMOTO and a negatively charged site:

where the symbol (=) distinguishes surface compIexes from soluble complexes. KS, and K,, are the first and second surface acidity constants defined by the reactions (la) and (lb), respectively. -F;,, and I(,* will vary with ionic strength. Fl,’ is the activity of the proton at the solid surface. The Boltzman equation is used to relate the activity of a solute in the bulk solution to the activity at the surface {H:}

= {H,‘} exp( -F@/RT)

(2)

where R, T, and F are the gas constant, Faraday constant, and absolute temperature, respectively. tP is the potential difference across the electric double layer, measured in volts. Substituting the Boltzman equation into the mass action laws, and assuming that the activity coefficients for the surface complexes are equal[ll], and the activity coefficients for the bulk and surface activities are equal[l2], yields:

K<,,

=

~=SOH”IW,‘lexp( - F@/RT) [=SOH;]

K<‘z= ]=SG-I{&?} [=SOHO]

exp( - F

(3a)

W)

where [ ] and { } represent molar concentrations and activities, respectively. The exponential term can be considered as a correction term included in the mass action laws to account for the electrostatic interactions. The material balance eqn for surface sites is: N, = [=SOH;]

+ [=SOH=‘] + ]=SO-]

(4)

where N, is the total concentration of a site in moles/ L. N, can be expressed in moles/g or moles/cm* if the concentration and specific surface area of the solid are known. 2.1.2 Monoprotic surface site model. Snoeyink and Weber[8] have reported that phenolic and lactone functional groups may be responsible for the amphoteric behavior of activated carbon, while Mattson and Mark[9] have suggested carboxyl and quinone groups. Regardless of the specific functional group(s) present on the surface of the carbon, it would seem plausible to model the carbon surface as a number of weak monoprotic acids rather than a single diprotic acid. There are two types of monoprotic sites to consider for the charge of the carbon surface to be modeled properly, a positively charged site:

where i is an index to differentiate between sites. Each of these reactions will have associated with it a pK, and N,. The acidity constants for the two types of reactions are written as fQ,,

=

n

~=p’ow]{H;} [=POH,‘]

K:” =

exp( - FORT)

t=~o-lwb+~exp(_ F@,Rq [=N’OH”]

(6a)

(6b)

For a two-monoprotic site representation, there is one of each type of site. For the three- and fourmonoprotic representations, there can be several combinations of eqns (Sa) and (5b). However, there must be at least one of each type of site to account for the change on sign of the surface charge with PH. 2.1.3 Potential-surface charge density relationship. The potential can be related to the surface charge through a number of different electric double-layer models, such as the constant capacitance model, the Gouy-Chapman diffuse layer model, and the Stern model[l3]. The constant capacitance model requires one capacitance, while the Stern model requires two. While capacitances have been estimated experimentally for metal oxides, there has been no such work using PAC. Thus, the Gouy-Chapman model, which does not require a specified capacitance, was chosen to represent the EDL. Westall and Hohl[l3] have reported that all these electrostatic models represent data equally well, but with different corresponding parameters. In addition, the Gouy-Chapman model has been used by several researchers in the study of activated carbon surfaces[5,6,7]. The Gouy-Chapman diffuse layer model is reprsented by the following eqn: c = 0.1172 i1’2sinh(.zF&/2RT)

(7)

where 0 is the surface charge in coulombs per surface area, (C/ml), Q,, is the potential at the surface of the solid, I is the ionic strength of the medium, and z is the valence of the background electrolyte. If 4r, is approximately equal to the potential at the plane of the closest approach of adsorbed ions, then Cp,is also the potential difference across the electric double layer in eqns (3) and (6). 2.2 Determination of surface acidity parameters The pH-a-@ relationship is determined experimentally by performing acidimetric-alkalimetric titrations as described by Huang[l4]. The surface charge-pH relationship is calculated experimentally using the following expression: ~ = (Ae~)(96,5~

C/equivalent) &C,V

(81

1193

Surface acidity of activated carbons S, is the specific surface area (ml/g), C, is the concentration of the solid (g/L), V is the volume titrated (L), and Aeq is the amount of acid/base added in equivalents, at each pH value. Aeq is taken from the net titration curve, corrected for the pH at zero point of charge (pH,,,). The pH,,, is defined, in the absence of specifically adsorbed anions or cations, as the pH at which the proton excess at the surface is zero. When the pH > pH:,,, the net surface charge is negative, and when pH < pHzpf the net surface charge is positive. Experimentally, the pH,, can be determined from the intersection of the net titration curves at low ionic strengthsjl41, and by titrating a solid with an inert salt solution and determining the change in pH with increasing ionic strength[4,15]. The addition of an inert electrolyte to a solid suspension changes the pH in the direction of the pli,,. Various mathematical methods exist by which values of the surface acidity parameters can be determined, Huang[l4] presented a graphical method for the single diprotic representation, while Westall[ 16,171 has developed a statistical parameter optimization procedure, entitled FITEQL, by which surface parameters could be determined for various surface site representations. In this study, both the graphical and statistical method will be used for the single diprotic surface representation. For the multiple surface site representations, only the statistical method is applicable. The important aspects of both methods are presented below. The subscripts on 4, and o- are not included for ease of presentation. When the surface is positively charged (pH < pH,,,,) the surface charge can be approximated by the surface proton balance, assuming that [=%-I is negligible, where

