these hydrocarbons also form ideal solutions on porous adsorbents.
specific surface area of adsorbent molar surface area of adsorbate Go molar Gibb’s free energy of pure component in ideal gas state a t 1 a t m K = Henry’s law constant k = Boltzmann constant .lI = molar mass m = mass of adsorbed gas per gram of adsorbent -Y = number of components n = number of moles per gram of adsorbent n, = monolayer capacity per gram of adsorbent P = pressure Po = equilibrium pressure of pure component R = gasconstant T = absolute temperature 2 = adsorbed phase composition, mole fraction y = gas phase composition, mole fraction Z = compressibility factor = = =
GREEKLETTERS a
om y
e I.(
x
= = = = = = = = =
i
= componenti
m = monolayer, also used for mixture 1 = more volatile component
Nomenclature
A a
SUBSCRIPTS
constant of two-dimensional van der Waals equation constant of two-dimensional van der Waals equation constant of two-dimensional van der m aals equation for mixed adsorbate activity coefficient fractional coverage chemical potential chemical potential of pure component spreading pressure molecular area of adsorbate
2
=
less volatile component
SUPERSCRIPTS a g
= =
adsorbedphase gasphase
Literature Cited
Constabaris, G., Sams, J. R.,Jr., Halsey, G. D., Jr., J . Phys. Chem. 65,367 (1961). Chien, 31-T.W., M.S.thesis, Clemson University, Clemson, South Carolina, fp69. De Boer, J. H., The Dynamical Character of Adsorption,’’ 2nd ed, Oxford University Press, London, 1968. Friederich, R. O., Ph.D. Dissertation, Clemson University, Clemson, South Carolina, 1970. Hoory, S. E., Ph.D. Dissertation, University of California, 1966. Hoory, S. E., Prausnitz, J. >I.,Chem. Eng. Sci. 22, 1026 (1967). Myers, A. L., Znd. Eng. Chem. 60,45 (1968). Myers, A. L., Prausnitz, J. AI., A.I.Ch.E. J. 11, 121 (1965). Ross, S., Olivier, J. P., “On Physical Adsorption,” Interscience Publishers, New York, N. Y., 1964. Van Ness, H. C., IXD. ENG.C H E ~ FUNDAM. ~, 8,464 (1969). Young, D. hl., Crowell, A. D., Physical Adsorption of Gases,” pp 365-406, Butterworths, Limited, London, 1962. RECEIVED for review Bugust 16, 1971 ACCEPTED May 15, 1972 Financial support for this work was provided in part by the National Science Foundation (Grant GK-24860), the Clemson Alumni Foundation, and E. I. du Pont de Nemours & Co., Inc. One of the authors was the recipient of an KDEA Title IV fellowship.
Adsorption of Organic Solutes from Dilute Aqueous Solution on Activated Carbon C. J. Radkel and J. M. Prausnitz” Chemical Engineering Department, L-niversity of California, Berkeley, Calif. 94i20
Experimental data are reported for adsorption of propionitrile and 2-propanol from dilute aqueous solution at 0, 25, and 70°C. Acetone, p-cresol, and p-chlorophenol were studied u t 25°C. The adsorbent was activated carbon (Filtrasorb 300) with a BET surface area of 1000 m2/g. The data cover a concentration range from 1 0-5 to 10-1 M. p-Cresol and p-chlorophenol are adsorbed much more strongly than any of the other organic solutes. A new three-parameter empirical equation i s successful for fitting the isotherms over the entire concentration range. The experimental results are used to establish a semiquantitative corresponding-states correlation.
C u r r e n t , interest in removing organic pollutant’s from waste waters has stimulated investigation of various possible processes for water purificabion; some of these utilize adsorption (Weber, et al., 1970). In t,he design of such purification facilities, equilibrium adsorption information is required. Although it has long been recognized that’ various adsorbents, notably 1 Chemical Engineering Department, Pennsylvania State University, University Park, Pa. 16802.
