can be compensated for in experimentation by obtaining a greater portion of the d.ata points during the rapidly changing stage of the concentration-time curve. Nomenclature = matrix in Equation = kinetic coefficients
A Bk
7
(rate parameters), presumed const-nt = dependent variables = initial values (at t = to) of the dependent variables
Cj Coj
,
,
~ , i =: (~Y ,~~- pijj tvij = objective function for least-square minimization = matrix in Equation 7 = index for upper limit of integration on time of
F
G i
R,,,
1L i L P = index for number of dependent variables, 1 L j L M 1 = index for number of kinetic coefficients, 1 L k L N k M = number of components = number of rate parameters N P = number of time intervals between measurements of dependent variable P 1 = number of me,asurements for one Cj, including initial value rJ* = multivariate correlation coefficient Rj,& = any function of concentrations and of time as selected by the user; j and k designate positions in matrix t = independent variable, time = any time, t , > t o t, to = initial time = weight for least-squares fit W i j
+
Xijk
=
J:’R,,kdt,modified experimental independent vari-
Yij
=
able for regression C J ( t , ) - C,(io), modified experimental dependent variable for regression
pij
=
literature Cited
Ames, W. F., Ind. Eng. Chem. 52, 517 (1960). Ames, \V. F., IND.ENG.CHEM.FUNDAMENTALS 1, 214 (1962). Ark, R., IND.ENG.CHEM.FUNDAMENTALS 3, 28 (1964). Bak, K., Acta Chem. Scand. 17, 985 (1963). Ball, W.E., Groenweghe, L. C. D., IND.EN^. CHEM.FUNDAMENT A L S 5, 181 (1966). Bellman, R., “Stability Theory of Differential Equations,” McGraw-Hill, New York, 1953. Bellman, R., Kalaba, R., “Quasilinearization and Nonlinear Boundary Value Problems,” American Elsevier, New York, 1Oh5
Blaiemore, J. W., Hoerl, A. E., Chem. Eng. Progr. Symp. Ser. 59, No. 42. 14 (19633. Box, G. E. P., Ann. Math. Statisttcs 25, 484 (1954). BOX,G. E. P., Hunter, I V . G., Technometrics 4, 301 (1962). Cull, N. L., Brenner, H. H., Ind. Eng. Chem. 53, 833 (1961). Garfinkel, D., Rutledge, J. D., Higgins, J. J., Comm. Assoc. Computing Machinery 4, 559 (1961). Howland, J. L., Vaillancourt, R., J . SOC.Ind. Appl. Math. 9, 165 (1961). Katarov, V. V., Lutsenko, V. A., Intern. Chem. Eng. 5 , 623 (1965). Kittrell, 3. R., Mezaki, R., LVatson, C. C., Ind. Eng. Chem. 58, 51 11966).
Lapidus, L.’, Chem. Eng. Progr. Symp. Ser. 57, No. 36, 126 (1961). Lerwick, T. R., Technometrtcs 7, 51 (1965). Levenspiel, O., “Chemical Reaction Engineering,” Wiley, New York, 1962. Lindsay, K . L., IKD.ENG.CHEM.FUKDAMENTALS 1, 241 (1962). Moe, J . M., San Francisco Meeting, A.I.Ch.E., May 1965. Peters, M. S., Cupit, C. R., Chem. Eng. Sci. 10, 57 (1959). Peterson, T. I., Chem. Eng. Progr. Symp. Ser. 56, No. 31, 111 (1960). Peterson, T. I., Chem. Eng. Sci.17, 203 (1962). Rubin, D. I., Chem. Eng. Progr. Symp. Ser. 59, No. 42, 90 (1963). Schrodt, V. N., Frank, L. E., Parisot, P. E., American Chemical Society Meeting, Houston, Tex., December 1963. Siddiqui, M. M., Ann. Math. Statistics 31, 929 (1958). Steiner, R., Schoenemann, K., Chem. Ing. Tech. 37,101 (1965). LVatson, G. S., Biometrika 42, 327 (1955). IVei, J., IND.ENG.CHEM.FUNDAMENTALS 4, 161 (1965). \Vei, J., Prater, C. D., Aduan. Catalysis 13, 204-390 (1962). \Vright, B. S., Brit. Chem. Eng. 9,758 (1964).