[&OH;] B is a conversion using the Faraday cific surface area solid (g/L). With site mass balance duces to

=

G/B

(9)

factor relating C/m’ to mole/L constant (96,500 C/mole), the spe(m’ig) and concentration of the the above assumption, the surface (eqn 4), upon rearrangement. re-

[=SOH"] = N, - olB

00)

Substituting eqn 10 into the first acidity eqn and rearranging gives

(11) The term {H;} is equal to exp(-~~/~~)/{~~~. From a plot of l/o versus l/{H,+}, K,,, can be calculated from the intercept and N, from the value of the slope. For pH > pff,,,,, [=SOH +] is assumed negligible and performing the same type of manipulations as before yields

{H;}= BK,,$f,f(-a) - I<,:

where K,#? and N, are determined from the 1icr versus {H:}plot. FITEQL determines the values of the surface acidity constants and N, based on minimizing the sum of squares of errors in the titration data. The reader is referred to several reports by Westall[l6,17] for details of the statistical theory behind FITEQL. 3. MATERIALS AND METHODS Two commercially available powdered activated carbons were investigated: Darco HDB (American Norit Company) and Nuchar SN (Westvaco Company). Selected properties of the two carbons are given in Table 1. Data were provided by the manufacturer unless otherwise indicated. Average values for surface area were used in model calculations. Both carbon were washed, rinsed, and stored according to the method suggested by Huang[ 141. For Nuchar SN, during the final rinsing step, Nuchar SN failed to settle, causing the loss of large amounts of carbon during decanting. Thus, the final rinses for Nuchar SN were done with a solution of ionic strength of 2 x IO-’ M (NaNO,), which allowed the Nuchar SN to settle adequately. Rinsing of Nuchar SN with the 2 x lo-’ M NaNO, solution continued until the conductivity of the suspension was constant. Rinsing with the NaNO, solution was not expected to affect the Nuchar SN titrations, as NaNO, was used as the background electrolyte. The consumption of protons or hydroxide ions by the carbon surface as a function of pH (i.e., the net

Table 1. Selected properties of Darco HDB and Nuchar SN’ Particle Size Distribution, (% thou) Carbon

Ash (%)

Surface

Areaz,(m2/g)

Apparent ~u~i~,(kg/~3)

100 Mesh

200 Mesh

325 Mesh

DarcoHDB

NA

600-650

500

99

9.5

90

Nuchar SN

3-5

140@1800

350

95-100

85-95

65-85

* Manufacturer’s Data

2 Nitrogen BET Method

(12)

NA: Not Available

1194

B. E. REED and M. R. MATSUMOTO

tiration curve) is determined by subtracting the titration curve of the filtrate of the carbon suspension from the suspension titration curve[l4]. For each ionic strength investigated, four samples containing approximately 10 g/L carbon each were prepared. Two of the samples were titrated directly, one with 0.1 N NaOH and the second with 0.1 N HNOI. The remaining two samples were filtered using glass-fibre filters (Whatman GFIC). The filtrate was saved and titrated with either NaOH or HNO,. The acid and base legs of the suspension titrations were combined, as were those for the filtrate titrations. The filtrate titration curve was subtracted from the suspension titration curve, to give the net titration curve. The net titration curve was corrected for pH,,, by subtract~ng/adding the equivalents of acid/base at the pH,,,, from each titration point of the net titration curve. Titrations were carried out using a Tanager Scientific Systems IDG-8800 automatic titration system in conjunction with an IBM XT computer. An Orion Research combination pH electrode (Model #9105) was used to monitor pH. Samples were closed to the atmosphere during titration by sealing the pH electrode and titration reactor connection with parafilm. The titrator was programmed to deliver a volume of titrant such that the change in pH for each addition was 0.15 pH units. A five-minute period between additions of titrant was used. If the pH had changed more than 0.02 units during the last 30 seconds of the five-minute period, the next aliquot of titrant was not added and the sample was allowed an additional five minutes to equilibrate. Equilibrium was observed to be rapid (less than five minutes) and omission of a titrant addition seldom occurred. Huang[l4] has recommended using a fast titration, two to five minutes between titrant addition, to minimize the effect of slow pH drift. NaOH was stored in a reservoir with a soda lime scrubber to prevent contamination by CO,. NaOH was standardized using ~~u~~~~~ methods procedure 401[ IS]. HNOJ was standardized by titrating a known volume of HNOJ with NaOH of known normality to pH 7. Titrations were carried out at 22°C. Three ionic strengths were investigated, lo-‘, lo-?, and 10mi N (2 x 10. i for Nuchar SN). NaNO, was used as the background electrolyte and the titration volume was 75 mL. Carbon was stored as a slurry and enough of the stock solution was delivered to the titration vessel to produce a carbon concentration of approximately 10 g/L upon dilution to 75 mL. The titration vessel was filled to 75 ml with a NaNO, solution, such that the final ionic strength of the sample was either 10 -I, lo-‘, or lo-” N (2 X 10m2for Nuchar SN). Samples were allowed to equilibrate with the electrolyte for approximately 12 hours prior to the start of titrations. Titrations were duplicated for several ionic strengths. Actual carbon concentrations were determined using Method 209A of Standard Methods[ IS]. Salt titrations of the carbons were carried out by