activated carbons, greatly improve water quality, fe\v systematic studies are available for adsorption from dilute aqueous solution over wide ranges of loading ( L e . , amount of solute adsorbed) and concentration. This lack of extensive and accurate data impedes progress toward establishing useful engineering correlations for prediction of adsorption equilibria. For over 50 years the Langmuir and Freundlich equations Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4 , 1972
445
have been used to represent adsorption isotherms for solut.es from dilute liquid solution over small ranges of concentration. Unfort'unately, no general procedure is available to make a priori estimates of the parameters. Manes and Hofer (1969), Wohleber (1969), and Wohleber and ;\lanes (197la) have applied Polanyi pot'ential theory to adsorption of solids and partially miscible solutes from dilute solution. Since Polanyi theory for adsorption from solution is valid only for those solutes t,hat can undergo separation into a nearly pure solute phase, completely miscible liquids and industrially important partially miscible liquids such as phenols in water cannot be treated by this theory. Furthermore, as Hansen and Fackler (1953) point' out, Polanyi theory is not symmetric with respect to solute and solvent and therefore cannot be general. Thus if a solute adsorbs positively from dilute solution, the solvent must in turn adsorb negatively when dilute in t.hat same solute. To account for this discrepancy, Hansen and Fackler modified the Polanyi t'heory. Although their modification is applicable to partially and completely miscible liquids, the thermodynamic origin is questionable and the agreement viith experiment ivas not, satisfactory without' an additional arbitrary assumption (Hansen and Fackler, 1953). Recently, Wohleber and Manes (1971b) employed wit'h great,er success the Hansen and Fackler modificat,ion of the Polanyi theory for correlating the adsorption of completely miscible organic liquids from dilute aqueous solution. The arbitrary division of solutes into solid, parbially miscible, and complet,ely miscible does not provide a uniform account of the adsorption process which must ultimately depend on molecular forces, and it prevents prediction of solute mixture adsorption for those solutes that, lie in different divisions. I n this work we present new experimental results and me describe a corresponding-states method for estimating adsorption of organic solutes from dilute aqueous solution, regardless of whether or not these solutes are complet.ely miscible or whether they are above or below their melting points. The molecular corresponding-states treatment is presently confined to dilute solutions and to homogeneous surfaces but can be extended t o include nonuniform adsorbents Tvhen data become available for solids of differing heterogeneity. As in classical correspondiag-states theory, different classes of corresponding stat,es must be established when the forces controlling the adsorption of solutes from dilute solution are not. similiar. Experimental Section
Materials. The adsorbent was a commercial activated carbon, Filtrasorb 300, supplied by Calgon Corporation ; its specific BET surface area is 1000 m2/g. Prior t o use, the adsorbent was screened to 10 x 32 mesh and dried a t 150°C for 6 hr. Acetone and 2-propanol were spectroqualjty grade obtained from Matheson Coleman and Bell. Propionitrile was reagent grade from Eastman Organic Chemicals. Gas chromatographic analysis of these solutes revealed less t,han 0.1% impurities. p-Chlorophenol and p-cresol were from Aldrich Chemicals, Gold Label (99+%). Gas chromatographic analysis of the phenols detected no impurities, but separation of close boiling impurities was not possible. Procedure. Adsorption isotherms were determined by contacting a volume V (100 em3) of solut,ion of known concentration \%-it#h a mass m ( 5 t,o 15 g) of adsorbent in 125-ml Erlenmeyer flasks sealed with 15-mm poly (ethylene-copropylene) 0 rings. The flasks were then continually shaken in a wristshaker thermostated to within i0.05OC a t 70.0, 446
Ind. Eng. Chem. Fundam., Vol. 1 1 , No.
4, 1972
25.0, or 0.1OC. The time required for equilibrat,ion was 30 hr for the phenols and 15 hr for the other solutes. After equilibrium was attained the carbon was allowed to settle for a t least 2 hr before a supernatant sample was removed for analysis of the concentration decrease Aci. Filtration of t'he sample was required only for t8he lowest temperature isotherms and was accomplished with a syringe filter holder (Millipore Swinnex-25) and 0.45-p filters. Concentrations as low as 3 ppm were determined by a Varian gas chromatograph with a flame ionization detector. X 1 ft x in. 0.d. column operat.ing a t 165 i 0.2OC and packed with Poropak P was used to analyze the phenols; a 6 ft X in. 0.d. column operating a t 140 i.0.2"C and packed with Poropak Q was used in the analysis of propionitrile, 2-propanol, and acetone. Helium carrier-gas flow rate was controlled a t 25 cm3/min, and the helium, hydrogen, and bott,led air flow rates were kept in a 1:1:12 ratio. K t h a 9-pl injection size, concentrat'ions down to 5 X 10-5 were detectable. Larger injection sizes extinguished the hydrogen flame. The use of Poropak P as a stationary phase to resolve phenols from water was not ent'irely satisfactory as these polar aromatic solutes t'ended to "stick" to t'he packing. Repeated injections of mater, followed by rejection of the first few chromat,ogram peak areas, however, gave reproducible results. To increase the accuracy of the gas chromatography concentration analysis a n int.erna1 standard technique was employed. The solute concent.ration was determined as a previously calibrated function of the response factor R defined by
