Ind. Eng. Chem. Res. 1987,26, 1593-1597
stitute of Technology for his assistance with the Beckman DU spectrophotometer and for lending some required attachments. We thank Yong C. Seo, graduate student, for his cooperation on some aspects of the equipment design as well as his help with the analysis of some data. We also thank Tung Chan Ma, graduate student, for the data on the bed expansion with different kinds of particle material. Nomenclature a = half major axis of the idealized elliptical bubble, cm b = half minor axis of the idealized elliptical bubble, cm d = bed depth in the immaterial dimension, cm E = electric field strength, =AV/w, kV m-l L f = bed height, in. Lfo = bed height at AV = 0, in. Q = total gas flow rate fed to the bed, L min-' Qb = gas flow rate through the bubble phase, L min-' Q, = gas flow rate through the emulsion phase, L min-l Qmf = total gas flow rate at minimum fluidizing conditions, L min-I Ub = velocity of rising bubbles, cm s-l Umf= superficial gas velocity at minimum fluidizing conditions, cm s-l = volume of an individual bubble, cm3 w = bed width = distance between electrodes, cm Greek S y m b o l s AV = applied electrical potential between the electrodes, kV v = bubble frequency, no. of bubbles s-l o b = residence time of a bubble in the bed, s Registry No. KI, 7681-11-0; 03,10028-15-6; H20, 7732-18-5; 12, 7553-56-2; 02, 7782-44-7; KOH, 1310-58-3.
1593
Literature Cited Ademoyega, B. 0. M.S. Thesis, Illinois Institute of Technology Chicago, 1981. Beeckmans, J. M.; Inculet, I. I.; Dumas, G. Powder Technol. 1979, 24, 267. Colver, G. M. Powder Technol. 1977, 17, 9. Colver, G. M. NSF Workshop: "Fluidization and Fluid-Particle Systems, Research Needs and Priorities", Rensselaer Polytechnic Institute, Troy, NY, 1979. Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: London, 1963. Dietz, P. W.; Melcher, J. R. AZChE Symp. Ser. 1978a, 74(175), 166. Dietz, P. W.; Melcher, J. R. Znd. Eng. Chem. Fundam. 1978b, 17, 28. Frye, C. G.; Lake, W. C.; Eckstrom, H. C. AZChE J. 1958, 4, 403. Gidaspow, D.; Lin, C.; Seo, Y. C. Znd. Eng. Chem. Fundam. 1983,22, 187. Gomezplata, A.; Schuster, W. W. AZChE J. 1960, 6, 454. Hovmand, S.; Davidson, J. F. Trans. Znst. Chem. Eng. 1968, 46, T190. Johnson, T. W.; Melcher, J. R. Ind. Eng. Chem. Fundam. 1975,14, 146. Katz, H.; Sears, J. T. Can. J. Chem. Eng. 1969, 47, 50. Kobayashi, H.; Arai, F.; Izawa, N.; Miya, T. Kagaku Kogaku 1966, 30, 656. Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969. Lewis, W. K.; Gilliland, E. R.; Glass, W. AIChE J . 1959, 5, 419. Murray, J. D. Chem. Eng. Prog. Symp. Ser. 1966,62(62), 71. Orcutt, J. C.; Davidson, J. F.; Pigford, R. L. Chem. Eng. Prog. Symp. Ser. 1962,58(38), 1. Scott, W. W. Scott's Standard Methods of Chemical Analysis, 5th ed.; D. Van Nostrand: New York, 1939; Vol. 2, p 2370. Zahedi, K.; Melcher, J. R. Air Poll. Con. Assoc. J . 1976,26(4), 345.
