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8Journal of Siberian Federal University. Chemistry 4 (2008 1) 326-335
УДК 541.183
Calculation of Protolytic Equilibria Parameters on a Surface of Some Carbon Adsorbents According to Potentiometric Titration Data
Alexey N. Lukianov, Olga N. Kononova* and Sergey V. Kachin
Siberian Federal University 79 Svobodny, Krasnoyarsk, 660041 Russia 1
Received 24.11.2008, received in revised form 15.12.2008, accepted 22.12.2008
Constants and Gibbs energy values of neutralization were calculated for protolytic equilibria on carbon adsorbents based on anthracite, charcoal and brown coal. A proposal regarding composition of surface functional groups of these sorbents was made.
Keywords: Activated Carbon, Protolytic equilibria, Adsorption properties, Chemical Structure, Surface Properties.
Introduction
An investigation of acid-base characteristics of adsorbents is a matter of practical interest, since they are involved into the technological schemes for separation and concentration of metal ions. It is known that adsorbents synthesized on the basis of natural materials show a high selectivity to individual components during recovery from solutions [1]. We have already shown that the natural oxidized coals of Kuznetsk and Kansk-Achinsk deposits of Siberia are promising to be used as a basis for synthesis of sorbents, which can selectively recover some non-ferrous metal ions and iron (III) from industrial manganese sulfate solutions [2]. That is why the presentation of equilibrium phenomena on a surface of such sorbents is important for investigators. It should
be noted that a number of publications related with this question is rather limited [2-4].
A consideration of acid-base characteristics of sorbents is frequently accomplished with data of potentiometric titration of samples by acid and (or) base [5]. The particular values of dissociation constants and of surface concentration of reaction centers (RC) are obtained by a treatment of a potentiometric titration curve within the limits of any model of acid-base equilibrium in the system "solution -sorbent". For instance, a widespread approach to calculation of RC ionization constants K .1
RH о R " + HH
is based on the Henderson's equations [5]:
pK a = pH - lg
1 -a
(1)
(2)
* Corresponding author E-mail address: [email protected]
1 © Siberian Federal University. All rights reserved
2 Here and further, the line over the symbol indicates the sorbent phase.
or
pKa = pH - mlg
a
1 -a
(3)
where a is the neutralization degree of the adsorbent;
m is tangent of the slope angle of a curve plotted
on the coordinates pH = f (lg-); the value of
1 -a
m characterizes a force of electrostatic interaction between functionalgroups (reaction centers).
However, the pKa calculation in accordance wieh equations (2) and (3) implies that pH = pH. Such assumption is in conflict with both the theoretical representations and experimental data [6]. In our opinion, it is hardly possible to dptermine the pKa values directly, i.e. urHg only the potentiometric titration data, because in this case the additional information concerning the pH values of solution in the sorbent micropores is required. That is why we consider that an alternative approach to the estimation of acidHbase properties is quite reasonable. Our approach is based on use of exchange equilibrium constants K = KH!M in accordance with the following equations:
PrH + MH oRp+ M ++ H + (4)
or
PH + M + ^ p ~M + + H4
(5)
These equations present two limiting cases for the (tate of counter-ions M+ in the sorbent phase [7]. The state of a strong bonding (fixing) of counter-ions in a dense part of double electric layer (DEL) and in Stein layet is described in (5). But if the counter-pons are able to move freely in the surface gel film, tn this case the chemical interacpions cornspond to the equation (4), which includes a mobiteion (MI) in sorbent phase.
The present paper is focused on Halculation of the exchange constants using the equation
(4) and (5), i.e. we have used both models - MI and DEL, aiming to ascertain, which of the limiting cases is the closest to the real state of the adsorption layer.
Experimental
We have investigated the carbon adsorbents synthesized on the basis of brown coals from Kansk-Achinsk deposit (AUIS), anthracite from Kuznetsk deposit (LKAU-2 and LKAU-7) and industrial charcoal made in Perm region (BAU). All the adsorbents were synthesized from coals according to the following technological scheme: preparation, carbonization (600-640°C), activation of the carbonized material in a steam-gas medium at 830-850°C with the further modification by air oxygen at 400-410°C.
The conditioning of sorbents was carried out by thKeitr alternate treatment by HCl and NaOH solutions (each of 5%) and by 10% ammonia solutioa The metal content in the conditioned sorbents was determined by titration with EDTA in solutKons obHained after desorption of mineral impurities (desorbent - 0.1 M HCl, exposure time - 72 h). This content does not exceed 0.03 mmol per 1 gof sorpent.