where A i and A i , represent, peak areas of solute and internal standard obtained from a Variaii digital integrator, wi and w i r are known solut,ionweights of solute and internal standard, and c i s is a known internal-standard solution concentration. To measure concentrations to within 3% reproducibilit'y required a quadratic calibration curve since the ionization detector had a slightly nonlinear response over the 4-decade concentration range studied. Because concentrations were determined a t 23OC, a small correction to t,he 70°C concentrations was indicat'ed. This correction, given approximately by the ratio of the density of m-ater a t the two temperatures, was within experimental error, and therefore was neglected. Concentrations of the phenols below 5 X 10-5 N were measured wit.h a Beckman DU spect'rophot,omet,er.p-Cresol and p-chlorophenol were first converted to phenolates with concentrated sodium hydroxide (approximately 1 drop/5 cm3 of solution) and analyzed a t 236 and 243 mp, respectively. Data Reduction
Experimental measurements actually determine an invariant adsorption niCof solute i defined by
where nia and nsa are the amounts of solute and solvent adsorbed per unit. mass of adsorbent (defined relative to the solid), ci is the solute concentrat,ion, and & and os are liquidphase partial molar volumes of solute and solvent'. For strongly adsorbing solutes, in t,lie limit, of zero concentratioll, niC = ni' (Radke, 1971; Sircar, et al., 1970). The origin of eq 2 is discussed elsewhere (Radke, 1971). Figures 1, 2, and 3 show the adsorption isotherms for the five organic solutes. Loadings (i.e,, amount of solute
Table I. Experimental Parameters for Eq 3
r, o c
Solutea
Propionitrile
b
a
0.1 25.0 70.0
0.9832 0.4781 0.1006 2-Propanol 0.1 0.3008 25.0 0.1972 70.0 0,06862 Acetone 25.0 0.5095 p-Cresol 25.0 159.8 p-Chlorophenol 25.0 293.1 a c, in mmoles/l. nn,oin mmoles/g.
0.3117 0.2368 0.1918 0.2488 0.2072 0.2060 0.2568 1.875 2.018
P 0.4486 0.4965 0.4964 0.3969 0.4526 0.4519 0.4004 0.1555 0.1395
,
Oooil
10-4
1
I
I
10-1
10-3 10-2 Concentration, mole/liter
Figure 2. Adsorption of 2-propanol from aqueous solution
Q
E
1.0-
1 9 2
A $-Chlorophenol
af
0001 10-5
10-4
10-3 10-2 Concentration, rnole/liter
10-1
1 10-6
0.01
Figure 1 . Adsorption of propionitrile from aqueous solution
I
, 10-4
I
103
J
1
I
10-2
IO'
Concentrat ion, mole /I iter
Figure 3. Adsorption from aqueous solution at 25OC
adsorbed), nit, are expressed in millimoles per gram and concentrations c1 are expressed in moles per liter. The solid black lines in these figures indicate a best fit to the three-parameter empirical equation
Equation 3 is successful for fitting adsorption isotherms over wide ranges of loading and concentration. When concentrations are expressed in millimoles per liter and loadings in millimoles per gram, values for the parameters a, b, and p for each of the isotherms are given in Table I. Detailed experimental data are listed in Appendix 11.
ber of experimental points. Loading values span a 2-3-decade range requiring a 4-&decade range of concentration measurements. There is little scatter in the data; concentrations are reproducible to within 3.5%. Experimental errors in loading are less than 1% as the mass of activated carbon used was adjusted to control the final solute concentration to be approximately 10% of the initial concentration. Figures 1 and 2 indicate that as the temperature rises, the adsorption a t a given concentration decreases; this effect is more pronounced a t the lower concentrations. Thus, as in gas-phase adsorption, adsorption from dilute aqueous solution is a n exothermic process. Examination of Figures 1-3 also reveals that the isotherm slopes a t the lowest concentrations of propionitrile, 2-propanol, and acetone are near unity, and they approach closer to unity as the temperature increases. Thus, a t these low concentrations, adsorption of propionitrile, 2-propanol, and acetone is almost in the Henry's law region. This conclusion, however, is not valid for p-chlorophenol and p-cresol. The adsorption of the phenols is almost 100 times stronger than that of the other solutes a t the lowest concentrations, indicating that the interaction between the phenols and the activated carbon surface is much stronger than that between propionitrile, 2-propanol, or acetone and the activated carbon surface. The extensive loadings of the phenols, even in concentrations of IOp6 ,M lends support to the spectroscopy studies of Mattson, et al. (1969), who conclude that aromatics form charge-transfer complexes with activated carbon surfaces.
