ISSN 1061-933X, Colloid Journal, 2007, Vol. 69, No. 5, pp. 671–674. © Pleiades Publishing, Ltd., 2007. Original Russian Text © E.S. Jakubov, T.S. Jakubov, O.G. Larionov, 2007, published in Kolloidnyi Zhurnal, 2007, Vol. 69, No. 5, pp. 714–717.
Adsorption Volume and Absolute Adsorption: 2. Adsorption from Liquid Phase E. S. Jakubova, T. S. Jakubovb, and O. G. Larionova a
Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow, 119991 Russia e-mail:
[email protected] b Royal Melbourne Institute of Technology (RMIT University), GPO Box 2476V, Melbourne, 3001 Australia e-mail:
[email protected] Received December 8, 2006
Abstract—A critical analysis of the isotherms of excess and absolute adsorption, as well as the adsorption space performed in the first part [1] is continued; however, as applied to the equilibrium physical adsorption from the liquid phase. The correct method is proposed for evaluating the adsorption volume of solid adsorbents with an arbitrary structure by the isotherm of excess adsorption of binary mixture of liquids. This method is successfully tested for nine different adsorption systems. DOI: 10.1134/S1061933X07050213
INTRODUCTION The overwhelming majority of the measurements of the adsorption of liquid mixtures are performed under the assumption that the excess autoadsorption of adsorbing components is equal to zero, which is a rather good approximation for a large scope of systems. Consequently, in this case, we are dealing not with the change in the density of adsorbate components in the vicinity of solid surface, but with the change in the concentration due to selective adsorption used in practice for the separation (in a general meaning of this term) of the components of liquid mixtures. In this work, we also adhere to this approximation. Note that the adsorption volume is a characteristic of the adsorbent–adsorbate system and that, in case of adsorption, this volume is a function of its composition. It is this fact that is associated with the experimentally observed nonadditive character of the limiting values of adsorption that correspond to different compositions and that is why, in common procedures for determining the adsorption volume, both temperature and adsorbate are standardized. The adsorption volume is not only the space where the adsorbed molecule is placed, but also the space where the molecule can reside. For example, adsorption volumes determined by ethane and n-dodecane are virtually equal because the structures of their molecules ensure equal accessibility for adsorption volume, whereas adsorption volumes determined by ethane and neopentane are markedly different. The approach proposed in this work determines the adsorption volume of an adsorbent by the predominantly adsorbing component of liquid mixture, although this
result can also be recalculated for the second component. DETERMINATION OF ADSORPTION VOLUME The experimental study of the adsorption of liquid solutions consists of finding the component excesses in the adsorption phase by the changes in the concentration of the bulk solution. The excess adsorption isotherm is plotted by performing the experiment at a constant temperature. The typical form of this isotherm is shown in Fig. 1. Usually, this isotherm refers to the n1e 0.20
0.15
0.10
0.05
671
0
0.2
0.4
0.6
0.8
Fig. 1. Isotherm of excess adsorption of p-xylene from mixture with n-octane on zeolite NaX at T = 303.15 K.
1.0 c1
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JAKUBOV et al. cs2m
cs2m
Adsorption phase
l'
e n1m
2
Adsorption phase
l'
e Vn1m
2
Bulk phase
l
e ne2m = – n1m
2'
Bulk phase
l
Vne2m
2'
0
1
c1m
Fig. 2. Schematic representation of the adsorption system in the point of maximum on the excess adsorption isotherm. Rectangle areas are proportional to the total amount of substance in each phase.
