9050
J. Phys. Chem. 1981, 85,3050-3059
Application of the Polanyi Adsorption Potential Theory to Adsorption from Solution on Activated Carbon. 11. Adsorption of Organic Liquid Mixtures from Water Solution Mlck Greenbank and Milton Manes" Chemistry Department, Kent State Universitr. Kent, Ohio 44242 (Received: March 2, 198 1; In Final Form: June 26, 198 1)
The Polanyi model has been extended to the adsorption, from water solution onto activated carbon, of multicomponent mixtures of organic liquids that are partially miscible in water and completely miscible in each other. The model has been applied to the following binary and ternary solute systems: diethyl ether (EE)-ethyl acetate (EA), propionitrile (PN)-EA, PN-1,2-ciichloroethane (DCE),EE-DCE, dichloromethane (DCM)-DCE, DCE-1-pentanol (PEN), EE-EA-PN, EE-EA-PEN, and DCM-DCE-PEN (all at 25 "C);EAphthalide (PHL) and PEN-PHL (62 "C); EA-coumarin (COU) and PEN-COU (63 "C); and EA-p-nitrophenol (PNP) and PEN-PNP (42 "C). The full model (nonuniform adsorbate) incorporates the Hansen-Fackler treatment for adsorbate nonuniformity resulting from adsorption selectivity that is most pronounced in regions of high adsorption potential (fine pores); the approximate model (uniform adsorbate), which assumes adsorbate uniformity, is computationally simple and accounts satisfactorilyfor all of the (25 "C) binary and ternary systems, which are relatively homogeneous in adsorption energy (potential) density. The full model is necessary for the adsorption of PHL, COU, and PNP. The Polanyi model was used to circumvent some problems in evaluating integrals for the Radke-Prausnitz (IAS) method, which was then applied to the binary systems; the thussupplemented U S model accounted quite well for the 25 "C systems,but only some of the elevated-temperature systems. It went out of bounds for others, all of which were within the scope of the Polanyi-based model.
Introduction This is the first of a subseries of articles that reports on the adsorption, from water solution onto activated carbon, of multiple organic liquids and of various mixtures of liquid and solid solutes. This subseries is an extension of earlier articles by Wohleber and Manes'i2 on the adsorption from water of single liquids, by Schenz and Manes3 on the adsorption of mixed organic liquids, and by Rosene and Manes4fiand Rosene, Ozcan, and Manes6on the adsorption of mixed organic solids. We here consider the adsorption from water solution of multicomponent mixtures of organic liquids that are partially miscible with water and completely miscible in each other. The Polanyi-based model' and the HansenFackler modification for nonuniform adsorbates,8both of which were earlier applied to both aqueous112and nonaqueous3systems, are here extended to an indefinite number of components, and experimental data are presented for some binary and ternary solute mixtures. The binary mixtures comprise the following: diethyl ether-ethyl acetate, propionitrile-ethyl acetate, propionitrile-1,2-dichloroethane, diethyl ether-dichloroethane, dichloromethane-dichloroethane, and dichloroethane-pentol, all at 25 "C; ethyl acetate-phthalide and 1-pentanol-phthalide at 62 OC;ethyl acetate-coumarin and 1-pentanol-coumarin at 63 "C;pentanol-p-nitrophenol at 42 "C; and ethyl acetate-p-nitrophenol at 42 "C.The ternary systems, all at 25 "C, comprise the following: diethyl ether-ethyl acetate-propionitrile, diethyl ether-ethyl acetate-pentanol, and dichloromethane-dichloroethane-pentanol. Except for 1-pentanol, all of the (room-temperature) liquids (1)D.A. Wohleber and M. Manes, J. Phys. Chern., 75, 61 (1971). (2)D.A. Wohleber and M. Manes, J. Phys. Chem., 75,3720 (1971). (3)T.W. Schenz and M . Manes, J. Phys. Chern., 79, 604 (1975). (4) M. R. Rosene and M . Manes, J . Phys. Chern., 80, 953 (1976). ( 5 ) M. R. Rosene and M . Manes, J. Phys. Chern., 81, 1646 (1977). (6)M.R.Rosene, M. Ozcan, and M. Manes, J.Phys. Chern., 80,2586 (1976). ~ ..,.. (7) M. Polanyi, Verh. Dtsch. Phys. Ges., 16,1012(1914);Z. Elektrochern., 26,370 (1920);Z. Phys., 2, 111 (1920). (8) R. S. Hansen and W. V. Fackler, J. Phys. Chern., 57,634(1953). 0022-3654/81/2085-3050$01.25/0
studied at 25 "C had been previously investigated as single-component adsorbates by Wohlebere and by Wohleber and Manes.' Phthalide, coumarin, and p-nitrophenol (PNP), which were here studied as liquids above their underwater melting points, were previously investigated both as liquid and solid single adsorbates by Chiou and Manes;'" we shall soon consider why they were chosen. Finally, the use of the same carbon as in the preceding 10 publications in this series makes it possible to test both current and future theoretical approaches on a large, varied, and increasing body of data. We shall see that the extension to multicomponent solutes of the earlier single-solute model (for partially miscible so1utes)l postulates both that the adsorbate consists essentially of a separate liquidlike organic phase and that its composition may be significantly nonuniform. The incorporation of adsorbate nonuniformity into the model leads to the expectation that the adsorbate from a saturated multicomponent solution in water should be the same as from the organic liquid mixture in equilibrium with it; this expectation satisfies a thermodynamic consistency condition that was derived by Myers and Sircar.ll Although major nonuniformity effects were neither expected nor found for any of the (room-temperature) liquid solute mixtures that we studied, we expected nevertheless that such effects would be experimentaIIy unequivocd in solutions of mixed liquids with sufficiently large differences in refractive index. The choice of the molten aromatic (room-temperature)solids (phthalide, coumarin, and PNP) as components was primarily due to their high refractive indexes, but also due to their significant water solubility, which made for experimental convenience. The somewhat elevated temperatures were necessary to keep them above their adsorbate melting points.1° As will be seen, the predicted nonuniformity effect was generally confirmed ~~
(9)D. A. Wohleber, Ph.D. Dissertation, Kent State University, Kent, OH,1970. (10)C.C.T.Chiou and M. Manes, J. Phys. Chem., 78, 622 (1974). (11)A. L. Myers and S. Sircar, J. Phys. Chern., 76, 3412 (1972). (12)C. J. Radke and J. M. Prausnitz, AIChE J.,18,761 (1972).