adding sufficient quantities of NaNO, to slurries of Darco HDB and Nuchar SN to change their ionic strengths from 10d3 to 10-l and from lo-” to 10-I without introducing a significant dilution error (< 1%). Prior to NaNO, addition, the pH of the slurries were adjusted so that the initial pH of the slurries ranged from approximately 3 to 9. After each NaNO, addition, the samples were shaken for 24 hours, and the pH of the solution was recorded. Changes in pH from the initial value after each addition of NaNO, were calculated. The effects of dilution and change in ionic strength as titration proceeded were taken into account, as were the experimental errors associated with the delivery and preparation of the titrant, and measurement of the carbon concentration. 4. RESULTS AND DlSCUSSlON 4.1

Titration curves and pH,,,

The net titration curves for Darco HDB and Nuchar SN at each ionic strength are presented in Fig. 1. The pH,,, is determined from the intersection of the net titration curves of lower ionic strengths[l4]. The 10-I and 10-l N Darco HDB curves intersected at PI-I = 7.45, and the 2 x 10-j and lo-” N curves for Nuchar SN intersected at pH = 5.35. In subsequent calculations, these pH values were taken to be the pH at the point of zero charge (pBpi,).

a. 0.4 _’ + 0.3 ii 2 0.2

Darco HDB

5 A 0.1 .L. P 0.0 'Z 69 w -0.1 : -0.2 PH

b. 0.4 I

E -0.2 j

3

4

5

6

7

a

9

10

11

PH

Fig. 1. Net titration curves for a) Darco HDB and b) Nuchar SN.

IIY5

acidity of activated carbons

Surface

Based on literature results for other solids, the amount of titrant required to reach a given pH increases with ionic strength[l3]. This trend was not observed for the base leg portion of the titration curve of Darco HDB at I = lo-‘. While this phenomenon has been reported by Corapcioglu and Huang[S] for several Darco-brand activated carbons, it is unclear why this occurred. Because of the limited scope of the study it was not investigated further. Titrations of the carbons with NaNO, were carried out to provide a check on the pH,,,, calculated from the acidimetric-alkalimetric titration curves. The results of the NaNO, titrations of both carbons are presented in Fig. 2. The pH range for which ApH approaches zero is 7.0 to 7.5 for Darco HDB and 5.5 and 6.25 for Nuchar SN. Although an exact pH,,,, cannot be calculated using the salt titration method, a possible range for the pH,,,, can be determined. The range of pH,,,, determined by NaNO? titrations is in good agreement with the values of pH,,, calculated from the intersection of the low ionic strength acidimetric-alkalimetric titration curves. Both carbons required addition of base to reach their pH,,,<. The amount of base required to reach the pH,,,, was subtracted from the base leg and added to the acid leg of the net titration curve, to produce the net titration curve corrected for pH1,,. The net titration curves corrected for pH,,,, are presented in

a. 0.3

I Darco

0.

HDB

-0.2

B -0.3 3

4

5

6

7

6

9

10

11

PH

b 0.4 7 -

Nuchar

SN

0.3 :

z

0.2

L

s T a .d

0.1 0.0

: cr -0.1 :

Fig. 3. Net titration

curves corrected forpH_, HDB and b) Nuchar SN.