e
s
s
e
s
s
n2 = n2 c1 – n1 c2 ,
(1) e
exist between excess amounts of components, n 1 and e
s
n 2 , and their real quantities in adsorption phase, n 1 and s
n 2 , which hereafter we will express in grams per adsorbent gram. In Eq. (1), c1 and c2 are the weight fractions of components in an equilibrium bulk phase. Let us write down relations (1) for the maximum excess in the adsorption isotherm slightly transforming them as n 1m = n 1m c m2 – n 2m c m1 = n 1m – ( n 1m + n 2m )c m1 , (2) e
s
s
s
s
s
n 2m = n 2m c m1 – n 1m c m2 = – n 1m + ( n 1m + n 2m )c m1 .(2a) e
s
s
s
s
s
According to relations (2) and (2a), as well as from relations (1), we obtain e n 1m
=
e – n 2m . e
Here, the minus sign denotes that excess n 2m refers to the bulk phase. As is known, the adsorption equilibrium is determined by the component concentrations in the bulk phase rather than its dimensions, which can be arbitrary. However, for this work, it is reasonable to assign a certain volume to the bulk phase. Let the bulk phase contain the same amount of components (in grams or moles) as the adsorption phase. Let us consider the adsorption equilibrium in the point of maximum. The situation is illustrated by the schematic Fig. 2, where the areas of rectangles are proportional to the total amount of substance in each phase and the larger side of rectangle is proportional to the concentration expressed in weight fractions. Then, in the adsorption phase, the amount of the first component is propore tional to the total area of rectangles 1' and n 1m and is s
1
c1m
Fig. 3. Schematic representation of the adsorption system in the point of maximum on the excess adsorption isotherm. Rectangle areas are proportional to the volumes occupied by solution components at equal total amounts of substance in each phase.
excess of the predominantly adsorbing component as a function of its concentration in the bulk phase. The exact relations n1 = n1 c2 – n2 c1 ,
0
equal to n 1m , while the amount of the second component is proportional to the area of rectangle 2. Corre-
spondingly, in the bulk phase, the amount of the first component is proportional to area 1, while that of second component is proportional to the total area of recte angles 2' and n 2m . Areas 1 and 1' and, respectively, 2 and 2' are equal to each other by the definition of excess. Now, if we transform Fig. 2 so that the rectangles would be proportional to the volumes occupied by the solution components, the situation is changed fundamentally, as is schematically shown in Fig. 3. Speculations and numerical calculations given below are based on the two following assumptions: (1) The density of the bulk solution is the additive function of the densities of single components, that is ρ 12 = ρ 01 c 1 + ρ 02 c 2 = ρ 02 + ( ρ 01 – ρ 02 )c 1
(3)
= ρ 01 – ( ρ 01 – ρ 02 )c 2 ,
where ρ12, ρ01, and ρ02 are the densities of solution and pure components, respectively, and c1 and c2 are the weight fractions of components. However, this assumption is not obligatory. If the real nonadditive dependence of ρ12 on densities ρ01 and ρ02 is known, its use does not require changes in the general approach. (2) The density of the adsorption solution also obeys relations of type (3); i. e., the adsorption and bulk solutions having identical compositions also have identical densities. This assumption is stronger, however, it is used universally in adsorption practice. Thus, as follows from the assumptions and is seen from Fig. 3, volumes 1 and 1' and, correspondingly 2 and 2' are equal to each other because they contain equal amounts of substance with equal densities. As for excesses, the amounts of substance are equal but the densities are different. Consequently, the excess amount of the second component in the bulk phase occupies the volume differing form that occupied by the excess of the first component in the adsorption e e phase by the n 2m /ρ 02 – n 1m /ρ 01 magnitude. As before, we denote the adsorption volume per gram of adsorbent COLLOID JOURNAL