Discussion of Results
Corresponding-States Correlation
Experimental data in Figures 1 through 3 cover wide ranges of loading and concentration with a substantial num-
Corresponding-states arguments suggest that it may be possible to establish a semitheoretical correlation of the ad-
(3) where the parameter @ is constrained to be less than unity. Equation 3 has several desirable properties : at low concentrations it reduces t o Henry's law for adsorption lim
niC =
aci
ci-0
and at higher concentrations it becomes t'he Freundlich equat,ioii niC =
bc;@
(5)
Furt,hermore, the Langmuir equation emerges from eq 3 in the special case that t,he parameter p is ident,ically zero
Ind. Eng. Chem. Fundam., Vol. 1 1 , No.
4, 1972 447
Table It. Reducing Parameters for Generalized Isotherm Solute
r,
O c
Bi',
c;'
AHTb,b
cm3/g
A
kcol/mole
TcF O K
Propionitrile
0.1 983 5.0 7 . 8 5 564 25.0 478 70.0 101 2-Propanol 0.1 301 5.1 9 . 7 3 508.2 25.0 197 70.0 68.6 Acetone 25.0 510 5.0 6 . 9 5 509.1 p-Cresol 25.0 160,000 6.0 11.25 704.6 p-Chlorophenol 25.0 293,000 5,95 ... ... From Bondi (1968). * R. C. lieid and T. K. Sherwood, "The Properties of Gases and Liquids," LlcGraw-Hill, Sew York, S . Y., 1966. Q
Reciprocal Reduced Temperature, c:,/kT
figure 4. Henry's adsorption constant from 4-1 0 potential
where f i is an unknown generalized function, Q. is the specific surface area of the adsorbent, -Y.k is dvogadro's number, u and e l l + are characteristic size and energy parameters for lateral potential of mean force interactions, and B1+is the adsorption second virial coefficient or Henry's adsorption constant. B1' considers the vertical potential of mean force interaction between one solute molecule and the adsorbent; it can be related theoretically to the temperature by (Radke, 1971)
Reduced Adsorption,
N A A F a
Figure 5. Generalized adsorption isotherm
sorption data. Such a correlation, in preliminary form, is described here. The basis of the correlation follows from a formal st'atistical-mechanical treatment of adsorption from dilute liquid solution which leads to an adsorption "virial" equation (Radke and Prausnitz, 1972). The adsorption virial equation suggests t,he appropriate form for a generalized adsorption isot'herm with two basic assumptions: (1) the infinitely dilute pot'ent.ial of mean force interactions (Hill, 1962) between solute molecules and the adsorbent caii be divided into a vertical potent'ial of mean force interact,ion for each solute molecule with the surface and lateral potential of mean force interactions among the solute molecules confined to a plane parallel to t,he adsorbent surface; (2) in dilute solution the second term of eq 2 is negligible so that the invariant adsorpt'ion nic of solute i equals t,he moles of solut'e adsorbed nia. K i t h these two assumptions, the adsorption virial equat'ion c,an bo transformed to siiecify the form of a corresponding-states isotherm. This transformation is given in Appendix I ; we cite here only the result (7) 448
Ind. Eng. Chem. Fundom., Vol. 1 1 , No.
4, 1972
where f, is a known function derived from a 4-10 solute-surface potent.ia1 of mean force, d is the distance where the 4-10 potential is zero, and elc+ is the depth of the 4-10 potential a t it.s minimum value. The function f, is shown in Figure 4. Use of eq 7 is similar to using directly the adsorption virial equation except that the difficult calculation of the adsorptioii virial coefficients higher than the second is avoided by the generalized function f i . Equation 7 suggest's that at, a given lateral reduced temperature k T / t n + , a plot of B1+cl,Inlc us. S ~ u * n l ~should /a collapse all dilute-solution isotherms onto one, generalized isotherm. If t'his generalized isotherm can be det'ermiiied from esperjniental data for several solutes, prediction of the adsorption of ot,her solut,es follon.s, provided t,he parameters u, ell+, arid B1+caii be estimated. Discussion of Generalized Isotherm