For a) Darco

a

Dal-co

5

A

:

0

:

6

d

1c3 -> 1o-z -_)

7

Initial

Fig. 3 for both carbons. The surface of Nuchar SN will have a net negative charge at pH values > 5.35, while the surface of Darco HDB will be negative at pH values > 7.45.

HDB

lo-’

6

9

10

pH

b. 1.5

(

I Nuchar

1.0

A

: 2 I 1om3-> 1c

Cl

0.5

SN

1o-z->

10-l

z

-151”‘1”““‘1”‘1”““,1 3 4

5

6 Initial

Fig. 2. NaNO,

titration

curves

7

6

9

pH

for a) Darco HDB and b)

Nuchar SN.

4.2 SCF model results SCF model simulations of the acidimetric-alkalimetric titrations were performed using the surface acidity parameters (determined from either the graphical method or FITEQL) and compared with experimental results, to determine which surface site representation best describes the amphoteric nature of the PAC surface. 4.2.1 Single diprotic site representation. Theoretically, the values of N, calculated from eqns (11) and (12) should be equal. However, due to the error associated with the assumption that all surface sites behave amphoterically, the two values of N, are rarely equal[7]. Thus, the value of N, calculated for pH < pH :,,, is referred to as N; and for pH > pHI,,, is referred to as N,Results from eqns (11) and (12) for Darco HDB and Nuchar SN. at the three ionic strengths investigated, are presented in Fig. 4. The straight lines represent best-fit approximations of the linear portion of the data. Huang[l4] recommends using this portion of the data for the calculation of K,,(s) and N,(s). Values of pK,,,, pK,?, N;, and N,- calculated by the graphical method are listed in Table 2. The

I196

B. E. REED and M. R. MATSUMOTO Table 2. Graphical method surface acidity parameters for the single-diprotic representation

a 4e+O07

millimole/L 2e+007

Carbon

2

I

PKal

pKa2

Ns+

Ns

10-l 10-2 10-3

6.52

8.47

6.89 7.18

8.33 7.62

1.14 1.19 0.98

1.53 2.61 1.98

10-l 4.53 10-2 4.21 2 x 10-3 4.45

6.26 6.31 6.38

1.27 1.50 0.61

1.21 1.16 0.84

Y -

Oe+OOO

lkuco HDB -2e+007 0.0

0.5

1.0

1.5

2.0

2.5

3.0

l/U

Nuchar SN Derco HDB

3e-008

ze-008 - le-008 d - Oe+OOO -le-008 -2e-008

0

-3e-008 0.0

0.5

: I = 10-3 1.0

1.5

l/u

b

I

0

20

15

5 $7

1.5e-006

l.Oe-006

5.0e-007 a E 0.0e+000

-5.oe-007

-i.oe-008

0

1

4

2

5

which portions of the data in Fig. 4 were used in the calculation of pK,,, pK,,, N:, and N;. The pH,, for Darco HDB is 7.45 and for Nuchar is 5.35. Values of pH,*,, for Darco HDB at ionic strengths of lo-‘, lo-‘, and 10-j were found to be 7.5, 7.61, and 7.4, respectively. Values of pH$,. for Nuchar SN are 5.4,5.26, and 5.42 for I = lo-‘, lo-?, and 2 x 10m3,respectively. Thus, eqn (13) was satisfied, within 2 0.1 pH units, for all cases except Darco HDB at I = lo-‘. The average of N: and N;, at each ionic strength, were used in SCF model simulations. Values of K,,,, Ku2,and N, calculated by FITEQL are presented in Table 3. N, has only one value and eqn (13) is automatically satisfied because the entire titration curve is employed when using FITEQL. Also included in Table 3 is the term WDF, the sum of squared errors divided by the degrees of freedom. SS/DF is an indicator of the goodness of fit to the experimental data. A value of SS/DF between 0.1 and 20 indicates an adequate fit to the experimental data[16,17]. For both carbons, at all ionic strengths investigated (except Darco HDB at I = lo-‘), the value of SWDF was close to 20, indicating a poor fit. In addition, for Darco HDB at I = 10mJ, pKn, > pK,,,, which is chemically impossible. termining

5

Table 3. FITEQL surface acidity parameters for the single-

13/u

diprotic representation

Fig. 4. Results of the graphical method for a) Darco HDB and b) Nuchar SN.

surface site densities are based on a carbon concentration of 10 g/L. The values of pK,,, and pK,, must satisfy the condition (PKJ, + pKdl2

= pH,,

(13)

The left side of eqn (13) is referred to as pH$,. Satisfying this condition was a major factor in de-

carbon

I

N,,

millimole/L

SS/DF

P%

&2

10-l

6.26

a.59

10-2 10-3

6.82 7.58

8.12 7.19

0.94

10.8 18.5 16.9

IO-’ 10-2 2 x 10-3

4.03 3.88 3.75

6.68 6.77 6.82

2.34 2.20 1.82

18.9 17.9 22.3

LJarco HDB 1.81 1.74

Nuchar SN

Surface acidity of activated carbons

/ -4’

3

’ 4

5

I 6

8 7

i 6

.