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ADSORPTION VOLUME AND ABSOLUTE ADSORPTION
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The values of adsorption volume for nine different systems calculated by Eq. (5) Γ1m, g/g
T, K
ρ01, g/cm3
c1m
ρ02, g/cm3
W, cm3/g
Benzene–cyclohexane–zeolite NaX [2] 303.15
0.203455
0.047058
0.8685
0.76915
0.276
338.15
0.192773
0.058489
0.830562
0.735107
0.277
363.15
0.182939
0.071138
0.803619
0.710399
0.274
Ethanol–benzene–zeolite NaX [2] 303.15
0.22944
0.016523
0.7810
0.8685
0.269
338.15
0.22299
0.013859
0.7485
0.8306
0.273
0.69428
0.296
0.74163
0.235
0.6837
0.298
0.76915
0.255
0.7698
0.256
0.8885
0.179
0.8685
0.264
p-Xylene–n-octane–zeolite NaX [3] 303.15
0.194933
0.061617
0.861176
Tetradecene–dodecane–zeolite NaX [4] 303.15
0.154097
0.11778
0.76416
Benzene–isooctane–zeolite NaX [2] 303.15
0.196464
0.046663
0.8685
p-Xylene–cyclohexane–zeolite NaX [2] 303.15
0.18458
0.064067
0.861176
m-Xylene–cyclohexane–zeolite NaX [2] 303.15
0.1880
0.049928
0.8556
Ethanol–ethylacetate–zeolite NaX [2] 303.15
0.142858
0.090573
0.7810
Ethylacetate–benzene–zeolite NaX [2] 303.15
0.21545
0.063254
by W. The partial density of the first component in the adsorption phase in the point of maximum (see Fig. 1) is equal to ρ 1 = ( Wρ 12 c 1m + n 1m )/W = ρ 12 c 1m + n 1m /W e
e
= ρ 02 c 1m + ( ρ 01 – ρ 02 )c 1m + n 1m /W, 2
e
e
In order to decrease the excess adsorption n 1m of the first component to zero, the first component should replace s e in the adsorption phase n 2 grams and n 2m + n2 (or, that is s
the same, n 2m + n 2 ) of the second component in the bulk phase. Different between these value is just equal to | n 2m | = e
| n 1m |. Thus, volume 2 contains n 1m (ρ01/ρ02 – 1) of the first component and its partial density will be equal to e n 1m (ρ01/ρ02 – 1)/W. e
e
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The sum of the partial densities should yield the density of the pure first component and, thus, we have ρ 02 c 1m + ( ρ 01 – ρ 02 )c 1m + n 1m /W 2
e
+ n 1m ( ρ 01 /ρ 02 – 1 )/W = ρ 01 . e
(4)
Solving relation (4) with respect to W, we finally arrive at
while the partial density of the second component in the adsorption phase in the point of maximum is equal to s ρ2 = n 2 /W.
e
0.8885
2007
n 1m ρ 01 -. W = --------------------------------------------------------------------------------ρ 02 ( 1 – c 1m ) [ ρ 01 + ( ρ 01 – ρ 02 )c 1m ] e
(5)
Thus, formula (5) makes it possible to evaluate the adsorption volume by the experimental data concerning liquid-phase adsorption. As a rule, the second term in square brackets comprises units of percents of the first term (e.g., for the p-xylene–n-octane system, it accounts for ≈ 1.2%); therefore, it can be ignored and simplified equation (5) then acquires the following form: W = n 1m / [ ρ 02 ( 1 – c 1m ) ] = n 1m / ( ρ 02 c 2m ). e
e
(6)
Using Eq. (5) and the published data, we determined the adsorption volumes of nine different systems at dif-
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JAKUBOV et al.
ferent temperatures. Results of these calculations are summarized in the table. All values of obtained adsorption volumes are reasonable and agree with other definitions. CONCLUSIONS The calculation method proposed is a simple and reliable procedure that permits us to estimate the adsorption volume of adsorbents with arbitrary structures from the experimental excess adsorption isotherm for binary liquid mixtures.
REFERENCES 1. Jakubov, T.S. and Jakubov, E.S., Kolloidn. Zh., 2007, vol. 69, no. 5, p. 709. 2. Shayusupova, M.Sh., Cand. Sci. (Chem.) Dissertation, Moscow: Institute of Physical Chemistry, the USSR Academy of Sciences, 1979. 3. Larionov, O.G. and Jakubov, E.S., Langmuir, 1988, vol. 4, p. 1223. 4. Herden, H., Einicke, W.-D., Messow, U., Quitzsch, K., and Schöllner, R., J. Colloid Interface Sci., 1984, vol. 97, p. 565.
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2007