Simple relationships for predicting multi-solute adsorption from dilute aqueous solutions

SIMPLE RELATIONSHIPS FOR PREDICTING MULTI-SOLUTE ADSORPTION FROM DILUTE AQUEOUS SOLUTIONS M. JARONIEC* and A. DERYEO Institute of Chemistry, M.Curie-Sklodowska University, 20031Lublin, Poland (Received 10 April 1960; accepted 24 October 1980) Ahatraet-This work presents simple relationships for predicting multi-solute adsorption from dilute aqueous solutions by means of the data for single-solute adsorption. These relationships are derived by assuming ideality of the surface and the bulk phase and energetic heterogeneity of the adsorbent surface. In the case of homogeneous adsorbent these relationships lead to simple expressions. The relationships are examined by using the experimental data for adsorption of acetone-propionitrile and p-cresol-p-chlorophenol mixtures from dilute aqueous solutions on activated carbon at WC.

INTRODUCTION

Theoretical results obtained for multi-solute adsorption from dilute aqueous solutions on porous solids are very important for programming the process of wastewater purification in a large-scale. From a practical view point, the urediction of multi-solute adsorotion from dilute aquebus solution by means of the’ single-solute adsorption data is the problem of great importance. Many theoretical and experimental works have been published on this subject[l-51. In this paper the relationships for predicting multisolute adsorption from dilute aqueous solutions are derived in terms of the general theory of adsorption from multicomponent liquid mixtures on solids[6-81. Recently, Jaroniec[6] derived an equation for adsorption from multicomponent liquid mixtures on heterogeneous solids of quasigaussian energy distribution. This equation may be written as follows [6]: Yi =

VLxik)”

for

i=l,2,...,n

For dilute aqueous solutions the concentrations of solutes are very small: then c, is in a good approximation constant. Defining a new constant in eqn (3): K, = KiJc,, we have: y, _

(KCi)”

I

(5)

For a single-solute adsorption system eqn (5) becomes: (Kicf)“’ YT= ] + (K$f)“’

(1)

(6)

where the asterisk at the symbols yi and ci refers to the single-solute adsorption of the ith compound from dilute aqueous solution. The parameters riri characterizing the single-solute adsorption systems may be different from the parameter m referring to the multi-solute system. Let us consider two different solutes i and j. Then, from eqns (5) and (6) we have:

0yi“In Yi

_Q -K_c I,

z.‘l’“i K& +=K_~c

I I

(2)

for for

i#j i#j

and and

i,i=1,2 i,i=1,2

,.._, n ,...,

n

Y! .G =I-y:.

i = 1,2,. . . , n. (3)

(7) (8)

where

where ci and c, are concentrations of the ith solute and water in the bulk phase, we obtain: If the concentractions condition.

“=-$ *Author to whom correspondence

i= 1,2 ,...,n.

,=I

where xi and x. are the mole fractions of the ith solute and water in the bulk phase, respectively; yi is the mole fraction of the ith solute in the surface phase; n is the number of solutes; Ki, is the equilibrium constant characterizing the phase exchange reaction between two molecules of the ith solute and water; m is the heterogeneity parameter determining the shape of quasigaussian energy distribution. The parameter m is characteristic for the whole multi-solute system. Taking into account in eqn (1) the following relationship:

for

for

1+ i: WJC,)”

I+ ,$, (Kja XjlXa)”

XJX, = CJC,

(4)

ci

should be addressed. 1017

for

(9)

ci and CT satisfy the following

i#j

and

i,j=l,2

,.,.,

n

(10)

hf. JARONIEC and

lOl8

A.

DERYZO

then eqns (7) and (8) give:

wherezjfori=1,2,..., n is defined by eqns (9). If the heterogeneity parameters m and mi satisfy the following condition:

Summation of eqn (11) with respect to the ith subscript gives:

from eqn (12) we have:

mi=m

yj = 1+ zj-4”’ [

I

.o

I

2 g=‘- -:(I- y,) :;t

C-O.6

5 c-

i=1,2,...,n

yj=[lcz~‘~zi]-‘.(l-Y.). ifi

(12)

\

for

(13)

(14)

Equation (12) may be used for predicting the multisolute adsorption from dilute aqueous solutions on heterogeneous solids of quasi-gaussian energy distribution, when the parameters m and mi for i = 1,2,..., n are different. Equation (14) is considerably simpler than eqn (12); it refers to the adsorption systems showing identical heterogeneity parameters m and mi for i=1,2 ,...,n. Equation (3) with m = 1 generates, moreover, one relationship, which may be useful in studies of multisolute adsorption[9]. It is:

(15)

0.3

where

c=i: ei. i=,

0.0

Fig. 1. The linear dependence (nJnf) vs (I&) for adsorption of acetone(lbpropionitrile(2) (white circles) and p-cresol(l~pcMorophenol(2) (black circles) from dilute aqueous solutions on activated carbon at 25*C[2,3].