I 9

I 10

’

3

4

5

7

6

PH

6

9

10

PH b.

b.

4

3 7

3 ii 2 ‘d T

3 2 1

P 0 2 2 -I -1

-

Graphical

z! -2 3

4

5

6

7

6

9

-3

10

3

4

5

2 ,

7

6

PH

6

9

10

PH

I Nuchar

SN

-

7

7

PH

PH

Graphical FITEPL

Fig. 5. SCF model simulations of Darco HDB titration curves for the single-diprotic representation using constants determined by the graphical method and FITEQL. Ionic strengths of a) 0.1, b) 0.01, and c) 0.001.

Fig. 6. SCF model simulations of Nuchar SN titration curves for the single-diprotic representation using constants determined by the graphical method and FITEQL. Ionic strengths of a) 0.1, b) 0.01, and c) 0.002.

In Figs. 5 and 6, experimental titration data and SCF model simulations, using a single diprotic surface representation, are presented for Darco HDB and Nuchar SN, respectively. The solid and dashed lines represent the titration curves simulated using constants determined by the graphical method and FITEQL, respectively. It is apparent from the results presented in Figs. 5 and 6, that modeling the acidbase behavior of the two PACs studied as a single diprotic acid (using constants from either the graphical method or FITEQL) is not adequate. The SCF model, using the single diprotic representation, predicts several noticeable inflection points, while the experimental data are relatively smooth and void of

any noticeable inflection points. A lack of noticeable inflection points in the titration data may suggest that several sites, capable of binding and releasing protons, exist on carbon surfaces. As the number of different amphoteric sites increase, individual inflection points are blurred and the titration curve becomes relatively smooth. 4.2.2 Multiple site representations. Complicating the selection of which surface-site representation to use is the fact that as the number of constants used to describe the titration data increases, a better model fit to the experimental data may result, regardless of whether the representation is physically correct. Thus, several surface-site representations

1198

B. E. REED and M. R. Table 4. Summary

MATSUMOTO

of FITEQL

Convergence

3 monoprotic

1 dipmtic Number of hramelers Carbon

13)

4 monopmtic

2 dipmtic

2 monoprotic

2 pos, 1 neg

1 pos, 2 neg

3 pas, 1 neg

2 pos, 2 neg

(6

(4)

(61

(6)

(8)

(81

1 pos, 3 neg

(8)

I

Lkwco HDB 10-l

c

C

C

C

NC

NC

NC

NC

10-2 10-3

c c

C NC

C NC

C NC

NC NC

NC NC

NC NC

NC NC

10-l c 10-2 c 2 x 10-3 c

NC NC NC

C C C

NC NC NC

C C C

NC NC NC

NC NC NC

C NC NC

Nuchar SN

C: FITEQL Converged NC: NTEQL Did Not Converge

were investigated. The single diprotic acid representation has already been presented. A two-diprotic and two-, three-, and four-monoprotic surface-site representations also were investigated. If there are too many adjustable parameters (i.e., pK,,(s) and N,(s)), or the proposed reactions are not physically possible, or if there is not enough experimental data, FITEQL will not converge. In Table 4, a summary of the convergence of FITEQL for each type of representation is presented. The values in the parentheses are the number of adjustable parameters associated with each type of representation. Results for the single diprotic representation, using FITEQL, are included for completeness. For Darco HDB at I = 10-l and lo-‘, FITEQL converged for the one- and two-diprotic, two-monoprotic, and three-monoprotic (2 positive sites, 1 negative site) representations. At I = 10-j FITEQL converged only for the single diprotic acid representation. The values ofpK,(s) and N,(s) for the systems which converged are presented in Table 5 for Darco HDB. The failure of FITEQL to converge at I = lo-“. for the representations with a higher number of adjustable parameters, may be caused by a lack of data. At I = 10-l and lo-’ there were = twice the number of data points compared to I = 10m3. For Nuchar SN, at I = lo-‘, FITEQL converged for the one-diprotic, two-monoprotic, three-monoprotic (1 positive site, 2 negative sites), and fourmonoprotic (1 positive site, 3 negative sites) site representations. At I = lo-’ and 2 X 10e3 FITEQL converged for all the representations listed above, except for the four-monoprotic site representation. The values of pK,,(s) and N,(s) for the systems which converged are presented in Table 6 for Nuchar SN. Darco HDB SCF model simulations, for the surface-site representations which converged, are presented in Fig. 7. The single-diprotic site simulation,

which was presented previously in Fig. 5, is included in Fig. 7 for completeness. The two-diprotic and three-monoprotic simulations are practically identical and both describe the titration data adequately. Each of these two representations has six adjustable parameters. Thus, on a purely stochastic basis, their ability to “fit” to the experimental data should be similar. The single-diprotic and two-monoprotic representation satisfactorily reproduced the titra-