0 1981 American Chemical Society
Adsorption of Organic Liquid Mixtures from Water and was in several instances quite striking. The theoretical treatment to be presented was in part &e., without adsorbate uniformity) reported by Wohleber? and the incorporation of the Hansen-Fackler8 treatment of adsorbate nonuniformity is not essentially different from its application by Schenz and Manes3 to mixed organic liquids. The extensive of the Polanyi model to multicomponent organic liquid adsorbates with possible adsorbate nonuniformity therefore presents no essentially novel concepts. Other models have been proposed that can be applied to multicomponent liquids from water, of which the most prominent is the ideal adsorbate solution (IAS) model of Radke and Prausnitz,’2 which has recently been applied by DiGiano et al.I3 and by Jossens, Prausnitz, et al.;14 although this model has been applied to both liquid and solid adsorbates, we here consider it only in its application to liquids. Although the model is derived from different postulates than the Polanyi model, it leads to essentially the same calculations when applied to liquid adsorbates that do not exhibit large differences in refractive index. Whereas the Polanyi model requires low-capacity adsorption data for only one component (to characterize the carbon), the IAS model requires such data for each component in order to evaluate integrals that extend in principle to infinitely low capacities; the avoidance of these sometimes awkward integrals has been the object of an approximation method by DiGiano et al.I3 We have here applied an alternative approach in which we use the Polanyi-based model to estimate liquid-phase adsorption isotherms to low capacities from gas-phase isotherms (for which low-capacity data are more easily available) and thereby in effect to estimate these integrals quite conveniently. Although its application to ternary systems presented some computational problems that we did not attempt to solve, we have here applied it to all of the binary systems within its scope.
Theoretical Section The Polanyi-based model’ is described in earlier publication~.’-~The basic model postulates an “adsorption space” which was originally depicted schematically by Polanyi as one pore of varying cross section but which may also be imagined as consisting of pores of various (unspecified) shapes and sizes. The “adsorption potential”, E , of an adsorbate molecule (which is the negative of the energy of adsorption) varies with location in the adsorption space because of variable proximity to the adsorbent and should therefore increase with decreasing pore size. In vapor-phase adsorption, bulk vapor condenses to a liquid wherever the adsorption potential suffices to concentrate the vapor from (bulk) equilibrium to saturation concentration, i.e., wherever the reduction in energy suffices to balance the effect of the reduction in entropy on concentrating the vapor from bulk to saturation concentrations. This condensation, together with the usually much smaller effects of vapor concentration in the remainder of the adsorption space, accounts for physical adsorption. In the adsorption of partially miscible organic solutes from water solution, each organic component concentrates in the adsorption space to an extent that depends on its net energy of adsorption, i.e., on the excess of the adsorption energy of the adsorbate over that of an equal volume of displaced water. An organic-rich phase separates (13)F. A. DiGiano, G. Baldauf, B. Frick, and H. Sontheimer, Chem. Eng. Sci., 33, 1667 (1978). (14) L. Jossens, J. M. Prausnitz, W. Fritz, E. U. Schlander, and A. L. Myers, Chem. Eng. Sci., 33, 1097 (1978).
The Journal of Physical Chemistty, Vol. 85, No. 2 1, 198 1 305 1
out wherever a single pure adsorbate attains its saturation concentration or, in the extension to adsorbates, wherever the composition of a multicomponent solution satisfies the conditions for phase separation. A multicomponent organic phase is of uniform composition if all components have the same adsorption potential per unit volume, E / Vi; otherwise the component(s)with the higher value(s) of €/Vi concentrate within the organic phase to an extent which we shall soon consider. We now consider the problem of calculating the adsorption of each of an indefinite number of organic liquid solutes from water solution, where each individual solute is partially miscible in water and all are completely miscible in each other. We assume that individual adsorption isotherms are available; it will be convenient, but not necessary, to assume that they can all be derived from a single “correlation curve” by application of an appropriate abscissa scale factor, which can either be determined experimentally or else estimated, as by the method of Wohleber and Manes.’ We first seek to determine both the volume of the multicomponent organic adsorbate and its composition at the presumed adsorbate-water interface. We assume that the individual adsorption isotherms give as ordinate the adsorbate volume V per unit mass of carbon; the abscissa may be any of the following, which are interconvertible: the equilibrium concentration,c*; the adsorption potential, E ; or the adsorption potential per unit volume, E / Vi, where Vi is the (bulk) liquid molar volume. Our problem first consists of finding the adsorbate volume, V , and the individual mole fractions, xi, at the presumed organic-water interface. A conceptually simple approach is to consider each individual adsorbate component as a liquid with (modified) solubility ci*(V), where ci* is the equilibrium concentration of the component in water if it is adsorbed as a single component at adsorbate volume V. The mixed adsorbate is assumed to be a mixture of these liquids, each with equilibrium solubility ci*(V), where V now refers to the t~taladsorbate volume. The conditions for equilibrium at the adsorbate-water interface are
where the ci values are the individual equilibrium concentrations and the yi values are the activity coefficients in the adsorbate (Raoult’s law convention). If one assumes an adsorbate solution approaching ideality, then the yi values become unity. The calculation of the interface adsorbate composition from a set of ci values then consista simply of assuming some value of V and thence the set of ci* values (from the individual adsorption isotherms), followed by calculating a tentative set of xi values, determining their sum, and adjusting the estimate of V until their sum equals unity. One may also (as we have done in this article) use the approximation that all individual adsorption isotherms in water transpose to correlation curves, i.e., to plots of adsorbate volume vs. (T/Vi) log (c,/c) (or e/(4.6Vi)) where c, and c are the saturation and equilibrium concentrations. These curves may in turn be made to coincide with some standard correlation curve (such as the hydrocarbon correlation curve for the carbon) by application of an abscissa scale factor that in turn may be either estimated from refractive indexes by the method of Wohleber and Manes1 or else determined empirically. This leads to an alternative and quite equivalent calculation of V and xi. At the common adsorbate interface we have an equation that is quite analogous to the equation of Grant and Maned6 for