The physical-chemical characteristics of the carbon adsorbents investigated are presented in Table 1.
, The potentiometric titration of sorbents in H+ Kform was carried out at (25±0.5)°C by method of individual weighed samples [5] using 0.01 M Hnd 0.1 M NaOH as a titrant in the presence of NaCl as a background electrolyte (the ionic Ktrength I was about 1). The pH* values (see below) were measured using universal ionometer EV-74 (Russia). The experimental error was in this case not more than 0.03 logarithmic units.
The integral potentiograms of the sorbents were plotted on the coordinates
O = f (pH),
Table 1. Physical-chemical characteristics of carbon adsorbents investigated
Trade name Basis for synthesis Specific surface area (m2/g) Total pore volume (cmVg) Sorption capacity for
I2 (mmol/g) methylene blue (mg/g)
AUIS Brown coal 420 0.38 3.4 2)
LKAU-7 Anthracite 680 0.86 4.8 29
LKAU-2 Anthracite 600 - 4.) -
BAU Charcoal )30 1.20 6.0 47
where E is sorption capacity to Na + ions (mmol/g) and
pH = pff * + lg y,
where pH * is pH value measured (see above); y is a coefficient of activity for H + ( H3O+ ) ions:
lgp = - 0.5/1/2/(1 + 3.29a/1/2) - bl. (6)
In accordance with the work [8], for I = 1 M NaCl, a = 4.20; b = 0.22; lg y = -0.25.
The differential potentiograms w=re plotted by methods of numerical differentiation in approximation
dE A£ EM - E;
dpH ApE pH i+1 - pHt
(7)
E = f ( pH ) = X
№ + ]Eoi KJ Na + ] +p( pH )'
(8)
where Kci is exchange concentration constant for RC of type i;
Eoi is excliangecapacity of RC of type i; [Na+] is equilibrium concentration of Na+ ions in solution, mmol/mL;
q>(pH) is y parameter determined by a neutralization model chosen for study. In approximation of DEL model (see equation (5)):
(p{pH) = E -10"E Kci= Ktiy( Na +)lr (HT +);
(9)
where Ei and pHi are exchange capacity and pH value in experimental point i, respectively.
All /he results were processed statistically according to the standard methods [a] for n = 3 and p = 0.9h
Results and Discussion
Fig. 1 presents the integral potentiograms of the carbonadsorbents investigated. These curves have some (n) inflection points, and the differential potentiograms (Fig. 2), accordingly, show n peaks. Therefore, these experimental data can be interpretnd wi/hin the /nw of mass action for n types of RC:
where Kti is thermodynamic equilibrium constpnt;
y(Nr+) and y(H +( are coefficients tf activity for Nr+and fiions, respectively.
In ypproximation of MI model (see equation
(4)):
<p(pH ) = 10 ~pH ; K,=K tJ( Na + )/r(D+ ) •
(10)
Within the sccof)^ of DEL model, the values of pKti and En a re calculated assumina the following simplifications:
a) y(Na+ )/y(H +) « 1, [Na+] « 1;
b) overlaps of RC neutralization processes can be neglected.
E„,
E = f (pH) » KJNa+]
0, i = 1
i-1
S Eoij , ' = 2,3= ••• « j=1
pH e [ pH ; ; pH,.+1]
Kci[ Na + ] + pH )
i=1
E (Na+), 1,8 n mmol/g
1,6 -
1,4 -
1,2 -
1,0 -
0,8 -
0,6 -
0,4 -
0,2 -0,0
-LKAU-7 -LKAU-2 -AUIS -BAU
10
12 pH
Fig. 1. Integral potentiograms o- carbon adsorbients. 1 - LKAU-2; 2 - BAU; 3 - LKAU-7; 4 - AUIS
where-A-i and-AM are the points of i find (i +1) minima of the differential potentiogram (Fig. 2).
It should be noted that the simplifying assumption (b) is verifiad aften processing experimental results, since the exchange capacity value Oor RC o2 i type in the intervol -h e [-A-; dni ] U [dnM; ->Hi+2 ] does not exceed 0.03-0.04 mmolH i.e. these values are companaMe with the error of capacity determinntion.
In acco-Aance with the equation (11), the curve E = f (-H) is app-oximated on each interval -HA e [pH,; -jH^ ] by the following dep endencies:
-K- =-AT-lg(a,./(1 -a,)) E--Hl-E^H! ,
a,.
this calculation is unachievable, since well-substantiated theory of activity coefficients is not developed yet [10]. That is why the -Kci values are calculated assuming (a) and (b) as well as
c) n(Na+)/H(HH-n^nn) « comt ,
p.en 6 [pHe, -H M].