Table

5. Darco HDB surface acidity parameters for several surface representations*

1 Dipmtic Site I

10-I 10-2 10-3

2 Dipmtic I

10-l 10-2 10-3

61’ 4.95 4.59 -----

6.26 6.82 7.58

8.59 8.12 I. 19

Ns

SS/DF

1.81 1.74 0.91

10.8 18.3 16.9

PK~

N,’

pK,I*

PK~

N,’

1Sl 1.37 -----

6.74 1.29 -----

11.1 7.95 -----

pK,P’

N,p’

pK,*’

Ns”l

SSIDF

6.19 6.92 _

1.93 1.43

8.54 8.32

1.69 2.52 -----

8.93 4.99

pK,P’

NE@

pK,p’

Nsp2

pK,“’

N,“’

WDF

4.94 5.48 -----

1.57 0.82 -.~--

6.73 7.50 -----

0.89 0.86 -----

8.47 8.15 -----

1.64 2.37 -----

1.16 0.62

* N, in millimoleiL

0.88 1.04 -----

WDF

8.43 8.45 -----

10-l 10-2 10-3

10-l 10-2 10-3

pKti

Sites

I

1

PK,I

1.1, 2.57

1199

Surface acidity of activated carbons 7‘ahle 6. Nuchar SN surface acidity parameters for several surface representations’ I

Dipmfic Sire

I

P%I

10-l 4.03 10-z 3.88 2 x 10-3 3.75

pKa2

WDF

Ns __

6.bR 6.77 6 82

2.34 2.20 1.82

18.9 18.0 22.3

2 Monopmtic Sires pK,p’

1

10-J 4.48 , o-2 4.47 2 x 10-3 4.49

N,@

pKan’

N,“’

SSIDF

1.14 0.88 2.52

6 76 6.78 6.75

2.64 2.38 I 81

9.64 8 12 7.54

3 MonopmUc Sifm I

pK,p’

tion curve above

pH 7. but not for pH values less

than 7. SCF model simulations for Nuchar SN are presented in Fig. 8. For all three ionic strengths investigated, the single-diprotic and two-monoprotic representations did not adequately simulate the experimental titration curve. At I = 10 ’ the fourmonoprotic site model gave a slightly better fit to the data at higher pH values than the three-monoprotic site representation. The four-monoprotic site model has eight adjustable parameters compared to six for the three-monoprotic site representation, thus a better fit is expected. pro~~ided FITEQL. converges. The three-monoprotic site representation

a.

N,p’

pK,“’

N,ol

pK,0*

NT2

WDF

5,

h

I

Nuchar SN 10-l 4.61 10-2 4 64 2 x 10-3 5.57

1.08 0.80 0.22

6.19 6.22 6.02

1.22 I.09 0.71

a.52 8.35 7 81

2.21 1.98 1.4,

0.79 0.39 2 39

4 Monopmlic Sid pK,@ = 4.65

N$' = I.07

pK,"l = 5.98

N,"' = 0.89

,%'I2 = 7.58

N,* = 1 12

pKan3 = 9.13

Nsn3 = 1.59

1 diprotic

-

2 monoprotic

3 monoprotic 4 monoprotic

:

SSiDF = 0.37 ___4

' N, inm,llunole,l.2 ConvergedonlyforI = lo-’ N.

5

6

7

6

9

10

PH

a.

b.

*.A

-

: < 0 a

3 monaprotic

4

0 -1

f

diprotic 2 monoprotic 3 manoprotic

_-

-2

i

-3 3

4

5

6

7

PN

6

9

10

PH

b. T

4

:

3

2

2

E

1

‘; a ;

0 -1

.A > -2 “c 4 -3

-

3 2 monoprotic monoprotic

-4 3

4

5

6

7

6

9

10

PH Fig. 7. SCF model simulations of Darco HDB titration curves for several surface representations. Ionic strengths of a) 0.1 and b) 0.01.

E-2

(1 3

/

4

5

1 6

”

” 7

I1

”

6

9

10

PH

Fig. 8. SCF model simulations of Nuchar SN titration curves for several surface representations. Ionic strengths of a) 0.1, b) 0.01. and c) 0.001.