3052
The Journal of Physical Chemistry, Vol. 85, No. 21, 1981
multicomponent vapors, i.e. (T/Viyi) log (xC,/C)i = (T/Vjrj) log (xCs/C)j
(3)
for all i and j, where the yi and yj values are the appropriate abscissa scale factors (not activity coefficients). In this calculation one starts with a trial value of one of the xi values and calculates all of the others. The set of xi values that sums to unity is the correct one. Substitution of any xi in the appropriate member of eq 3 gives the abscissa of the hydrocarbon curve, from which one obtains the adsorbate volume. If the adsorbate is of uniform composition, we can proceed to determine the adsorbate mole numbers. The adsorbate molar volume ? is given by
P = z:xjvi*
(4)
where the Vi* values are individual adsorbate molar volumes (which may differ from the bulk molar volumes4J0), and the adsorbate mole numbers ni are given by ni = xiV/P (5) This completes the calculation for uniform adsorbates. In general, however, the adsorbates are not necessarily uniform, because the components with the highest adsorption potential per unit volume (€/V*) tend to concentrate in the regions of highest adsorption potential, like dense liquids tending to concentrate toward the bottom of a centrifuge tube. The appropriate equations for calculating the composition in each element of adsorbate volume are readily derived by the method of Hansen and Fackler.8 The molar free energy of adsorption of each component is zero at the equilibrium adsorption interface. Within the adsorbate it is given by AGi = --(ei - q*) + RT In ( x r / x i * ) (6) where the first term represenb the energy (assumed equal to enthalpy) difference and the second term the approximate entropic free-energy difference (TAS)between any location in the adsorbate and the interface. The condition of constant volume in the adsorption space is that for any virtual displacement of one adsorbate by another Vi* dni + Vj* dnj = 0 (7) dnj = -(Vi*/Vj*) dnj
(8)
The condition of equilibrium dG/dni = 0 = AGi - AGj(Vi*/Vj*) leads to the relation ti - ti* RT X r €j - €j* -+ - 1n - = -vi* vi* xi* vi*
RT
(9)
Greenbank and Manes
numerical integration over the adsorbate volume from zero to the equilibrium adsorbate volume V. Equation 10 leads to the expectation that the uniform adsorbate approximation will exhibit the most error for systems with widely differing values of t/ V* (which tends to correlate with refractive index1J6);for these systems the errors should be greatest at the highest (total) loadings, where relatively large net adsorption energies (e - E*) can develop. The approximationworks best on systems which, as pure organic mixtures, do not exhibit appreciable selectivity of adsorption; this is in keeping with the thermodynamic consistency condition of Myers and Sircarel’ We anticipate that for many systems the individual adsorption isotherms may be predicted to sufficient accuracy by the method of Wohleber and Manes’ and the uniform adsorbate assumption will suffice. For these systems the calculations become quite simple, given a carbon for which one has a correlation curve or its equivalent in adsorption data. Both the full and the approximate model lead to the expectation that all componenb that are present at relatively low mole fractions everywhere in the adsorbate (or at the adsorbate interface for systems that follow the uniform adsorbate approximation) will exhibit linear isotherms, for which the proportionality constant may be derived from the model. For the uniform adsorbate approximation, where we also assume ideal solution in the adsorbate, the mole fraction of any component is given as If xi is very small, the value of ci*, which depends on the total adsorbate volume, is almost constant. For components exhibiting nonuniform adsorption, if xi is small everywhere in the adsorbate, the Hansen-Fackler treatment again results in a linear dependence of adsorption on concentration everywhere in the adsorbate, except that the proportionality factor is location dependent. Under these conditions one again expects overall linearity between adsorbate loading and concentration for the trace component. On the other hand, a trace component with a high value of E/ Vi may concentrate to high values of xi at least somewhere in the adsorbate, in which case its adsorption will not follow Henry’s law. Both kinds of behavior are predicted by the model and illustrated in the experimental results. We now consider the elimination of a difficulty in applying the IAS model.I2 In this model the postulate that each component should be evaluated at equal “spreading pressure” is equivalent to the condition that
Xf
+In - (10) vj* xj*
for all i and j. Here we assume that the known quantities are the individual adsorption potentials and mole fractions at the interface, and the adsorption potentials ti(W as a function of adsorbate volume. For each element of volume dV, eq 10 determines the ratios of all of the adsorbate mole fractions. These ratios and the condition that their sum shall be unity leads to a set of adsorbate mole fractions x r for each volume element. The mole numbers, dni, are given by xi dV dni = &Vi:,* and the adsorbate mole numbers ni are determined by (16) R. J. Grant and M. Manes, Ind. Eng. Chem. Fundam., 5 , 490 (1966).
where ni and nj are the moles of adsorbate per unit mass of carbon and and ej the net adsorption potentials in water solution. Following the procedure of Grant and Maned6 (in gas-phase adsorption) we can rewrite eq 13 as
where the integrals may be seen to be proportional to the area under each correlation curve and to the right of a vertical line at any given value of the abscissa. To evaluate these integrals, one needs low-capacity adsorption data, which are frequently impossible to obtain because of unmeasurably low equilibrium concentrations. If, however, one makes the approximation that the adsorbate correla(16) M. Manes and L. J. E. Hofer, J. Phys. Chem., 73, 584 (1969).