To check the validity of a corresponding-states correlat,ion, the nine experimental isotherms are plotted in Figure 5 as suggested by eq 7. In bhis work @ was 1000 m2/g. Values of the reducing parameters used are shown in columns 3 arid 4 of Table 11. The Henry's adsorption constants B1+ are esperjmental (as estimated from the parameter a of eq 3), and the lateral size parameters u are t,aken from Bondi's (1968) compilation of van der Waals radii. Figure 5 shows that the generalized plots for the phenols do not coincide with those for the three other solutes. The B1' values of the phenols are uncert,ain because t'he adsorption isotherms of t'hese substances are far removed from Henry's law region a t the lowest measured concentrations (see Figure 3). Changing t'liese B1+ values, however, only shifts the generalized plot along the ordinate and does not change its curvature. The st'eepness of t8hegeneralized plots arid t'he large B1+values of the phenols again suggest a specific chemical interaction of t,hese solut,es xith the actiyated carbon
surface. If the phenols do, in fact, interact specifically with Table 111. Experimental Isotherms for Propionitrile activated carbon, $hen their generalized plots should not be r = 70.00~ r = 0.1 oc expected to coincide with those of the three other solutes. -r = 25.0'~ Clr nP,a Clr nic, c1, nic, We originally expected the lat.eral energy parameter ell+ moIes/I. mmoIer/g moIes/I. mmoIes/g moIer/I. mmoles/g to be small so that the generalized isot'herm would be inde5,723-5' 0.0350 5.893-5 0.0191 6,003-5 0.00524 pendent of temperature. Figure 5 clearly shows that this is 5,753-5 0.0349 5.983-5 0,0192 6,04E-5 0.00553 not the case. If the corresponding-states arguments are 5,863-5 0,0347 6,183-5 0.0191 6,133-5 0.00549 correct, then a cross plot of the logarithm of Bl+cl/nlcus. 0,0265 9.443-5 0.00790 the logarithm of temperature a t specified values of N ~ u * n ~ ~ / @ 9.44E-5 0,0494 8.583-5 9.593-5 0.0491 8.573-5 0.0265 9.463-5 0.00794 should be superimposable by a single translation along t.he 1.573-4 0,0733 8.983-5 0.0265 2.03E-4 0.0171 abscissa. The propionitrile and 2-propanol isotherms are 1,323-4 0.0374 2.063-4 0.0171 1.60E-4 0.0732 superimposable when plot,ted in this manner. These limited 1.623-4 0,0735 1.40E-4 0,0372 2.10E-4 0.0170 temperature-dependent data, however, do not establish the 2.873-4 0,0666 5.173-4 0.0389 6.503-4 0.178 validity of a corresponding-states correlation. Confirmation 3,013-4 0.0663 5.213-4 0.0390 6,573-4 0.178 4.683-4 0.0958 9.913-4 0.0661 1.953-3 0.349 of the generalized adsorption isotherm must await more ex1.12E-3 0 , 1 7 5 9.93E-4 0.0659 2.013-3 0.350 perimental data on the temperature dependence of adsorp1.15E-3 0.175 2.203-3 0.126 6.56E-3 0,677 tion from dilut,e aqueous solution. 0.335 2,273-3 0.125 0.679 3.383-3 6,743-3 The Henry's adsorption constants in Table I1 can be 3.403-3 0.335 3.003-3 0.149 1.633-2 1 . 0 2 correlated if the vertical size and energy parameters d andele+ 4.743-3 0.420 5.883-3 0.267 1.633-2 1 . 0 2 can be estimated. We attempt correlation only of the pro4.893-3 0.419 1.803-2 0.558 8.853-2 2.24 pionitrile, 2-propanol, and acetone Henry's constants since 1.813-2 0.557 9.683-3 0.649 8.943-2 2.24 t,he large B1+ values of p-cresol and p-chlorophenol probably 9.883-3 0.644 3.423-2 0.835 arise from a different adsorption mechanism. The vertical 2.063-2 0.984 3.423-2 0.837 size parameter d is assumed t o be proportional to one-h@f the 2.143-2 0.977 8.963-2 1 . 5 1 3.293-2 1 . 2 2 9,043-2 1 . 5 0 sum of the van der Waals radius of a carbon atom (2.5 A) and 3.343-2 1 . 2 1 the lateral size parameter u in Table 11; the vertical energy 8.393-2 2.06 parameter elc+ is assumed to be proport,ional to the square 8.493-2 2.05 root of some measure of the dispersion forces between the a nlo = VAcl/m. b E n= 10". solute molecules. Typical measures of these dispersion forces are heats of vaporization or critical temperatures which are 1ist.ed in columns 5 and 6 of Table 11. Since the B1+ values of 2-propanol are about one-half of those of propionitrile or and the International Business Machines Corporation. For acetone but the heat of vaporizat,ion and critical temperature many helpful discussions we are indebted to John Kewman. of 2-propanol are not proportionately lower than those of propionitrile or acetone, elc+ values estimated in this manner Appendix I are not satisfactory. A refinement can be made by assuming that ele+ is proportional t o the square root of a dispersion Corresponding-States Theory. I n this section we outline energy factor minus the energy of