Received for review January 27, 1986 Accepted April 26, 1987
Prediction of LLE Using UNIFAC for Organic Acid-Water-Toluene Systems Raymond
W.K. Leung and A m i r B a d a k h s h a n *
T h e Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, Alberta, Canada T2N IN4
Experimental ternary liquid-liquid equilibria are presented for the systems butyric acid-water-toluene and formic acid-water-toluene at temperatures ranging from 5 t o 50 O C . These data are used in comparisons with the liquid-liquid equilibria predicted by the UNIFAC activity coefficient model. New group interaction parameters based on the data presented and on data previously acquired for three other organic acid-water-solvent systems are obtained for the UNIFAC model. An empirical modification t o the temperature term of the UNIFAC model is introduced which gives some improvement t o the predictions. Earlier investigations (Badakhshan et al., 1985) showed that the liquid-liquid equilibria (LLE) of several organic acid-water-solvent systems exhibited a significant temperature dependency. The temperatures at which the LLE were measured ranged from 2 to 50 "C. Data were collected for the acetic acid-water-toluene, propionic acidwater-toluene, and propionic acid-water-cyclohexane systems. A comparison of these data with the LLE predicted by the UNIFAC (Fredenslund et al., 1977) activity coefficient model was made. The group interaction parameters used in the predictions were those of Magnussen et al. (1981), which are parameters intended specifically for use in LLE prediction. It was found in this earlier work that the UNIFAC model failed to give satisfactory predictions of the LLE and its temperature dependency for the tested systems using the Magnussen parameters. Further investigation has been undertaken, and the homologous series of organic acids has since been extended 0888-5885/87/2626-1593$01.50/0
to include formic and butyric acids for the organic acidwater-toluene systems. The LLE data for these two additional systems were measured at temperatures ranging from 5 to 30 OC for the butyric acid system and from 5 to 50 "C for the formic acid system. The UNIFAC model and the Magnussen interaction parameters were again used to predict the LLE for these two systems. New UNIFAC group interaction parameters were determined based on all the systems in the homologous series. An empirical modification to the temperature term in the UNIFAC model was also tested. Experimental Section Materials. The formic acid was obtained from the Aldrich Chemical Company and was 98.0% pure (1.8% water, density at 20 "C = 1.220 g/cm3). The butyric acid was obtained from the Fisher Scientific Company and was 99.0% pure (density at 20 "C = 0.960 g/cm3). The toluene 0 1987 American Chemical Society
1594 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 Table I. Mutual Solubility Data for the System Formic Acid-Water-Toluene" a t 5.0 "C a t 30.0 "C to1u en e water formic acid toluene water formic acid 62.73 0.35 36.92 0.31 66.70 32.99 51.21 0.45 48.34 0.34 58.78 40.88 38.68 0.60 60.72 0.52 50.81 48.67 31.35 0.91 67.74 0.61 43.15 56.24 1.02 26.61 72.37 0.73 39.10 60.17 22.83 75.90 1.15 1.27 34.08 64.77 19.77 78.58 1.56 23.65 1.65 74.79 17.18 2.07 1.83 80.99 19.20 78.73 13.41 84.26 2.42 2.33 16.07 81.51 3.13 9.74 87.13 3.27 11.92 84.81 4.10 3.48 8.06 88.46 87.54 8.36 89.39 7.16 3.87 6.74 90.98 1.86 4.54 4.86 90.60 4.96 3.77 91.27 5.85 2.10 92.05 a
formic acid 43.53 60.11 67.62 72.69 70.58 75.74 75.04 77.90 79.45 86.05 87.40 87.10 87.74 87.90 89.13 88.19
Compositions in wt %.
Table 11. Tie-Line Data for the System Formic Acid-Water-Toluene' Solute Distribution phase a t 5.0 "C phase a t 30.0 "C phase a t 50.0 "C solvent water solvent water solvent water 0.11 36.28 0.23 33.96 0.56 31.19 0.61 54.31 0.94 55.26 1.25 53.67 1.06 76.11 1.44 72.27 1.73 70.21 3.71 92.61 5.93 90.54 8.18 88.34 a
at 50.0 "C water 55.90 39.06 31.11 25.67 27.65 22.19 22.68 19.76 17.56 8.67 6.55 6.63 4.95 4.25 1.82 1.80
toluene 0.57 0.83 1.28 1.64 1.77 2.07 2.28 2.34 2.99 5.28 6.05 6.27 7.31 7.85 9.05 10.01
Composition in wt %.