Adsorption of Organic Liquid Mixtures from Water tion curve on a given carbon is the same as (for example) the corresponding hydrocarbon correlation curve, except for an abscissa scale factor, yi, then the integrals are readily evaluated, since the hydrocarbon correlation curve may readily be determined to low capacities. Equation 14 becomes
where each integral refers to the hydrocarbon correlation curve. This procedure may also be considered as a means for extrapolating individual adsorption isotherms to the low capacities that are required by the IAS model. Finally, one is obviously not limited to a hydrocarbon correlation, but may use any gas-phase or liquid-phase data that cover a sufficient capacity range to characterize the carbon. The condition of equal spreading pressure in the IAS model becomes equivalent to the evaluation of individual adsorbate properties at the same adsorbate volume in the Polanyi model when the individual abscissa scale factors are identical. For such systems, and to a reasonably good approximation when these scale factors are not too widely divergent, the IAS and Polanyi-based models may be expected to give essentially the same results. As we shall see, for liquid adsorbates it takes rather extreme systems to produce large differences between the two models, and the Polanyi approach provides the criteria for finding them. Experimental Section and Data Reduction Materials. The activated carbon (Pittsburgh Activated Carbon Co. Grade CAL,Lot 2131,200-320 mesh) was from the same uniform batch that has been used in earlier work.14 It was used as received, followed by drying at 115 "C. The hydrocarbon correlation c w e for this carbon was determined at the Calgon Corp. research laboratories1' by continuous butane desorption, using the method of Semonian and Manes.l* For convenience in computation the plot of adsorbate volume (cm3/(100 g of carbon)) vs. A (=(T/ v) log (p,/p)) was fit to the following polynomial equation, which is valid to a lower adsorbate volume limit of 0.1 ~m3/(100g of c): log v = 1.762 - 0.05244 - (5.35 X 10-4)A2- (4.98 X 10")A3 (16) The computation also used the following inverse equation in Y (= log V), which is valid over the same limits: A= 20.74 - 7.17Y - 1.35Y2 - 0.427Yj - 0.131Y4 - 0.0191yS (17) Similar equations could have been obtained from, for example, the earlier data of Wohleber and Manes.' The (room-temperature) liquids were all used as received. Less than 0.1% impurities was detected by gas chromatography. However, in experiments with one component at mole fractions less than 0.01, the dominant components were run through an activated carbon column to remove any possibly interfering impurities. Moreover, in experiments at overall trace concentrations, the water was also prepurified in a carbon column. The coumarin, the phthalide, and the PNP had been previously recrystallized in earlier work.4 Apparatus. All of the experiments were carried out in a minicolumn apparatus that was essentially as described (17) J. E.Urbanic, Calgon Corp., private communication. (18) B. P. Semonian and M. Manes, Anal. Chern., 49, 991 (1977).
The Journal of Physical Chemistry, Vol. 85, No. 21, 1981 3053
by Rosene and Manes.4 Further details are given by RosenelQand by Rosene et a1.20 The column technique made it possible both to fii the equilibrium concentrations and to vary them in systematic fashion, and thereby to improve both the interpretation and the presentation of the data. Test solutions of known composition were pumped from a reservoir vessel to a temperature equilibration coil (10 ft of 1/16-in. stainless-steel tubing) and thence to the carbon column and an effluent reservoir. Both coil and column were in a thermostated water bath. The pump was a standard Minipump (LDC Division, Milton Roy Co.) with an upper pressure limit of 5000 psi and a flow rate adjustable from 0.5 to 5 mL/min. Each carbon sample was packed into a column made of stainless-steel tubing, either of 0.25-in. outside diameter with wall thickness to suit the sample size or else (for the smallest samples) of 1/16-in.tubing. The sample was retained in the column by a 5-10-pm stainless-steel fritted plate ("snubber"), sometimes backed by a cotton plug. The effluent composition was monitored either with a W detector or else by repeated sampling in an automatic sampling valve and analysis by gas chromatography, using a &ft, 0.125-in. stainless-steel column packed with Poropak Q (Waters Associates). Adsorption Experiments and Data. Carbon samples varied in size from 0.5 mg to 4 g. Each weighed sample (originally at 200-320 mesh) was further ground to well below 325 mesh and quantitatively transferred to the column. A check comparison of columns with ground and unground samples showed only the expected differences in width of the breakthrough curves at transition, but no detectable difference in equilibrium capacities. In the determination of adsorption capacities for single adsorbates (e.g., l-pentanol and 1,2-dichloroethane), an accurately prepared stock solution in the influent reservoir was first pumped through the open connection to the column, after which the joint to the dry carbon-packed column was connected; pumping was initiated with the entire system initially dry downstream from the column entrance. All effluent liquid (initially containing no solute) was collected and weighed. At the beginning of breakthrough, a new collection vessel was substituted, and solution was collected until near the end of breakthrough. Finally, a third collection vessel collected the last effluent to full breakthrough, i.e., at equal concentration of influent and effluent. The amount adsorbed was taken as the total carbon-treated volume, multiplied by the overall concentration deficit. Since all of the colleded volume had passed through the sample, there was no need for a dead-space correction. A small correction could be made, if necessary, for the volume loss due to adsorption, which would produce a small discrepancy between the collected volume and the carbon-treated volume. The calculation method was designed to give maximum precision without any assumption of constancy of flow. The volume before breakthrough almost invariably comprised well over 90% of the total volume, and both ita volume and concentration deficit (equal to the inlet concentration) were known with high precision without any necessity for effluent analysis. The volume of the second fraction collected was also known accurately, and its average concentration was determined by gas chromatography or UV spectrophotometry; the error of analysis made (19) M. R. Rosene, Ph.D. Dissertation, Kent State University, Kent,
OH, 1977.
(20) M. R. Rosene, Robert T. Deithorn, John R. Lutchko, and Norman J. Wagner in "Activated Carbon Adsorption of Organics from the Aqueous Phase", I. A. Suffet and M. J. McGuire, W.,Ann Arbor Science Publishers, Ann Arbor, MI, 1980, p 309.