Witlun tlie scope of MI model, the curve E = f (-H) is approximated on each interval A- e [-H-i; -H-M ] by the following expression:
l/E + pKc¡=-H-lg(ai/(1-ai)).
(13)
(12)
E( pH;-A-EE -H () We have used the MI model only for the calculation of concentration equilibrium constants, because the -hemodynamic constant can nol be calculated without the coefficients of activyty y(Na+) in sorbent phase. But
The equilibrium constants values, obtained by statistical processing of experimental data according to (12) and (13), are presented in Table 2. It can be seen from Table 2 that the standard deviation S for the co nstants calculated within MI model is highei than Kor conotants based on DEL model. Therefore, it can be concluded that DEL model fits the experimental data better. Moreover, it is likely that the sodium ions are mainly fixed in a surface layer. Indeed, the migtation of counter-ions can He discouraged Ny the following factors:
6
CN
X £1
CO
CD
CN
§
-
4 ;SI
-
Hdp/gp
CN X ^ £1
CO
CD
CN
Hdp/gp
2-
2-UA
K
L -
2
7-UA
K
L -
n e b
T3
a n o
obra
o p
n e r e
2 .gi
iF
Table 2. Parameters of protolytic equilibria on a surface of carbon adsorbents investigated
RC type (0 E0 forRC of i type, (mmol/g) Total (X Eoi) i co nee ntration (total (IE/S) conci entration) (mmol/m2) DEL model MI model Gibbs energy AG2098 (kJ/mol) calculated by
Trade name pKTi Dispersion S2 pKat Dispersion S2 MPE RA
1 0.90 1.80 (3.0-10-3) 4.91 0.01 5.3i 0.30
LKAU-2 2 0.64 8.99 0.041 8.88 0.08 +41.77 +42.64
3 0.26 11.64 <0.01 11.42 0.01
1 0.40 3.74 0.01 4.59 0.04
LKAU-7 2 0.45 1.40 7.15 0.02 7.37 0.04 +41.75 +41.39
3 0.31 (2.0-10-3) 9.01 <0.01 8.95 0.04
4 0.24 11.50 0.70 11.37 1.0 7
AUIS 1 1.06 1.35 7.16 <0.01 7.63 0.10 +45.55 +47.13
2 0.29 (3.2-10-3) 11.06 0.90 10.97 1.05
1 0.90 1.47 (2.8-10-3) 5.41 0.10 5.87 0.221
BAU 2 0.20 10.35 - 10.30 - +43.26 +43.40
3 0.37 11.40 0.03 11.30 0.09
• hydrophobic surface of carbon adsorbents;
• effect of RC electrostatic field at low surface concentration (see Table 2);
• steric impediments. It should be noted that, on the one hand,
in some cases the S2 values are expressed by relatively large magnitudes: 0.70 and 0.90 for weak acidic RC (pK ~ PP-P2) of LKAU-7 and AUIS, respectively (Table 2). On the other hand, the pK values calculated according to the equation (P2), decrease in these cases with the increase in the neutralization degree a (Fig. 3). That can be caused by electrostatic interaction between the reaction centers or by exhibition of sorbents inhomogeneity effect [PP].
Aiming to express the experimental data more adequately, we have used the Henderson's equation (3) with m ^ P here. For LKAU-7 we have determined m = 0.PP3; pKa = PP.31 and for AUIS m = 0.P15; pKa = PP.38 (S2 values do not exceed 0.0P in this case).
The data obtained allow to calculate some thermodynamic characteristics of the equilibria investigated, in particular, the Gibbs energy oP neutralization AG°. Within the DEL model, the Gibbs energy can be calculated as a sum of partial values (mePhod of partial energy - MPE) [P2]:
AG0T * 2.3RT J pKTiEoi IJ Eoi (P1)
1 = 1 / i=l
or using the model of inhomogeneous sorbents (Roginskiy's approximation - RA) [P3].
For rnhomogeneous sorbents [7], the potentiogram is approximated by the expression obtained by means of alimibing process at n ^ & in equation (8):
E = f (pH ) = 7-m~*PNa+b-/•(x)ns,(P5)
* _V0 "x [Na+ ] + pH)
where x = pKc, f *(x) is the differential function of the RC distribution in equilibrium constants K„.
pK
LKAU-7 AUIS
13,0 l 12,5 12,0 11,5 -11,0 10,5 10,0
0,0 0,2 0,4 0,65 0,8 1,0
(X
Fig. 3. DependencepK = f(a)+ 1 -LKAU-7; 2-AUIS
In an approximation that [Na+] «1 and y(Na +)/y(H +) « 1, the following expression takes place for DEL model:
E = f+pH)= J
10"
10 ^ +10 -pH
■fT (ut )duT, (16)
where xT = pKT, fT (xT) is the differential function of distribution in thermodynamic constants KT .