hydrogen bonding of the a development of the form of the corresponding-states cGrsolut,e molecules with water (there being two hydrogen bonds relation given in eq 7. The formal statistical-mechanical for 2-propanol but only one each for acetone and propionitreatment of adsorption from dilute liquid solution yields an trile). Because the Henry's adsorption constants are sensit'ive adsorption virial equation which expresses the amount of to the value of elc+, this refinement improves t.he calculated solute adsorbed as a power series in solute concentration B1+values only slightly. -4 priori estimation of the vertical (Radke, 1971) ; it is written here in the inverted form int.eraction energies of solut,e molecules with activated carbon in dilute aqueous solution is apparently a difficult task. Conclusions
Experimental data are presented for five organic solutes adsorbing from dilute aqueous solution on activated carbon: propionitrile and 2-propanol a t 0.1, 25.0, and 70.0°C, and acetone, p-cresol and p-chlorophenol a t 25.OoC. The adsorption isotherms cover wide ranges of loading and concentration. Adsorption of p-chlorophenol and p-cresol is much stronger than that of the three other solutes, indicating a specific interaction with the activated carbon surface. A new three-parameter empirical equation is presented ; this equation is successful for fitting adsorption isotherms over the wide concentration range studied. Finally, a correspondingstates correlation is discussed, and experimental isotherm data are used to test this correlation. Acknowledgment
For financial support we are grateful to the Standard Oil Company of California, the Kational Science Foundation,
where nlE is the moles of solute adsorbed per unit mass of adsorbent, c1 is the solute concent'rat,ion,and BI+,CU+,DIII+, etc., are the second, third, fourth, etc., adsorption virial coefficient.s. The adsorption virial coefficients are funct'ions of temperature, solvent chemical potential, and infinitely dilute potentials of mean force (Hill, 1962). B1+considers one solute molecule interacting with the solid adsorbent in an infinitely dilute solution, Cll+ considers two solute molecules interacting wit'h each other and with the solid adsorbent in an infinitely dilute solution, and similarly for the higher coefficients. Direct use of the adsorption virial equation is at present not practical since the higher coefficients are difficult t,o calculate and a large number of coefficients are required except at extremely low concentrations. The adsorption virial equation, eq A l , does suggest., homever, the form for a generalized or corresponding-states dilutesolution isotherm. With the assumptions listed in the text (see Steele (1967) for the exact nat.ure of the approximations Ind. Eng. Chem. Fundam., Vol. 11, No. 4,
1972 449
Table IV. Experimental Isotherms for 2-Propanol
r
= 0.1
CI,
moles/l.
6.78E-5b 6.833-5 8.543-5 8.823-5 8.883-5 9.873-5 9.923-5 9.963-5 1 ,233-4 1,723-4 1,723-4 7.633-4 1 . 013-3 1 ,043-3 2,063-3 2.08E-3 4.993-3 5,133-3 9,303-3 9.633-3 2,073-2 2.14E-2 2.153-2 2.163-2 5.17E-2 5.283-2 8.143-2 8.243-2 a
r
oc
nic,a mmoles/g
0.0170 0.0169 0.0204 0,0203 0.0203 0.0232 0.0232 0.0232 0,0262 0.0364 0.0365 0.112 0.138 0.138 0,219 0.219 0.361 0.358 0,510 0.507 0.742 0,734 0.729 0.729 1.13 1.12 1.34 1.36
nlC = VAcl/m.
*
r
= 25.00~
c1,
moles/l.
6.773-5 6.963-5 7.08E-5 7,643-5 7,723-5 7.793-5 9.483-5 9.753-5 9,763-5 1.513-4 1.553-4 3.76E-4 3.783-4 5,743-4 5,883-4 9.97E-4 1.003-3 1,923-3 1,983-3 4.61E-3 7.823-3 7,883-3 2.29E-2 2.353-2 4.413-2 4.423-2 7.753-2 7.903-2 En = 10".
nlc,
mmoles/g
0.0111 0,0111 0.0111 0.0125 0.0124 0.0124 0.0153 0.0152 0.0153 0.0225 0.0228 0.0464 0.0464 0.0662 0.0661 0.0996 0.0995 0.164 0.163 0.299 0.394 0.394 0.740 0.738 0.983 0.980 1.38 1.37
= 70.0~~
c1,
moles/l.
6.543-5 6.583-5 7. 883-5 8,053-5 9,20E-5 9,253-5 1.393-4 1.40E-4 3.373-4 3,39E-4 6.333-4 6,413-4 9.00E-4 9.083-4 2,173-3 2,193-3 3.793-3 7.393-3 7.503-3 2,073-2 2.08E-2 4.913-2 4.923-2 7.933-2 8.053-2
Table V. Experimental Isotherms for Acetone, p-Cresol, and p-Chlorop henol at 25.0 C
0.00416 0.00416 0.00494 0.00491 0.00597 0.00598 0.00882 0.00880 0,0193 0.0193 0.0352 0.0351 0.0467 0.0466 0.0981 0.0980 0.150 0.259 0,258 0.530 0.530 0.872 0.872 1.18 1.17
nic,a
Clr
moles/l.
