Letters to the Editor
734
acetylene but only in a limited region of relatively low temperatures, is consistent with a mechanism of filament formation that requires an exothermic step on the metal surface [I]. Acknowledgement - The authors wish to thank Mr. Michael Baxter of the Lehman College Department of Biological Sciences for preparing the scanning electron microphotographs. Supported in part by the City University Research Foundation, PSC/CUNY Grant #665203. Chemistry Department Lehman CollegelClJNY Bronx, New York 10468 U.S.A.
D.B. MURPHY R.W. CARROLL
REFERENCES
Figure 2. Scanning Electron Microphotograph of Platinum Residue Remaining After Combustion of Carbon Filaments in Oxygen at 1173 K. Original Magnification 6000X.
1. R.T.K. Baker and P.S. Harris, Chemistry and Physics of Carbon , (P.L. Walker, Jr. and P.A. Thrower, eds.) Vol. 14, pp. 83ff, New York, Marcel Dekker 1978. 2. P.A. Tesner and I.S. Rafal’kes. Dokl. Acad. Nauk. SSSR , 87, 821 (1952). 3. J.R. Fryer and 2. Paal, Carbon , 11, 665 (1973). 4. R.T.K. Baker and J.A. France, J. Catal., 39, 481 (1975). and D.B. Murphy, Extended 5. R.W. Carroll Abstracts, 16th Biennial Conference on Carbon, 1983. 114: D.B. Murnhv and R.W. Carroll, Extended Abstracts and P>ogram, 19th Biennial Conference on Carbon, 1989,446.
An isotherm equation for solute adsorption from dilute solutions on heterogeneous solids (Received I I August 1989; accepted in revisedfotm 21 February 1990)
Key words - Adsorbent heterogeneity,
adsorption isotherm, adsorption
Some years before Langmuir [l] published his wellknown isotherm equation for monolayer localized gas adsorption on homogeneous surfaces, Schmidt [2] proposed a semiempirical description of solute adsorption from dilute solutions, which leads directly to the following isotherm equation: 8 = n/n” = 1 - exp (-Kc)
(1)
K = K, exp [(E - QRT]
(2)
with
Here the relative adsorption 0 of a solute from a dilute solution on a homogeneous solid is defined as the ratio of the solute adsorbed amount n at the solute concentration c and the absolute temperature T to the solute monolayer capacity no; K is the Henry’s law constant defined by eqn. (2) for a homogeneous solid;
from solutions
Ko is the pre-exponential factor of the constant K; E is the solute adsorption energy; co is the solvent adsorption energy; and R is the universal gas constant. Because solute adsorption from dilute solutions is measured at low solute concentrations, the measurable solute adsorption excess ne in the surface phase may be identified with the solute adsorbed amount n [3]; therefore, the isotherm equations for solute adsorption from dilute solutions have mathematical forms similar to those that describe single-gas adsorption on solid surfaces [3,4]. In spite of this similarity of the isotherm equations, the physical meanings of the adsorption parameters differ for gas and solute adsorptions. While in single-gas monolayer adsorption, molecules adsorb on unoccupied adsorption sites; in adsorption from solutions, solute adsorption has a competitive character [3] because the solute molecules displace solvent molecules from the surface phase. In 1969, Jovanovic [5] used a kinetic model of
735
Letters to the Editor gas adsorption on a homogeneous solid surface to derive an equation analogous to eqn. (1). The Jovanovic equation was used to describe monolayer gas adsorption on ho~gen~us surfaces, andwasextendedto mixcdgas adsorption and to gas adsorption on heterogeneous so!id surfaces (cf., Ref. [3,6j and references therein). Also, the isothertii eqn. (1) was found to be useful for describing solute adsorption from dilute solutions [7]. At low solute concentrations, it can be shown that this equation reduces to a Langmuir-type equation; at very low solute concentrations, however, it fulfills Henry’s law. In this work, we extend eqn. (1) to solute caption from dilute solutions on he~gen~s solids with a gamma-type distribution function of the Henry’s law constant K, Also, we illustrate the applicability of this extended equation for representing experimental adsorption isotherms for organics from dilute aqueous solutions on activated carbon. The overall isotherm for a nondissociated solute from a dilute solution on an energetically-heterogeneous solid can be represented by the following integral [3]: 00
Brw
=
I
W, cl G(K) dK
(3)
yn
Here Ot (c) is the overall adsorption isotherm for a solute on a heterogeneous solid, the subscript t at the relative adsorption 8t = n&t0 refers to a heterogeneous solid, 9(K,c) denotes the’ isotherm eauation for solute adsor$ion on homogeneous adtition sites with the constant K, and G(K) denotes the normalized distribution function of K over the region (Km, -), i.e., I K,
G(K) dK = 1
(4)
Here Km is the minimum value of K. It was shown elsewhere [3,6,8] that a amma-type distribution function G(K) gives a satis f actorv descrintion of the energetic heterogeneity of many sbllds including also activated carbons. This distribution may be written as follows:
G(K) = &[K-Km)v-texp[-p(K-d]
(5)
8, = nt/n~ = 1 The slope of this isotherm equation in the region of Henry’s law is given by: lim c30
d9t = K, + v/p=K Z
Here K is the Henry’s law constant for a heterogeneous solid characterized by the gamma distribution function. The isotherm eqn. (8) may be liiearized as follows: C-IIn (1 -
R=
K,
+ v/p
(6)
- v [c-l
In (1 + c/pjj
(IO)
Equation (10) is useful for evaluating the parameters no. Km, v and p from the experimental isotherms of solu\e adsorption from dilute solutions. To verify eqn. (8), we used the experimental adsorption isotherms for p-cresol and p-chlorophenol on Filtrasorb 300 activated carbon at 298 K, these isotherms were measured by Radke and Prausnitz [9]. Figure I presents their experimental measurements plotted according to eqn. (IO), which is a linear form of the isotherm eqn. (8). It follows from this figure that eqn. (8) gives a good representation of the experimental isotherms s&died. Table 1 lists values of the parameters n: Km. K, and oK were obtained from the best-fit parameters Km, v, and p by means of eqns. (6) and (7).