was also obtained from the Fisher Scientific Co. and was 99.0% pure (density a t 20 "C = 0.866 g/cm3). The water used was distilled and deionized in the laboratory. Equipment. The necessary equipment include a Haake D3-6 constant-temperature bath, a Shimadzu GC-8A gas chromatograph, and a Varian 3700 gas chromatograph. The constant-temperature bath was precise to *0.02 "C. The GC packings used were Poropak Q and Poropak QS. Procedure. The procedure for determining the mutual solubility (binodal) data was basically that of Othmer and Tobias (1942). The tie-line data were determined by preparing two-phase mixtures in sample bottles and anaTable 111. Mutual Solubility Data for the a t 5.0 "C toluene water butyric acid toluene 0.87 50.71 48.41 0.52 1.74 40.40 57.86 1.16 3.16 33.29 63.56 1.74 4.73 28.13 67.14 2.59 6.67 24.15 69.18 3.53 8.37 21.10 70.52 4.91 9.91 18.83 71.26 6.09 11.81 16.29 71.90 7.51 13.04 14.81 72.15 8.66 14.52 13.13 72.34 9.85 16.30 11.53 72.17 10.99 18.49 9.86 71.64 12.80 21.31 7.91 70.78 13.82 24.90 6.21 68.90 14.93 29.77 4.33 65.90 17.45 36.55 2.75 60.69 21.03 46.69 1.63 51.68 24.58 59.47 1.03 39.50 29.47 65.14' 0.55' 34.31' 31.89 38.86 46.56 59.43 73.03'
'Compositions in wt
%.
lyzing the equilibrated phases in the GC. The experimental error using these procedures was estimated to be less than 1 mass %. These procedures are described in detail and have been checked against published data by Badakhshan et al. (1985). Results. The mutual solubility (binodal) and tie-line (solute distribution) data for the formic acid and butyric acid systems appear in Tables I-IV.
UNIFAC Predictions UNIFAC Model. Fredenslund et al. (1977) incorporated the advantages of the Analytical Solution of Groups (ASOG) model (Derr and Deal, 1969) with the Universal Quasi-Chemical (UNIQUAC) model which resulted in the UNIFAC (UNIQUAC functional-group activity coefficients) model. The UNIFAC model follows the ASOG model in that the activity coefficients in mixtures are related to interactions between structural groups. The UNIFAC equations resemble the UNIQUAC equations in the general form of a combinatorial and a residual contribution, as In yi = In yf
System Butyric Acid-Water-Toluene" a t 10.0 "C a t 20.0 "C water butyric acid toluene water butyric acid 60.79 38.69 1.08 62.89 36.03 50.56 48.27 55.79 42.61 1.60 43.17 55.09 2.16 48.47 49.37 37.59 59.81 2.89 42.73 54.39 33.16 63.31 3.66 38.60 57.74 29.46 65.63 4.52 35.33 60.15 26.48 67.42 6.24 29.93 63.83 23.74 68.75 7.50 27.31 65.19 21.84 69.50 8.46 24.92 66.62 20.03 70.12 10.07 22.18 67.75 18.47 70.54 12.39 19.06 68.55 16.33 70.87 16.88 14.36 68.76 15.06 71.12 14.99 16.30 68.71 14.02 71.05 10.84 21.75 67.41 12.04 24.92 70.51 8.90 66.19 9.14 69.83 29.04 6.67 64.29 7.41 68.01 5.64 32.01 62.35 5.30 35.74 65.24 4.14 60.12 4.58 63.53 2.99 41.66 55.34 3.06 58.07 2.31 46.37 51.32 1.90 51.54 1.20 59.37 39.43 1.10 78.81' 39.47 0.13' 21.06' 0.23* 26.74'
'Estimated plait point.
+ In !y
toluene
a t 30.0 "C water butvric acid
1.65 3.02 4.56 6.74 9.08 11.45 13.67 15.11 17.28 20.04 24.51 28.63 31.12 35.57 38.26 46.13 55.62 82.64*
59.04 48.52 39.32 32.13 26.91 22.98 19.94 18.02 15.78 13.41 10.37 7.99 6.89 5.38 4.57 2.82 1.29 0.08'
39.31 48.46 56.11 61.13 64.01 65.57 66.39 66.88 66.94 66.55 65.12 63.38 61.99 59.05 57.17 51.06 43.09 17.28'
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1595 Table IV. Tie-Line Data for the System Butyric Acid-Water-Toluene" ~Solute Distribution phase at 20.0 OC phase a t 10.0 O C phase a t 5.0 OC solvent water solvent water solvent water 13.64 4.17 12.87 13.85 4.01 4.07 24.92 6.00 24.89 6.04 23.64 6.93 8.14 36.57 36.62 8.54 36.49 8.79 10.39 49.19 48.51 48.89 10.61 10.79 11.23 58.67 58.35 12.25 58.68 12.87 11.68 61.40 61.66 13.18 62.21 13.20 13.25 65.12 65.23 13.34 66.89 14.39 13.38 68.00 69.27 14.66 70.00 15.26 13.74 68.52 69.63 15.08 70.70 15.41 14.43 68.91 70.77 15.66 71.93 15.97
phase a t 30.0 O C solvent water 13.62 4.10 25.33 6.26 36.25 8.24 49.23 9.85 59.11 11.26 61.16 12.04 64.70 12.80 66.34 13.43 66.66 13.85 66.69 14.97
aCompositions in w t %.