5 . 66E-5b 5.893-5 8.13E-5 8,303-5 8.31E-5 9.803-5 9.81E-5 1,783-4 3.153-4 3.243-4 3.323-4 7.843-4 8,223-4 3,143-3 3,203-3 5.863-3 5.983-3 9.073-3 9.153-3 1,063-2 2,053-2 2,163-2 3.35E-2 3.353-2 7.113-2 9.613-2 9.743-2
CI,
mmoles/g
0.0218 0.0218 0.0289 0.0289 0.0287 0.0352 0.0353 0.0520 0,0805 0,0798 0.0802 0,147 0,146 0,324 0,322 0,457 0,456 0,562 0.559 0.606 0,807 0.791 0.997 1.01 1.34 1.52 1.52
involved) the coefficients in eq A1 can be written as (Sams, et al., 1962)
and
where Q. is the specific surface area of the solid, N A is Xvogadro's number, and u and e l l + are lateral size and energy parameters. The symbols @I and @Z denote generalized functions. Equations A3 and A2 are combined with eq A1 to give
a
-p-Chlorophenol
p-Cresol
Acetone
nit, mmoler/g
nlc = BAcl/m.
b
moler/l.
8.663-6 1,013-5 1 ,223-5 1,283-5 2.61E-5 2.723-5 2.74E-5 2,823-5 2,883-5 4.683-5 4.943-5 4.98E-5 5.053-5 5.223-5 6.703-5 6.863-5 7.07E-5 7.45E-5 1.50E-4 1.593-4 1.643-4 3,013-4 3.08E-4 4.573-4 4.82E-4 4.853-4 8,403-4 8.603-4 9.113-4 1.563-3 1.623-3 1.643-3 2.743-3 4.473-3 1.80E-2 1.93E-2 5.97E-2
mo, mmoles/g
moles/\.
nit, mmoles/g
0.575 0.576 0.634 0.626 0.854 0.854 0.867 0.869 0.865 1.00 1.00 1.00 1.00 1.00 1.14 1.14 1.15 1.15 1.32 1.32 1.33 1.50 1.50 1.64 1.64 1.64 1.80 1.81 1.81 2.00 2.00 2.00 2.23 2.41 2.97 2.95 3.44
7.143-6 1.043-5 1.213-5 1.53E-5 1.633-5 1 ,643-5 4.01E-5 4.093-5 4.213-5 4.22E-5 4.343-5 7.233-5 7.37E-5 7.37E-5 7.633-5 8.303-5 8.373-5 9.193-5 9.41E-5 9.523-5 9.833-5 9.863-5 1.06E-4 1.47E-4 1.513-4 1,553-4 1.61E-4 4.653-4 4.78E-4 2.31E-3 2,553-3 2.58E-3 2.623-3 5.343-3 6.463-3 1.283-2 1.49E-2 3.68E-2 3.68E-2 7.93E-2 8.00E-2
0.712 0,815 0.812 0.895 0.904 0.902 1.15 1.16 1.16 1.16 1.15 1.31 1.31 1.31 1.31 1.31 1.31 1.40 1.40 1.40 1.40 1.40 1.40 1.51 1.52 1.52 1.51 1.82 1.83 2.30 2.30 2.31 2.31 2.62 2.62 2.96 2.95 3.30 3.31 3.63 3.61
Clr
En = 10".
Center Library subroutine, designated as POWELL. These parameters should not be used to extrapolate the isotherms to concentrations higher than 0.1 M. Nomenclature
a
Equation 7 of the text is a direct result of eq A4 as and @Z are generalized functions. Thus eq 7 has a semitheoretical basis. Appendix II
Experimental Data. Experimental data are given in Tables 111, IV, and V for propionitrile and 2-propanol a t 0.1, 25.0, and 7O.O0C, and acetone, p-cresol, and p-chlorophenol a t 25.OoC,adsorbing from dilute aqueous solution. The parameters of eq 3 of the text (see Table I) are obtained by minimizing the sum of squares of the percentage deviation in nlC with a University of California Computer 450 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
A
= parameter, eq 3 = chromatogram peak area
specific surface area of adsorbent parameter, eq 3 second adsorption virial coefficient B1+ ci solute concentration distance a t which 4-10 potential is zero d fl lateral generalized function vert,ical generalized function determined from 4-10 f, potential A H T ~= heat of vaporization a t normal boiling point k = Boltzmann's constant m = adsorbent mass nia = moles of solut,e adsorbed per uiiit mass of adsorbent (defined relative to solid) = invariant adsorption of solute i, eq 2 niC Q.