.v
B k X , J kpredicted , modified dependent variable for
RECEIVED for review February 1, 1967 ACCEPTEDJune 12, 1961
k=l
regression
ANOMAL.OUS OSMOSIS IN DIALYSIS OF ACIDS WITH ANION EXCHANGE MEMBRANES ROBERT D. HANSEN AND M E L V I N L. ANDERSON’ Physical Research Laboratory, The Dow Chemical Co., Midland, Mich.
The dialysis of four acids (HCI, “01, HzS04, and H 3 P 0 4 ) through anion exchange membranes wasstudied Anomalous negative osmosis-i.e., flow of solvent in direction opposite to the usual osmotic flow-was observed. When these acids were dialyzed from a solution containing a nondiffusible species, the concentration of this species was increased. Thus, the chief disadvantage of dialysis, dilution of the product, was overcornie. The anomalous water transport and the incremental increase in anomalous negative osmosis apparently caused by the presence of a polyelectrolyte support the theory of Schlogl.
ECENT
studies in this laboratory on the rather obscure
R phenomenon of anomalous negative osmosis have demon-
strated the importance of this effect in dialysis operations. Previous studies have usually been centered on systems of biological interest, with apparently lesser interest in the role of this phenomenon in the areas of separation and purification (Grim and Sollner, 1957). Present address, Rocky Flats Division, The Dow Chemical Co., Golden, Colo.
If a nonionic membrane separates two solutions containing solute a t different concentrations, solvent will be transported from the side of lower to the side of higher osmotic pressure. However, with ion exchange membranes, the flow of solvent behaves in an anomalous manner. If the flow of solvent is in the same direction as the flow found with a nonionic membrane of comparable porosity-Le., in the direction of the activity gradient--the increment is termed anomalous positive osmosis. If, on the other hand, the flow is in the direction oppoVOL. 6
NO. 4
NOVEMBER 1 9 6 7
543
site to the activity gradient, the increment is termed anomalous negative osmosis. This anomalous negative osmotic flow may be greater than the flow brought about by the normal osmotic processes, resulting in a n over-all flow of solvent in the negative direction; if, however, this anomalous negative osmotic flow is less than the normal osmotic flow it will only decrease the net flow of solvent. A theory to explain anomalous osmosis was advanced by Schlogl (1955), who stated that the requirements for anomalous osmosis were a charged membrane and a diffusible solute having ions of significantly different mobilities. H e postulated that the potential arising from the difference in mobility of the diffusing ions acted on the bound water in the membrane, with the bound water taking up the charge of the membrane counterions. Thus, this theory would predict anomalous negative osmosis for the dialysis of a strong acid using an anion exchange membrane. I n this instance, the rapidly migrating protons would build up a positive potential on the dilute side of the membrane, which would exert an attractive force o n the bound water containing the negatively charged counterions of the anion exchange membrane. Thus, the bound water would be driven to the dilute side of the membrane, or in the direction reverse to normal osmotic flow. I n the case of strong acids with an anion exchange membrane (counterions are anions), it has been observed in the present work that the flow of water is toward the dilute side, or in the direction opposite to the activity gradient-Le., negative osmosis. Thus, dialysis of a solution of a sulfonated polymer, SPVT (sulfonated polyvinyltoluene), and sulfuric acid against water results in a flow of water from the concentrated to the dilute side of the membrane, or in the same direction as the transport of HZS04. Thus, removal of HzS04 from a sulfonated polymer solution by dialysis using an anion exchange membrane results in a concentration of the polymer solution, thereby obviating the chief disadvantage of conventional dialysis-i.e., excessive dilution of the product. As a result of these findings, experiments Lvere carried out to measure solvent transport for several acids as a function of acid concentration, to determine the effect of the presence of the nondiffusible ionic species SPVT on the solvent transport, and to compare these results with predictions based on Schlogl’s theory. Experimental
T o study the transport of water as a function of sulfuric acid concentration, experiments were carried out in a dilatometric cell equipped with 10-ml. burets. The cell, illustrated in Figure 1, was essentially similar to one used by Mindick and O d a (1958) but modified to incorporate glass cooling coils in each cell compartment. T h e coils were connected to a constant-temperature (30.2’ + 0.7’ C.) water bath. The volume of each cell compartment was approximately 230 ml. The cell was made by drilling two 2-inch holes in adjacent faces of each Lucite block. Hence, the area of the membrane was 20.26 sq. cm. In the time allowed for each experiment, usually about 2 hours, volume changes were generally less than =k5 ml. The levels in the two burets were adjusted so that the water transport associated with the negative osmosis was against a hydrostatic head of from 3 to 6 inches. In experiments with deionized water on both sides of the membrane, it was shown that with a difference in liquid levels of 8 inches essentially no water flowed through the membrane. The precision of the water transport measurements is estimated to be 6 X 10-6 gram cm.-* min.-‘ T h e countercurrent dialysis separations were carried out in a Graver laboratory dialyzer. This is a conventional plate and frame dialyzer, set up to consist of two membranes separating three compartments. The membrane area is 10 X 13 inches. The center compartment contained spacers which maintained 544
l&EC FUNDAMENTALS
10 mi B U R E T S
CONSTANT T E M P E R AT LIRE BATH
-FROM
TO C O N S T A N T T E M P E RAT URE BATH
-STIRRER
S T I R R E R BAR-
/ Figure 1.