0.0
z
‘z;
\! = /;u? I
7
-5.0 -10.0 -15.0
2
-20.0
‘; 0
-215.0 -I
-30.0 0
where the parameters v and p of the gamma djstribution are greater than zero. The average value K and the dispersion cry associated with the gamma distribution function G(K) are given by:
eJ = -K,
50
100
150
200
c’lln(1 +c/p), (l/mmole) Figure 1. Experimental adsorption isotherms for pcresol and p-chlorophenol from dilute aqueous solutions on Filtrasorb 300 activated carbon at 298 K plotted according to eqn. (10).
and OK = P/p
(7)
The values of K and OK characterize the distribution function G(K) given by eqn. (5). Substitution of eqns. (1) and (5) into the integral eqn. (3) and integration gives the following overall isotherm equation for solute adsorption from a dilute solution:
Figure 2 presents the distribution function G(K) calculated according to eqn. (5) for p-cresol and pchlo~Dheno1 adsorntion on Filtrasorb 300 activated carbon: For both s&lutes, the distribution curves G(K) are exponentially decreasing functions. The distribution curves shown in Fig. 2 leave long tails because the d_ispersion values are large (cf., Table 1). The values of K and OK for p-chlorophenol are about two times gmater than thoso for p-cresol. These values reflect different interactions of solutes with activated carbon.
Letters to the Editor
736
Table 1 Adsorption parameters for p-cresol and p-chorophenol from aqueous dilute solutions on Filtrasorb 300 activated carbon at 298 K Monolayer Wa& nt @mole/g)
Solute
Average Henry constant K~~le)
Dispersion ~(~~~e)
p-cresol
3.1
0.12
51
143
p-chlomphenol
3.5
0.079
98
298
c ~ 0.4OTi ‘zi
El
v
~nimum Henry constant Km Wnmoie)
, I ’ I! 1 :
----
; ,
0.30.
$2
Acknowledgement - This work was supported in part by the Division of Chemical Sciences, Office of Basic Energy Sciences, Department of Energy.
p-Chlorophenol p-Cresol
I ’
Departmentof Physics Kent State University Kent, OH 44242 U.S.A.
M. JARONIBC’ x. LU
I~tit~e of C~mist~ WAT, 00908 Warsaw POLAND
J. CHOMA
RMADEY
Permanent address: Chemistry Faculty, M. CurieSklodowska University, 20031 Lublin. Poland.
l
3 5 2
0.004 0.0
:
I
0.5
1.0
Henry
Cons~t,
1.5
2.0
2.5
3.0
K (I/mmoie)
Figure 2. Distribution function G(K) associated with the isotherms shown in Figure 1.
REFERENCES I. Langmuir, J. Am. Chem. Sac. 40,1361 (1918). 1:G.C. Schmidt, Z. Phys. Chem. 77, 641 (191 I); 78,667 (1912). 3. M. Jaroniec and R. Madey, Physical Adsorption on Heterogeneous Solids, Elsevier, Amsterdam, 1988. 4. A. Derylo-Marczewska and M. Jamniec, SurJ?xe aM! Colloid Sci. 14. 301 (1987). 5. D.S. Jovanovic, Colloid Polymer Sci. 235, 1203 (1969). 6. M. J&oniec and J. Piotrowska, Chem. Zvesti, 40, 65 119861. 7. M. ‘Boio&kio and M. Jaroniec. Przem. Chem., 65, 263 (1986). 8. S. Sircar, Langmuir 3, 369 (‘1987); J. Colloid Intelface Sci. 101,452 (1984). 9. C.J. Radke and J.M. Prausnitz, Ind. Eng. Chem. Fundam, 11,445 (1974).