The combinatorial contribution is a function of the sizes and shapes of the molecules present and is given by
Empirical Modification Improvements to the UNIFAC model was proposed by the use of an empirical modification to the temperature term in eq 11. The modification is
(3)
(4) The residual contributions are functions of -group - areas and group interaction energies. In rf = Cvki[lnrk - In k
rp]
The reference temperature, T,, is 273.15 K and the constants C and p were determined by parameter fitting to be -0.337 and 1.014, respectively. The constants C and p were fitted simultaneously along with the interaction parameters. Parameter Estimation. A modified Simplex algorithm was used in the parameter fitting computer program. While more efficient algorithms are available, like the Levenberg-Marquardt algorithm, they require complex coding, knowledge of the derivatives, and may not converge for poor initial guesses. The Simplex algorithm, introduced by Nedler and Mead (1965), does not require derivatives, never diverges, involves no matrix operations, and is relatively simple. The objective function which is being minimized in the parameter estimation is of the form
F(p) = CCDfk + ZC@k l k
e,
=
Qmxm -
CQnXn n
l k
(13)
where the functions Dlkand Elkare the residuals for the binodal and solute distribution data, respectively. A detailed description of the parameter estimation method and the computer program is given by Leung (1986).
Results and Discussion
If the group areas (Qk)are all equal, then these equations become similar to those of the ASOG method. Interaction Parameters. Magnussen et al. (1981) developed a parameter table based on LLE data in the temperature range 280-310 K which gave much improved results for prediction of LLE over the predictions using other parameter tables which are based on vapor-liquid equilibrium data (Fredenslund et al., 1977; SkjoldJraorgensen et al., 1979). Approximately 100 binary and 300 ternary LLE data sets were used for this parameter table. A total of 512 group interaction parameters for 32 different groups are given.
The binodal curves (isotherms) predicted by the UNIFAC model, using the Magnussen interaction parameters, for the butyric acid-water-toluene system are shown in Figure 1. As was found previously by Badakhshan et al. (1985), the UNIFAC model tended to predict a weak temperature dependency as far as the binodal curves were concerned. A satisfactory match was achieved for the formic acid-water-toluene system, as shown in Figure 2. In this case, the experimental data also exhibited a mild temperature dependence. Examination of the distribution diagram for the formic acid system reveals that a good match was also obtained. While the distribution diagram for the butyric acid system shows close proximity between the UNIFAC predicted and the experimental data, the temperature dependencies exhibit opposite trends. This was not observed for the formic acid system.