3054
Greenbank and Manes
The Journal of Physical Chemistry, Voi. 85, No. 2 1, 198 1
TABLE 111: Diethyl Ether and Ethyl Acetate at 25 'C exptl vads,
liquid component concn, g/L diethyl ether 0.00695 ethyl acetate 0.0901 diethyl ether 0.0695 0.00451 ethyl acetate diethyl ether 0.00695 ethyl acetate 1.802 diethyl ether 2.78 ethyl acetate 3.60
cdc
7210 853 721 17100 7210 42.7 18.0 21.4
xads
0.0914 0.909 0.940 0.0598 0.00430 0.996 0.473 0.527
only a relatively small contribution to the overall error of capacity determination. The third fraction exhibited a quite small concentration deficit; even a large error in determining this deficit (up to 50%) made a negligible contribution to the overall experimental error. Reproducibility of column capacity for single components was estimated as better than *l% except at influent concentrations that approached the detection limits. Attainment of equilibrium at the end of a run was verified by checking the composition of the liquid in the column after it had been allowed to sit overnight in contact with the carbon. In multicomponent adsorption one can start with a dry column only when all of the components break through at about the same time. However, analysis of the effluent from a virgin sample is usually a very imprecise method for determining the capacity of a weakly adsorbing trace component in a multicomponent mixture because the trace component is first adsorbed and then displaced. Moreover, for a strongly adsorbing trace component, this procedure can be very time-consuming. The procedure of choice for binary and ternary adsorbates was to preequilibrate the carbon with a solution of the dominant adsorbate component(& following which the system was emptied of liquid downstream from the column exit joint and pumped to that joint with a binary solution now containing the second (or third) component but otherwise unchanged. Pumping started with the column initially full of the single-component solution; the fraction collection procedure was unchanged. For this procedure a dead-space correction had to be made, to correct for the effluent volume that had not been scrubbed of the second component. This volume was determined by weighing the packed column, first containing dry carbon and then after having been pumped with solution. The contribution of column dead-space error to the carbon capacity error depended on the ratio of effluent to column volumes. For very weakly adsorbed components (e.g., ethyl acetate in the presence of PNP), breakthrough volumes were not much larger than column dead-spacevolumes and precision was accordingly reduced. The experiment gave the adsorbed mass of monitored component, from which the adsorbed volume was calculated by use of the bulk density. The equilibrium concentrations were the same as the influent concentrations, which had been set in advance. Solubilities. Solubilities were determined by shaking excess solute with solvent in a thermostated shaker bath and analysis of the water layer by UV spectrophotometry or by gas chromatography. The solubilities in g/L and temperatures (in parentheses) were as follows: propionitrile, 105 (25); ethyl acetate, 77 (25), 80.5 (42), 83.5 (63); diethyl ether, 50 (25); 1,2-dichloroethane, 9.91 (25); dichloromethane, 15.7 (25); 1-pentanol, 20.6 (25), 25.0 (42), 27.4 (63); coumarin (liquid), 9.02 (62); phthalide (liquid), 25.0 (63); and p-nitrophenol (liquid), 35.1 (42).
cm3/ (100g) 0.626 5.81 4.53 0.269 0.0883 19.1 15.3 15.9
predicted Vad, uniform nonuniform IAS adsorbate adsorbate model model model
0.959 7.05 8.22 0.303 0.143 21.6 18.7 14.4
0.864 7.15 8.18 0.340 0.123 21.7 17.3 15.8
0.710 7.22 8.21 0.290 0.0916 21.5 16.0 12.9
estimated uncertainty in Vads, cm3/ (100g)
0.081 0.150 0.160 0.0210 0.0026 0.180 0.17 0.15
Calculations of Theoretical Valuesfor Adsorption. For the calculation of the 25 *C systems by the method outlined under the Theoretical Section, the individual correlation curves (V vs. (T/Vi)log (c8/c)J were derived from the hydrocarbon correlation curve (eq 16) by multiplying the abscissa values by abscissa scale factors, yi, that were estimated from the refractive indexes by the method of Wohleber and Manes.' The adsorbate molar volumes were taken as equal to the bulk molar volumes. For these systems this method gave results that were overall as close to experiment as those that were calculated from the experimental isotherms. The values for l / y that were used were as follows: ethyl ether, 1.51; ethyl acetate, 1.43; propionitrile, 1.43; dichloromethane, 1.20; dichloroethane, 1.56; and 1-pentanol, 1.29. For the systems studied at elevated temperatures (those that included PNP, coumarin, or phthalide) the adsorbate molar volumes, Vi*,were all estimated from a weighted best fit of the upper limit of the hydrocarbon correlation curve to experimental data, in which the highest weight was given to the points at the highest capacities. With the values of Vi* thus fixed, the values of the abscissa scale factors, yi, or, more conveniently, l/yi, were determined by a best fit of the experimental data to the hydrocarbon correlation curve. The data for liquid coumarin, phthalide, and PNP came from Chiou and Manes;lo the remaining data were from Wohleber and ManesI1except for l-pentanol, which was determined in this study. The values for V*/V and for l / y that were used in the higher-temperature runs were as follows: PNP, 1.15, 0.722; coumarin, 0.946,l.Ol; phthalide, 1.16,0.800, diethyl ether, 1.05,1.51; and 1-pentanol, 1.05, 1.43. The best-fit y value for water (calculated by the method of Wohleber and Manes1 with inclusion of 1-pentanol data and small corrections for V*) was unchanged from the earlier reported value of 0.28. The use of calculated scale factors for the low-temperature systems and empirical scale factors for the hightemperature systems was based on the intention of not adding any complications to the calculations that would not produce a demonstrable improvement in overall accuracy. For the high-temperature systems, the calculation was already complicated by the necessity of integrating over the adsorption space; moreover, the estimation of the adsorption isotherms of the molten solids was known,from the work of Chiou and Manes,lo to require both an empirical abscissa scale factor and an adjustment for adsorbate density. The calculation was therefore carried out with best-fit adsorption isotherms throughout. Results Table I (see paragraph at end of text regarding supplementary material) and Figure 1 give the single-component data for 1-pentanol as a single component, and Table I1 (supplementary material) and Figure 2 give both
a
The Journal of Physlcal Chemistry, Vol. 85, No. 2 1, 198 1 3055
Adsorption of Organic Liquid Mixtures from Water
Diethyl Ether, Ethyl Acetate, and Propionitrile at 25 'C
TABLE IX:
predicted V d ,
exptl concn, liquid component diethyl ether ethyl acetate propionitrile
g/L
cdc
ads
2.78 3.60 3.14
18.1 21.4 33.4
0.407 0.452 0.142
cm3/ (100 9) 13.7 14.2 3.25
9m
10
estimated nonuniform uncertainty adsorbate in v&, model cm3/(100g) 16.1 0.17 14.8 0.16 3.50 0.11
-
5 -
9m
0
v)
n
a
a w z
3 9
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Figure 1. Adsorption of 1-pentanol from water at 25 OC, plotted as unadjusted adsorbed volume vs. s/(4.6V1). The dotted line Is the theoretical line calculated from the hydrocarbon line and the refractive index, assuming equality of bulk and adsorbate molar volumes. The solid llne Is calculated from best-fit values of the adsorbate molar volume, V", and the abscissa scale factor. (0)Column points. (A) Shaker-bath points.