1200

B. E. REEDand M. R. MATSUMOTO Table 7. Surface acidity parameters for the three-site model millimole/L carbon

I

pKap’

pKap2

pK,“l

10-l

4.94

6.13

8.47

10-2

5.48

7.50

8.15

pKati

N,pl

Nsp2

N,“l

N$

______

1.57

------

0.82

0.89

1.64

-_____

1.20

0.86

2.37

______

0.62

SSIDF

lkwco HDB

Nuchar SN

10-l

4.61

_.____

6.19

8.56

1.08

____--

1.22

2.21

0.76

10-2

4.64

______

6.22

8.35

0.80

____--

1.09

1.98

0.39

2 x 103

5.57

______

6.02

7.81

0.22

____--

0.71

1.40

2.39

satisfactorily described the experimental data at both I = 10-l and 2 x lo-“. The choice of which surface-site representation to use to mode1 the acid-based behavior of an activated carbon cannot be based strictly on the goodness of the model fit to experimental data. Other criteria, such as consistency of the representation between the same carbon at different ionic strengths, and the coherence of the chosen representation with information reported in the literature, must be considered. For Darco HDB, the three-monoprotic and twodiprotic representations gave similar results. However, based on literature results, a number of monoprotic sites are thought responsible for the acid-base behavior of activated carbons[8,9,19]. For Nuchar SN at I = lo-‘, the four-monoprotic representation best described the titration data. However, the four-monoprotic representation did not converge for I = 10-l and 2 x 10-j. The three-monoprotic representation converged for all three ionic strengths investigated, and satisfactorily described the Nuchar SN titration curves. The three-monoprotic site mode1 was the only representation that adequately described the titration data for both carbons at all ionic strengths investigated (excluding Darco HDB at an ionic strength of 10-j). The three-monoprotic site model also was consistent with results reported in the literature regarding the number of sites thought to be responsible for the acid-base behavior of an activated carbon. In Table 7, a summary of the values of p&(s), N,(s), and SS/DF for the three-mono .atic site representation is presented for both carbons. Values of p&(s) and N,(s) for Darco HDB at I = 10-j were not available. The pK,,(s) listed in Table 7 are in the range considered to be weak acids (pK,, > 0.8) for solution chemistry[20]. Surface-site densities are on the order of 4 x 1Oe4M/g carbon for both carbons. For both carbons, pK{(s) increased and pK::(s) decreased with decreased ionic strength. The change in pK: with ionic strength can be explained partially by the variation in the activity coefficient of [Hb+]. However, this argument cannot be used to explain the variation in pK:’ with ionic strength.

Variations in the values pK:(s) and pK::(s), similar to those observed in Table 7, have been reported by Corapcioglu and Huang[S] for several activated carbons. Davis, et al.[21] have suggested that the variation of acidity constants with ionic strength occurs when the background electrolyte is specifically coordinated with the solid surface. When the binding/ release of the background electrolyte was included and the Triple Layer model was employed to describe the interfacial region, Davis, et al.[21] were able to describe electrokinetic data with a non-varying set of equilibrium constants over a wide range of ionic strengths. The rationales for using the GouyChapman mode1 and ignoring background electrolyte adsorption were discussed earlier. Ignoring the adsorption of the background electrolyte and using the ~

1o’

HDB'

Darco

: > ;; 10'

_

I = 10-l

P’OHO PZOIiD

-

P'O$+

. _ PZOH2+

dOEI

_

E

pq’g-

- - _

_,,<...---:’

,__.-

5.

\ i

10-z -

\ _...

.,“.

,..-

. ..’

‘/’ _... ’

1o-3

\

\

,_I.

\ \ \

4

\

\

\

\

_.I’

3

\ \

__:

,,.“,

,

,

,

5

6

7

\

.

\

_..’

1o-’

\

\

,_..

-

\. \

_:. t g

-.

\

I

a

9

\

I

10

.

11

PH

PH Fig. 9. Surface site speciation diagrams using the threesite model at I = 0.1 for a) Darco HDB and b) Nuchar SN.

1201

Surface acidity of activated carbons

model to describe the interfacial region results in the dependence of p&(s) on I. However, these constants are valid for a given ionic strength. Values of N,, from individua1 sites. generally increased with increased ionic strength. However, the total number of surface sites was relatively constant regardless of the ionic strength. Surface-site speciation diagrams based on the three-monoprotic site model at i = IO-’ N are presented in Fig. 9 for both carbons. Note that at the pH,,,,, the concentration of the predominant oppositely charged species are equal. Utilizing the surface-site speciation diagram in conjunction with metal adsorption data and the chemical composition of the aqueous phase, the SCF model can be used to predict heavy-metal speciation in the aqueous and solid phases. Examples of using the SCF model to describe metal adsorption have been presented by Corapcioglu and Huang[B] and Huang and Ostovic[7]. However, these authors have assumed that the carbon surface behaves as a weak diprotic acid. Based on the results of this research, that assumption may not be valid for all powdered activated carbons. Research investigating the metal-adsorption capabilities of the PACs and to what extent the SCF model can be used to describe metal adsorption is ongoing. It should be noted that describing metal adsorption using the SCF model is valid when multiple monoprotic sites are used. simpler

Gouy-Chapman

5.