1596 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 Table V. Grouo Interaction Parameters"
H20
H8
1 2
3 I
CH,
2
3 COOH
1 2
3 ACH
1
2 3 ACCH,
1
2 3
1300.0 685.2 550.6 652.3 594.4 1048.0 859.4 845.9 603.9 5695.0 5699.9 5958.3
CH? 342.4 349.5 331.2
1744.0 1731.1 2094.3 156.5 161.4 184.5 104.4 93.5 106.5
COOH -465.7 -473.8 -461.7 139.4 144.3 164.4
ACH 372.8 485.6 657.9 -114.8 -126.7 -173.8 75.7 31.3 85.6
461.8 463.0 431.2 339.1 345.0 357.0
ACCH, 203.7 213.5 191.7 -115.7 -110.8 -140.9 147.3 153.2 267.0 167.0 171.7 159.0
-146.8 -148.1 -147.3
'(1) Magnussen parameters, (2) new parameters, (3) modified UNIFAC parameters. ACID
ACID
\ SOLVENT
WATER
Figure 1. Isotherms for the system butyric acid-water-toluene: (-) 5.0 "C UNIFAC*, 10.0 "C UNIFAC*, (- - -) 20.0 "C UNIFAC*, (---) 30.0 "C UNIFAC*, (X) 5.0 "C exptl, ( 0 ) 10.0 " C exptl, (v)20.0 "C exptl, (W) 30.0 "C exptl (*Magnussen parameters). (e**)
I t is of interest to note that the only system having a good match with the UNIFAC predictions, the formic acid-water-toluene system, was the only Type I system in the homologous series studied. The systems containing acetic to butyric acids were all Type I1 systems. The UNIFAC predictions, using the Magnussen (1981) interaction parameters, were found to have a standard deviation from the experimental data of 4.1 mass %. By use of the experimental data presented and the data previously presented by Badakhshan et al. (19851, new UNIFAC interaction parameters were obtained for the functional groups involved. The new group interaction parameters are shown in Table V. Most of the new interaction parameters are within 10% of the Magnussen (1981) parameters, except for the CH2/H20 and the COOH/ACH interaction parameters which were about half of the Magnussen values. The new interaction parameters gave predictions having a standard deviation of 3.6 mass %. This modest improvement over the predictions using the Magnussen parameters is to be expected since we are fitting to a much smaller data base. However, no noticeable improvement was observed to the temperature dependence of the predictions. The parameters obtained for the modified UNIFAC model are also shown in Table V. By use of these parameters, the modified UNIFAC model gave predictions having a standard deviation of 3.1 mass %. Again, only a modest improvement was achieved, mostly through a
Figure 2. Isotherms for the system formic acid-water-toluene: (-1 5.0 "C UNIFAC*, 30.0 " C UNIFAC*, (- - -) 50.0 "C UNIFAC*, ).( 5.0 "C exptl, (X) 30.0 " C exptl, (A) 50.0 "c exptl (*Magnuwen parameters). (e**)
reduction in the negative effects of the UNIFAC temperature dependency. Conclusions Liquid-liquid equilibria for the formic acid-watertoluene and butyric acid-water-toluene systems are presented. These LLE data extend the homologous series of organic acid-water-toluene systems which were previously presented by Badakhshan et al. (1985). Based on these data the following conclusions are made: (1)The UNIFAC activity coefficient model can predict erroneous temperature dependencies for the organic acid-water-toluene systems'studied. (2) Predictions by the UNIFAC model were better for the Type I system than for the Type I1 systems. (3) Predicted solute distributions were better for the systems having solute distributions which strongly favor either the aqueous phase or the solvent phase. (4) The new interaction parameters based on the experimental LLE give a standard deviation of 3.6 mass %, compared to 4.1 mass % for the predictions using the Magnussen interaction parameters. ( 5 ) The modified UNIFAC model gives predictions having a standard deviation of 3.1 mass % for the systems studied. Acknowledgment We express their gratitude to Prof. R. A. Heidemann for his interest and valuable discussion. We also thank
Znd. Eng. Chem. Res. 1987, 26, 1597-1603
NSERC for partial financial support of the work. Nomenclature am,,= group interaction parameter C = constant in eq 12 Dlk = binodal residual of data point k in data set 1 Elk = tie-line residual of data point k in data set 1
F = objective function p = constant in eq 12
group surface area qi = effective molar volume, van der Waals surface area R = gas constant Rk = group volume ri = van der Waals volume T = temperature Uij = binary interaction parameter Xi = group concentration xi = mole fraction 2 = coordination number Qi =
Greek S y m b o l s
ri= individual group contribution to the activity coefficient yi = activity coefficient
vi, = number of group species j in molecule i
1597
p = parameter vector in eq 13 4i = area fraction Bi = volume fraction qm,, = binary parameter defined by eq 11 Registry No. Butyric acid, 107-92-6; formic acid, 64-18-6;
toluene, 108-88-3. Literature Cited Badakhshan, A.; Chowdhury, A. I.; Leung, R. J . Chem. Eng. Data 1985, 30, 416. Derr, E. L.; Deal, C. H. Inst. Chem. Eng. Symp. Ser. 1969,32(3), 40. Fredenslund, Aa.; Gnehling, J.; Michelsen, M. L.; Rasmussen, P.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1977,16,450. Leung, R. W. K. M.Sc. Thesis, University of Calgary, Calgary, Alberta, Canada, 1986. Magnussen, T.; Rasmussen, R.; Fredenslund, Aa. Ind. Eng. Chem. Process Des. Deu. 1981, 20, 331. Nedler, J. A.; Mead, R. “A Simpler Method for Function Minimization”, Comput. J. 1965, 7, 308-312. Othmer, D. F.; Tobias, P. E. Ind. Enp. Chem. 1942. 34, 690. Skjold-Jergensen,S.; Kolbe, B.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714.