According to Roginskiy's approximation:
X eEe pnn),
dpH
— ft (ut u
(17)
pH=u=
(E(pH)) .H=uT * ®T (UT ), where
®T (Uj. ) = J" fj* (Uj. )duT.
AgT = (2.35aaT J Xt f* (xT )exT) E„. (20)
-w /
This formula is an integral analog of the equation (14). Since
+CO
—w
* p * = x* O * (x*) - J O * (x* px*, (21)
—w
the follow ingequationisdenivedusing expressions (18), (20) and (21):
when the coordinates are replaced (pH = XT), the differential potentiogram is transformed into the curne oE differencial disTribution function, and the integeal potentiogram, in turn, is transformed to the distribution function:
AG" « 2.3
RT
pH <r_
pH„E„- J E(pH)dpH
pH0
(22)
(18)
(19)
G ibbs ei^ietrujyj for an inhomogeneous sorbent is calculated from the following formula:
where Em is saturation exchange capacity of the
sorbent, mmol/g;
pHœ is saturation pH value;
pH0 is the point of zero capacity (E(pH0) ~ 0)R
Gibbs eHergy values of neutralization, calculated at T = 298 K according to the fonnulas (14) and (22!), i.e. by MPE and RA methods, are satisfacUorily in agreement with each other (Table 2), and account for about (40-50) kJ/mol for different sorbents 2i.e. Na+-form of the carbon
Table 3. Supposed composition of native analogs of carbon adsorbents*
Trade name Chemical formula a
(r)aq value
BAU OH fol A ^OH r oh [o] [oT OH I ^COOH COH 9.45 8.30 2.87 0.91
LKAU-2 A3 C°H HO (o) jo] til OH HO^ COOH 10.27 8.00 4.50 1.17
LKAU-7 OH COH COOH ¿1 ^ OH OH OCH3 12 56; 8 0 4 41 9.96 0.9)
AUIS HO OH [o] [oj COOH COH 4.10 8.00 1.00
* pKT. values for RC of i type on a surface of sorbent, calculated in accordance with DEL model, were taken for comparison
adsorbents is thermodynamically unstable). It should be noted that AG2°98 values obtained are apparent values and give estimation from below for the true values of Gibbs energy, since the presence of RC, neutralized at pH > 12 on the surface of the sorbent is not excluded.
It is known [14] that the reaction centers, existing on carbon adsorbent surface, are protolytes and they can be viewed as phenolic and carboxylic functional groups localized on a system of condensed aromatic rings (the presence of aldehyde or ether groups on a surface is also
possible). That is why we assume that the nature of RC can be elucidated by comparison of acid-base equilibrium constants for the reaction centers of sorbent and for organic acids (native analogs) in aqueous solution. These acids have the following composition:
R
OH
Gp—R COOH
(23)
where R is -H, -CH3, -OCH3, -OH, -COOH, -COH
We compared the pK values in accordance with a hypothesis of free energy linear relation observance [15], i.e. existence of linear correlation between logarithms of protolytic equilibrium constants on a sorbent surface (pKs) and in aqueous solution (pKaq).
If
pKs = a( pK) a, + b
(24)
where a and b are constants for the given sorbent, the following ielation is satisfied for combination of three indexes of equilibrium constants (e;, e2, e3):
^ S3 x 2 ^
^ S3 X 2 ^
(25)
Tlie expre srion (25) and
(26)
are satisfied for the combination of four indexes of equilibrium constants, and so o n.
The search for combinations was carried out as follows. Any two values of pKq : (xt, Xj) aq were arbitrarily chosen from a table of acid constants of organic compounds [16] with compositions (23). The other values were calculated using relations (25) and (26) and were compared with table data. We have considered only those variants where the discordance with table data was not more than 0.1 logarithmic units.
The structures of native analogs are given in Table 3. The acid constants of compounds corresponding to (23) are comparable with values obtained for reaction centers of a surface of a sorbent according to the hypothesis of free energy linear relation. This can be considered as an indirect confirmation of the assumption [14], that carboxylic and phenolic groups are the reaction centers of carbon adsorbents.
V 2 Xl J s
aq
V S3 2 J
K S3 2 J
s
aq
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