103
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c& Figure 3. Adsorption at 25 OC of ethyl acetate (EA) from 3.14 g/L propionitrile (PN), PN from 3.60 g/L EA, 1,2dichloroethane (DCE) from 2.78 g/L diethyl ether (EE), and EE from 1.24 g/L N E . The ordinate in this and subsequent figures is the volume of the minor component. Numbers in parentheses In flgures indicate flxed concentrations in g/L. (-) Uniform adsorbate model. (- - -) Nonuniform adsorbate model. (- -) IAS model. (In the upper two plots ail models give essentially similar results.)
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Figure 2. Adsorption of 1,2dichloroethane from water at 25 OC, plotted as unadjusted adsorbed volume vs. €44.6VI). The dotted line is calculated from the hydrocarbon correlation curve and the refractive index. The solid llne is a best-fit calculation of the experimental data to the hydrocarbon line, using optimum values of the abscissa scale factor and adsorbate density. The dotted curve was used in the 25 OC systems and the solid curve In the systems with motten sollds. (0) Column points (this work). (A)Shaker-bath points (ref 1). (0) Shaker-bath point (this work).
new and old' data for 1,2-dichloroethane. Table 111,Tables IV-VI11 (supplementary material), and Figures 3-5 give experimental and calculated data for the binary solute systems at 25 OC: ethyl ether-ethyl acetate (Table 111); propionitrile-ethyl acetate (Table IV, Figure 3); propio-
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cs/c Figure 4. Adsorption at 25 OC of 1,2dichloroethane (DCE) from 3.14 g/L propionitrile (PN), PN from 1.24 g/L DCE, DCE from dichloromethane (DCM), and DCM from DCE. Legend as in Figure 3. (In the lower two plots the theoretical lines for the three models were too close for convenient presentatlon.)
nitrile-dichloroethane (Table V, Figure 4); diethyl etherdichloroethane (Table VI, Figure 3); dichloromethanedichloroethane (Table VII, Figure 4); and dichloroethane-pentanol (Table VIII, Figure 5). Table IX, Tables
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The Journal of Physical Chemistry, Vol. 85, No. 21, 1981
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103
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cs/c Flgure 5. Adsorption at 25 OC of the following: 1,2dlchloroethane (DCE) from 0.316 and 3.16 g/L l-pentanol (PEN); PEN from 1.24 g/L DCE. Legend as In Figure 3. (In the upper two plots the predictions of the nonuniform and IAS models practically coincided.)
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m e 8. Adsorptkn at 25 OC of the fdlowlng: dichloromethane (DCM) from a mixture of 1.24 g/L dichloroethane (DCE) and 0.158 g/L pentanol (PEN); DCM from 0.0124 g/L DCE and 3.16 g/L PEN: PEN from 2.78 g/L diethyl ether (EE) and 3.6 g/L ethyl acetate (EA). Legend as in Figure 3. (Plots for uniform and nonuniform models nearly coincided in upper two cases. IAS model was not applied to ternary systems.)
X and XI (supplementary material), and Figures 6 and 7 give similar data for the ternary solute systems at 25 "C: diethyl ether-ethyl acetate-propionitrile (Table IX); diethyl ether-ethyl acetate-pentanol (Table X, Figure 6); and dichloromethaneclichloroethane-pentanol (Table XI, Figures 6 and 7). Tables XII-XVII (supplementary material) and Figures 8-12 give the results for the higher-temperature binary (liquid) solute systems: phthalide-ethyl acetate (Table XII, Figures 8 and 11); phthalide-pentanol (Table XIII,
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c,/c Flgure 8. Adsorption of ethyl acetate (EA) at 63 OC from phthallde (PHL) solutions ranging from 0.0010 to 2.00 g/L. Legend as in Figure 3. The IAS model Is out of bounds for the PHL solutlon at 2.00 g/L (second from bottom). The muitlplicity of scales reRects the wide range of concentratlons and capacities.