SUMMARY

The two powdered activated carbons studied behaved as weak acids in solution. EmpIoying a weak single-diprotic acid representation to describe the amphoteric nature of the activated carbons did not produce good agreement between experimental and surface complex formation (SCF) model simulated acidimetri~-alkalimetric titration curves. Based on a number of criteria (goodness of fit, coherence to published results, and agreement at different ionic strengths), the amphoteric nature of the two PACs studied was best modeled as a number of weak monoprotic acids. SCF model simulations using a threemonoprotic acid representation for the carbon surface adequately described acidimetric-alkalimetric titration curves for both Darco HDB and Nuchar SN. The results of this study will be used as a starting point for research on modeling heavy metat removal by powdered activated carbons. Acknowledgements-II’he authors would like to express their appreciation

to Dr. John Van Benschoten

and Dr.

Jim Jenson for their assistance in conducting the acidimetric-alkalimetric titrations and review of this article. This research was partially funded by a grant from the New York State Center for Hazardous Waste Management and CECOS International, Inc. of Niagara Fails, New York. REFERENCES

1. B. Batchelor and R. Dennis, J. Water Pollution Control Federal~orl 59, 1059 (1987). 2. M. R. Matsumoto, A. S. Weber, J. H. Kyles. and K.

Malinowski, Chem. Eng. Comm. 86, 1 (1989). 3. W. Stumm and J. J. Morgan, Aquatic Chemistry. Wiley. New York (1981). 4. J. A. Davis and J. 0. Leckie. 1. Colloid lnterfuce Sci 67, 90 (197X). 5. M. 0. Corapcioglu and C. P. Huang, C&on 25, 569 (1987). h. M. 0. Corapcioglu and C. P. Huang, Wuter Reseurch 21, 1031 (1987). 7. C. P. Huang and F. B. Ostovic, J. Environmental Engineering Division, ASCE

104, 863 (1978).

8. V. L. Snoeyink and W. J. Weber, ~nvironme~tai

Sci

Technol, 1, 228 (1967).

9. J. S. Mattson and H. B. Mark, In Activated Carbon: Surface Chemistry and Adsorption From Solution. p. 129. Marcel Dekker, New York (1971). 10. J. C. Westall, J. L. Zachary, and F. M. M. Morel, MINEQL: A Computer Program for the Cakdation of Chemical Equilibrium Composition of Aqueous Systems, Technical Note No. 18. Ralph M. Parsons Lab-

oratory (1976). 11. D. Chan, J. W. Perram, L. R. White. andT. W. Healy, Chem. Sot..

Faraday Tram I, 71, 1046 (1975).

12. D. A. Dzombak and F. M. M. Morel, J. ~~dra~~iic Enpineerinn Division. ASCE 113. 4430 11987i. 13. J. Gestall and H. Hohl. Advances Colloib Inte>face Sci 12, 295 (1980). 14. C. P. Huang, In Adsorption of korganics at SolidLiquid lrzterfaces, (Edited by M. A. Anderson and A. J. Rubin), p. 183. Ann Arbor Science. Ann Arbor MI (1981). . 15. D. E. Yates and T. R. Healy, J. Colloid Interface Sci 52, 222 (19751.

16. J. C. Westall: FITEQL:

A Program for the Determination of Chemical Equiiibr~unz Constants from Exper~mentai Data Version 1.2. United States Depart-

ment of Energy, Contract #DE-AC0676RL0 1830 (1982). 17. J. C. Westall. FITEQL: A Program for the Determination of Chemical Equilibrium Constants from ~xperimentai Data Version 2.0. United States Depart-

ment of Energy. Contract #DE-AC06-7hRL0 1830 (1928). 1X. American Public Health Association, Standard Methods For The Examination of Wastewater. 16th Edition, Washington, D.C. (1985). 19. M. Korczak and J. Kurbriel, Water Research 23, 937 (1989). 20. V. L.. Snoeyink and D. Jenkins, Water Chemistrv. Wiley, New-York (1980). 21. I. A. Davis, R. 0. James, and J. 0. Leckie, J. Colloid lnfecface Sci 63, 480 (1978).