b
= = = = = = =
.V* R
T
0,
V
w
= = = = = =
Hansen. R. S.. Fackler. W. V.. J . Phus. Chem. 57. 634 11953). Hill, T: L., “An Introduction to StGistical The;modynamics,” p 348, Addison-Wesley, Reading, Mass., 1962. Hofer, L. J. E., J . Phys. Chem. 73, 584 (1969). Manes, M., Mattson, J. S., Mark, H. B., Malbin, >I. D., Weber, W. J., Crittenden, J. C., J . Collozd Interface Sci. 3(1), 95 (1969). Radke, C. J., Dissertation, University of California, Berkeley,
Ivogadro’s number response factor absolute temperature partial molar volume of solute i volume weight of solution
Calif - ----- . 1971 -
GREEKLETTERS 6 = parameter, eq 3 ell+ = lateral energy parameter = depth of 4-10 potential a t minimum el,+ U = lateral size parameter
I
Radke, C. J., Prausnitz, J. XI., J . Chem. Phys. 57, 714 (1972). Sams, J. R., Constabaris, G., Halsey, G. D., J . Chem. Phys. 36, 1334 (1962). Sircar, S., Myers, A. L., Nolstad, hL C., Trans. Faraday Sac. 6 6 , 2354 (1970). Steele, W. A.: “The Solid-Gas Interface,” E. A. Flood, Ed., Vol. I, Chapter 10, Marcel Dekker, New York, N. Y., 1967. Weber, W. J., Hopkins, C. B., Bloom, I{., J . Water Pollut. Contr. Fed. 42(1),-83 (1970). Wohleber, D. A.. Dissertation, Kent State Universitv, Kent, Ohio, 1969. Wohleber, D. A., Manes, XI., J . Phys. Chem. 75, 61 (1971a). Wohleber, D. A., Manes, AI., J . Phys. Chem. 75, 3720 (1971b).
SUBSCRIPTS 1
is S
solute internal standard = solvent = =
Literature Cited
RECEIVED for review October 20, 1971 ACCEPTEDJuly 20, 1972
Bondi, A., “Physical Properties of Molecular Crystals, Liquids, and Glasses,” Table 14.1, p 453, Wiley, New York, N. Y., 1968.
A Study of Homogeneous Catalysis by High-pressure Kinetics. The Mechanism of Catalysis of a Diels-Alder Reaction Bruce
E. Poling’
and Charles A. Eckert”
Departwient of Chemical Engineering, University of Illinois, Crbana, Ill. 61801
The application of high-pressure kinetics as a tool to investigate the detailed mechanism of catalysis of a reaction i s demonstrated. Activation volumes have been determined for the Diels-Alder addition of 2,3dimethylbutadiene to n-butyl acrylate, both uncatalyzed and catalyzed with AIC13. Also, partial molal volumes of reactants and products have been measured. From these data it i s shown that the volume profile along the reaction coordinate i s similar for both the catalyzed and uncatalyzed reactions. Further, both reactions proceed by a concerted one-step mechanism through a compact transition state with maximum accumulation of double bonds. Thus, the role of the Lewis acid in catalyzing the reaction i s not to alter the mechanism but rather to render the dienophile more reactive by making it more electron deficient.
High-pressure kinetics has been well recognized as a powerful tool for investigating mechanisms of chemical reactions (see, e.g., Gonikberg, 1963; Weale, 1967), but such studies are of primary interest to the organic chemist. Of much more direct interest to chemical engineers is the application of the same technique to ascertain the detailed mechanism by which a catalyst works. In this paper we present a n example of such a study, the homogeneous A1Cl3 catalysis of a Diels-Alder reaction. Although the possibility of acid catalysis of this cycloaddition reaction has been evident for some time (Rubin, et al., 1949; Yates and Eaton, 1960), the mechanism of the catalyzed reaction is still in doubt. X a n y examples of this type of reaction have been quoted (Allen, et al., 1962; Favorskaya and Auvinen, 1963; Fray and 1 Present address, Department of Chemical Engineering, University of Missouri, Rolla, >Io. 65401.
Robinson, 1961; Inukai and Kasai, 1966; Jahn and Goetzky, 1962) in which rllC13 or other Lenis acids were useful in catalyzing Diels-Alder reactions, especially for those cases where the dienophile contained a conjugated carbonyl group. From such investigations certain aspects of the mechanism are accepted. For example, it appears that the catalysis involves complexing of the llCls with the carbonyl oyygen, nithdrawing electrons from the conjugated system, and rendering the dienophile (the electron acceptor in the normal Diels-Xlder addition) more reactive. This conclusion is supported by infrared studies of complexes between ethyl acetate and group I1 and group IV halides (Lappert, 1961), as well as by some of the observations made about the kinetics of the reaction (Inukai and Kojima, 1967b; Soula, et al., 1966). Although the kinetics are incompletely defined, for cases \\-here the dienophile has a conjugated carbonyl group (or nitrile) the rate Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
451