Received f o r review August 27, 1986 Accepted April 13, 1987
Water Vapor Uptake by Ceramic Microspheres Enio K u m p i n s k y Polymer Products Department, D u Pont Experimental Station, Wilmington, Delaware 19898
Experimental studies on the water vapor uptake by ceramic microspheres have been carried out a t atmospheric conditions. Hysteresis has been found for the adsorption/desorption isotherm with respect to the relative humidity. Similarly, it is shown that the transient paths for the uptake exhibit a quick weight increase in the early stages of the process, followed by a n asymptotic period of very small weight gain. T h e process was modeled by simultaneous mass-transfer equations, which show that the rate-limiting step is molecular diffusion and not condensation of water vapor on the surface of the powder. Fillers are defined as relatively inert small particles which are added to plastics compounds for specific purposes (Schwartz and Goodman, 1982). Fillers are blended with polymers to provide satisfactory tensile strength and to improve stiffness, abrasion resistence, tear resistence (Billmeyer, 1984),gloss control, and thermal conductivity. Likewise, rheological properties can be improved by selecting the right filler and choosing the proper loading. In addition to modifying the composition’s properties, fillers can reduce its costs. Structurally, filler particles range from highly irregular masses to precise geometrical forms and can constitute either a major or a minor part of a composition (Grayson and Eckroth, 1980). The most commonly used fillers are kaolins and other clays, silicas, aluminas, calcium carbonates, talcs, barium sulfate, powdered metals, metal oxides, nylons, and poly(tetrafluoroethylene) (PTFE). Very fine fillers, such as carbon black and titanium dioxide, can act as pigments. Fillers are of paramount technological significance as shown by the thousands of patents and publications concerning filled polymers. It is not our intent to provide detailed information on fillers since other publications on the subject are available, such as Grayson and Eckroth (1980) and Katz and Milewski (1978). It is our intention to explore a problem whose final outcome is the degradation of matrix polymers during processing, i.e., the presence of hygroscopic moisture in fillers and pigments. Even small amounts of water can cause major damage to the matrix. For example, moisture in excess of 0.1% by 0888-5885/87/2626-1597$01.50/0
weight polymer can result in significant degradation of Hytrel (trade name), a polyester elastomer ( H y t r e l Handbook, 1981). Some publications on the adsorption of vapors by powders are found in the literature. The dynamical aspect of adsorption is covered in detail by de Boer (1953),while the adsorption in micropores of porous powders is explored by Dubinin (1966) and Pesaran (1983). Adams et al. (1970) studied the uptake of organic vapors by Saran (trade name)-carbon fibers and powders, finding adsorption hysteresis for some compounds. Likewise, adsorption hysteresis was reported by Tabibi (1982) during the uptake of water vapor by sugar powders. Transient curves of moisture adsorption by carbamazepine powders were obtained by Kaneniwa et al. (1984), who showed that different crystalline forms of the same compound can adsorb quite diverse amounts of water vapor. El-Dib and Aly (1977) present the effect of time on the adsorption of phenylamides on powdered carbon. Their results are in qualitative agreement with ours, although the systems are quite different. Gammage and Brey (1972) obtained stepped adsorption isotherms of water vapor on ground thorium oxide. This system also exhibits adsorption/desorption hysteresis that is qualitatively identical with that obtained here. Only a few experiments are found in the literature describing the transient moisture uptake by commercial powders. Additionally, there is no detailed description on the rate-determining step for the adsorption of hygroscopic 0 1987 American Chemical Society