Figures 9 and 11); coumarin-ethyl acetate (Table XIV, Figures 9 and 12); coumarin-pentanol (Table XV, Figures 9 and 12);p-nitrophenol-ethyl acetate (Table XVI, Figures 10 and 12); and p-nitrophenol-pentanol (Table XVII, Figures 10 and 12). For the binary and ternary systems (of which Table IV is an example) the tabulated information comprises the following: the individual equilibrium concentrations; the inverse relative concentrations, c,/c; the estimated adsorbate mole fraction; the capacity (or loading) of the minor component in cm3/(100 g of carbon); and the corresponding predicted loadings as estimated from (a) the Polanyi model, without ("uniform adsorbate") and with ("nonuniform adsorbate") the Hansen-Fackler-based treatment for solute nonuniformity, and (b) for binary systems, the Radke-Prausnitz (US)model, supplemented
The Journal of Physical Chemistty, Vol. 85, No. 21, 1981 3057
Adsorption of Organic Liquid Mixtures from Water 1p3 102
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by the Polanyi-based extrapolation method for the lowcapacity region. Data for systems with both diethyl ether and ethyl acetate, whether in binary or ternary systems, are given only in tabular form (Tables I11 and IX) because they do not lend themselves well to two-dimensional plots. The adsorbate mole fractions and relative concentrations in the tables are somewhat redundant but allow more convenient visualization of the experimental conditions and the relative adsorption of each component. In the figures the points are all experimental points. The loadings and inverse relative concentrations (ordinates and
Figure 12. Adsorption of the following: coumarln at 62 OC from 7.9 g/L pentanol and from 18.1 g/L ethyl acetate: and p-nitrophenol from 7.9 g/L pentanol and 18.1 g/L ethyl acetate. Legend as in Figure 3. Note multiplicity of ordinate scales (capaclty ranges for given cJcare all of the same order of magnitude). Vertical lines indicate upper limit of valldity of the IAS rodel. Only two curves are shown for the uniform adsorbate model; all are slmllar In shape.
abscissas) refer to the same (minor) component; the numbers in parentheses in the figures give the concentrations of the major component(s). The lines are theoretical lines computed for the corresponding models; a vertical line on the curve for the IAS model indicates an upper concentration limit beyond which the calculation cannot be carried out. Some theoretical plots are missing from the
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The Journal of Physlcal Chemistry, Vol. 85, No. 21, 1981
figures, either because of near coincidence with another plot or because the (IAS) model does not apply. The reasons for such omissions are given in the captions. Finally, much of the data and many of the theoretical plots in the figures, particularly in the low concentration ranges, show a linear relation between loading and concentration; where the correspondinglines do not appear to exhibit unit slope, it is due to inequality of the abscissa and ordinate scales.
Discussion We shall consider the following: the range and variety of the experimental results and how well they are accounted for by the various models; and the validity, applicability, and observed and expected limitations of the Polanyi-based approach. We first note that the multicomponent data comprise some 120 runs on binary and ternary mixtures of liquids of a variety of functionalities (alcohol, ester, ether, nitrile, chloroalkanes, lactones, and nitrophenol) over as wide a range of relative mole fractions as was experimentally accessible (in some cases over 7 orders of magnitude), and including systems (i.e., those with coumarin, phthalide, and p-nitrophenol) that were expected to provide severe tests for any theoretical model. The emphasis overall has been on the ability of the theoretical treatment to provide reasonable estimates of adsorption capacities over an extremely wide range of systems and conditions rather than on maximum accuracy for carefully selected systems. The observed differences between theory and experiment usually are due not to experimental error but to the limitations of the models and in the fit of single-component data to the (abscissa scale-adjusted) hydrocarbon line; however, for a wide variety of systems, the deviations exhibited here are probably conservative estimates of error. We first consider the 25 "C binary and ternary systems (Tables 111-XI, Figures 3-7). For these systems the uniform and nonuniform model, and, in binary systems, the IAS model, give quite similar predictions, as one would expect. The uniform adsorbate model, which is the simplest, also works best overall. The largest anomalies are in some systems with 1,2-dichloroethane(Figures 3-7) and at least in part reflect anomalies in the fit of the singlecomponent data to the single-componentmodel. Although we could improve the fit of the multicomponent data with dichloroethane by using its experimental isotherm (Table 11, Figure 2) rather than a calculated correlation curve, the improvement was not thought to be enough to justify complicating the otherwise relatively simple calculations for the room-temperature liquids. The expected Henry law dependence for the adsorption of trace components is generally confirmed. In the binary systems, the best agreement is exhibited by ethyl ether-ethyl acetate (Table 111),propionitrile-ethyl acetate (Table IV, Figure 31, and dichloromethane-dichloroethane (Table VII, Figure 4). For the systems containing dichloroethane, the quantitative agreement is better for the uniform than the nonuniform model, presumably because the scale factor calculated from refractive index overcorrecta for nonuniformity. Thus, for propionitrile-dichloroethane (Table V, Figure 4),the propionitrile exhibits the proper functional dependence on concentration, the uniform adsorbate assumption gives good agreement, and the nonuniform adsorbate calculation misses the capacities by a factor of -2, overestimating for dichloroethane and underestimating for propionitrile. In the dichloroethane-pentanol system (Table VIII, Figure 5), the pentanol loadings in 1.24 g/L dichloroethane follow the expected functional dependence but are somewhat lower than expected (from either uni-
Greenbank and Manes
formity assumption), and the adsorption of dichloroethane from various concentrations of pentanol is also somewhat low but again follows the proper functional dependence. We now consider the ternary systems. In the one run with the ethyl ether-ethyl acetate-propionitrile system, all components broke through approximately simultaneously. The tabulated data (Table IX) show good agreement with expectations; however, this system is not a very severe test of any model. In the dichloromethane-dichloroethane-pentanol system (Table XI, Figures 6 and 7) dichloromethane was the minor component at different ratios of the other two. For this system, like the preceding ones, the points show the proper functional dependence on the varied dichloromethane concentration and the capacities are either in very good agreement (over 3 orders of magnitude of concentration) or somewhat below expectations. The theoretical curves for uniform and nonuniform adsorption are not significantly different. For ethyl ether-ethyl acetate-pentanol (Table X, Figure 6), the experimental data were either for ethyl ether and ethyl acetate breaking through simultaneously on a column previously equilibrated with pentanol (not plotted) or else for pentanol being monitored on a column previously equilibrated with a mixture of ethyl ether and ethyl acetate. The