In the multi-solute adsorption from dilute solutions (17)

Yr = dno

Fii. 2. The linear dependence In(n,/n,) vs In(c,/c3 for adsorption of acetone(ltpropionitrile(2) aqueous solution on activated carbon at WC[3].

from dilute

Simple relationships for predicting multi-solute adsorption from dilute aqueous solutions where n, is the millimoles of the ith solute adsorbed per gram of adsorbent, and no is an empirical parameter indicating the fictitious maximum adsorption, viz. that achieved when ci +m. We assume that the parameter no is identical for multi-solute and single-solute adsorption systems. Equations (15) and (16) give:

zn nh

o-1

hr. * * , C” I=

n?(c)

1.

(18)

Equation (18) is analogous to the well-known relationship in mixed-gas adsorption[9]. Now, we examine the relationships (14) and (18) by using the experimental data for adsorption of acetone(lb propionitrile(2) and p-cresol(l)-p-chlorophenol(2) mixtures from dilute aqueous solutions on a activated carbon at 25°C reported by Radke and Prausnitz[2,3]. Figure 1 shows the plot n,/n: vs n2/n: for these adsorption systems; white circles refer to acetone-propionitrile mixture, whereas, black circles refer to p-cresol-pchlorophenol mixture. According to eqn (18) this plot should

be linear,

i.e. n,/n:

=

1- n2/nf.

(19)

It follows from Fig. 1 that the relationship (19) is fulfilled in a good approximation. Fire 2 shows the dependence ln(nI/nz) vs In (cI/cZ) from adsorption of acetone(l)-propionitrile(2) from dilute aqueous solution on activated carbon. This plot is described by the linear expression: In (n,/n*) = m In (KJ&)

t m In (cl/c2)

(20)

which results from eqns (5) and (17). The slope m is in a good approximation equal to unity. According to the studies of Radke and Prausnitz[Z], the single-solute adsorption systems are described by eqn (6) with rn; = 1, which is a special case of eqn (5). Since the parameters m and mi from adsorption of acetone and propionitrile from dilute aqueous solution on activated carbon are equal to unity, and eqns (5) and (6) lead to the relationship (14) we can deduce that these experimental data satisfy eqn (14). Figures 1 and 2 show that the relationships derived in this paper may be useful for predicting the multi-solute adsorption from dilute aqueous solutions.

1019

NOTATlON

c Cl2

ci Cf

i

sum of the concentrations of all solutes in aqueous solution concentration of water in the bulk solution concentration of the ith solute in n-component bulk solution concentration of the ith solute in bulk solution “i + water” subscript to the ith solute subscript to the jth solute equilibrium constant of the phase-exchange reaction between the molecules of the ith solute and water equilibrium constant defined by eqn (4) heterogeneity parameter for multi-solute system heterogeneity parameter for single-solute system number of solutes in water number of millimoles of the ith solute in the adsorbed phase number of millimoles of the ith solute in the adsorbed phase “i + water” empirical parameter defined by eqn (17) mole fraction of water in the bulk phase mole fraction of the ith solute in the bulk phase mole fraction of the ith solute in the surface phase mole fraction of the ith solute in the surface phase for the solution ‘5 + water” expression defined by eqn (4)

&.I Ki m m, n n, nf

REFWtENCEJ

111 Brown C. E. and Everett D. H., Colloid Science (Edited by D. H. Everett), Specialist Periodical Reports, Vol. 2. Chem. Sot., London 1975. 121Radke C. J. and Prausnitz J. M., Ind. Engng Chem. Fund/s. 1972 11 445. [31 RadkeC. J. and Prausnitz J. M., A.LCh.E./. 197218 761. [4] Jossens L., Prausnitz J. M., Fritz W., Schliinder E. U. and Myers A. L., Chcm. Engng Sci. 1978 33 1097. [S] Digiano F. A., Baldauf G., Frick B. and Sontheimer H., Chem. Engng Sci. 1978 33 1667. 161 Jaroniec M., .I. Res. Inst. Catalysis Hokkaido Univ. 1978 26 155. [71 Jaroniec M., Patrykiejew A. and Bor6wko M., Progress in Surface and Membrane Science, Vol. 14. Academic Press, New York 1980. [S] Bor6wko M., Jaroaiec M. and Rudzir%&.i W., 2. phys. Gem.

19792&J 1027. [9] Young ^ _D. M. and Crowell A. D., Physical Adsorption of Uses. Llutterworths, London 1962