latter data, plotted in Figure 6, show excellent agreement with the uniform adsorbate assumption and satisfactory agreement with the nonuniform model; the functional dependence is again the same for both. The (unplotted) data for ethyl ether and ethyl acetate as variable adsorbates show excellent agreement over wide variation of the mole fraction ratios. A comparison of the ternary with the binary systems shows no evidence of any special problems (other than experimental verification) in expanding the model from binary to ternary systems. Since the foregoing systems should be at least typical of many organic liquid mixtures (if anything, the mixtures with dichloroethane appear to have been somewhat anomalous for as yet unknown reasons), the relatively simple uniform adsorbate approximation appears to be capable of estimating the adsorption isotherms of many-component liquid mixtures on a characterized carbon, given only their solubilities, densities, and refractive indexes, with no adjustable parameters and, for a wide variety of adsorbates, with no explicit account of functionality. Although the IAS model requires more complex computations, especially for many components, this is not a major problem, and it should also be quite adequate for these systems. We now consider the binary systems with room-temperature liquids (ethyl acetate or pentanol) and molten solids (phthalide, coumarin, and PNP), and we first consider the adsorption of the liquid components from fixed concentrations of the molten solids (Tables XII-XVII, Figures 8-10). The nonuniform model accounts for the adsorption very well overall for ethyl acetate and pentanol from both phthalide and coumarin over as much as 4 orders of magnitude of concentration, and the uniform adsorbate assumption usually overestimates the adsorption by a factor of 2 or 3. The largest deviations are about twofold in PNP, but the slope of the theoretical line is again followed over some 4 orders of magnitude. The IAS model works reasonably well whever it applies, but it is out of bounds for coumarin, PNP, and the higher concentrations of phthalide. The effects of adsorbate nonuniformity become much more striking in the adsorption of molten phthalide, coumarin, and PNP from ethyl acetate and from pentanol (Tables XII-XVII, Figures 11 and 12). Here the as-
Adsorption of Organic Liquid Mixtures from Water
The Journal of Physical Chemistry, Vol. 85, No. 2 1, 198 1 3059
sumption of adsorbate uniformity is clearly inadequate, underestimating the adsorption by as much as 2 orders of magnitude. The agreement of the experimental results with the nonuniform adsorbate model is reasonably good overall. The IAS model does reasonably well where it applies, but again it goes out of bounds under experimental conditions that the Polanyi-based model handles with no difficulty. Finally, it is important to note that, since the selectivity effects of the liquid and molten solid components are in opposite directions, they cannot be accounted for by any manipulation of adsorbate activity coefficients that is consistent with the Gibbs-Duhem relation. To sum up, the Polanyi-based model appears to be capable of predicting at least reasonably well the adsorption from water of multicomponent liquid adsorbates of considerable variety and complexity; we have not yet found a limit to its concentration range; and it can readily be extended to liquid systems with any number of components. Moreover, we are here using essentially the same model that was applied earlier to the adsorption of single and multiple gases,16mixed organic liquid^,^ solids from organic solvents,16 and single and multiple solids from water.k6 Furthermore, for all but the most difficult systems, the simple uniform adsorbate model should suffice. Finally, although the prediction of individual isotherms has limitations, we have not yet found a system in which the full mixture model breaks down badly or goes out of bounds. We now consider the physical validity and thermodynamic consistency of the model. The simplified model with the uniform adsorbate assumption is quite analogous to the Polanyi-based model of Grant and Manes15 for the adsorption of multiple vapors, which did not incorporate adsorbate nonuniformity. Although the systems they dealt with (like some of the systems described here) did not exhibit significant adsorbate nonuniformity, their approximate model was lacking in generality because of the omission. Sircar and Myersz1 pointed out that in the general case this omission could lead to a thermodynamic inconsistency, in that the adsorbate from a saturated vapor mixture would not be the same as the adsorbate from the liquid mixture in equilibrium with it. We have seen how large this effect can be in liquid systems. However, the addition of the Hansen-Fackler treatment removes this inconsistency for both gas-phase and liquid-phase systems and therefore lays to rest the question of the thermodynamic consistency of the Polanyi-based model; whether the thermodynamic inconsistency of the uniform adsorbate
assumption has any experimental consequences depends, as we have seen, on the particular system. We now consider some limitations of the Polanyi-based approach to mixed liquid adsorbates. We separately consider the estimation of individual adsorption isotherms and of the adsorption of mixtures from either experimental or estimated isotherms. Although many individual isotherms should be well estimated by the Wohleber-Manes' method, the estimation may in many cases (as, for example, for our molten solids) require experimental determination of adsorbate densities and scale factors. One may expect the additional complication of steric factors for highly branched adsorbates,2zof some chemisorptive effects for relatively highly acidic compounds like acetic acid,z and, for relatively large molecules, of molecular sieving3effects. These have been recognized but remain to be thoroughly explored. Consider now the application of our model for mixed adsorption, given experimental isotherms that for the above reasons may not fit the single-component Polanyi model. We may here expect complications in our competitive adsorption model if the individual components do not compete for the same sites, for example, if one component exhibits chemisorptive or molecular sieving effects. Again, we have yet to explore such systems. We note further that, although all of the published data in this series have been obtained on a single batch of activated carbon, unpublished work with other carbons suggests that our carbon is sufficiently representative of generally available activated carbons. Nevertheless, one may find specialized carbons with unusual pore structures that may present problems for this and othei adsorption models. Finally, the column technique has proved to be a powerful and accurate method for determining the liquid-phase adsorption of single components and of relatively small amounts of one component in the presence of one or several others. With the addition of a constant-flow pump and continuous monitoring of effluent, it should be capable of even wider application.
(21)S.R. Sircar and A. L. Myers, Chern. Eng. Sci., 28,489 (1973).
(22) C. C. T. Chiou and M. Manes, J. Phys. Chern., 77,809 (1972).
Acknowledgment. We thank the Calgon Corp. and the National Science Foundation (Grant No. CME-7909247) for supporting this work. We also thank the Calgon Corp. for the butane desorption data on our carbon. Supplementary Material Available: Tables I, 11, IVVIII, and X-XVII (17 pages). Ordering information is available on any current masthead page.