MAGNETIC STIRRER
\/
BAR
\
MAGNETIC STIRRER
Cell for measurement of woter transport
the membranes in a fixed position under the small pressure differential existing between cell compartments. The solution containing electrolyte was passed upflow through the center compartment, while water was passed downflo\\ through the two outer compartments. Gravity flow was used, with the solutions metered by dual-syringe pumps. Results
Solutions of varying H ~ S O Iconcentration \vere dialyzed against water using anion exchange membrane 101A. manufactured by the .4merican Machine and Foundry Co. (AMF 101A), in the dilatometric cell. The rate of water transport was determined by observing the rate of change of volume with time, correcting for the transport of H2S04. The results are shown in Figure 2, where positive transport is transfer of Ivater from the dilute to the concentrated solution. Also shown are results with a constant amount of the polymeric SPVT on the acid side. Negative osmosis occurs at lok~H&04 concentrations with or without SPVT. In fact, SPVT accentuates the negative osmosis. despite the expected increase in osmotic pressure due to the polymer. The study of Lvater transport was extended to other strong and H a P o ? ) .using the same experimental acids (HCl, “ 0 3 , method. The results are shorvn in Figure 3, along with the curve for HlSOb from Figure 2. Hap04 exhibited negative showed osmosis at lower concentrations. lchile HCl and “ 0 3 only positive osmosis. Ho\cever, anomalous negative osmosis was obtained in all cases, as shown by comparison of the water transport found for these acids with the “normal osmosis’’ line shown on the figure. This normal osmosis line was drawn from a literature (Mindick and Oda, 1958) value of 5.6 X gram of HzO min.-’ crn,-* for a 1 S KaCl solution with a Nalco Chemical Co. Nalfilm D-20 membrane. This mem-
c I
I
A 0-AOUEOUS
HeSOq SOLUTIONS
lH2S04)
*-VARIABLE CONSTANT
0
=
IO.161 f 0 . 0 0 6 8 1
, SPVT
-2 0
1.0
2.0
3.0
H2S04
Figure 2.
W a t e r transport vs.
HA04
4.0
4.0
.-IC
E
3.0
N
E 0
0'
s?
2.0
x
c
a
B v) z a K
I-
1.0
a w c a
3 0
-I .o
0
4.0
I2.0
6.0
AVERAGE A C I D C O N C E N T R A T I O N (NORMALITY I
Figure :3.
Water transport
brane is of the neutral idialysis type but otherwise equivalent in its transport properties to the AMF 101A anion exchange membrane. (Acid transport rates between 1.45iV H2S04 gram rnin.? cm.? for solution and water were 4.3 X Nalfilm D-20 and 3.9 ;< gram m h - 1 cm.-? for AMF 101A.) Thus, normal osmosis for these t\vo membranes should be nearly identical. To demonstrate the different osmotic properties of nonionic and anion exchange membranes, a 5% solution of SPVT, 2 . 4 s in H 2 S 0 4 .was dialyzed countercurrently in a plate and frame cell, \vith the results shown in Table I. By use of nonionic membrane Nalfilm D-30, 300% dilution of SPVT was obtained, compared to a 1470 increase in SPVT concentration \Then a n anion exchange membrane was used. Studies were also extended to other systems of strong acids in solutions of polymeric substances. Using the same dialyzer a solution of hydroxymethylpropylcellulose (Methocel
Dialysis of Acids from Solutions of Polymers Change in Fraction Volume of Acid Polymer Solution Dialyzed Membrane Type Dialyzed Solution 5'; SPVTa2 4 s H2S04 Nonionicb 0.86 300y0 increase Anion 14% decrease exchanm? 0.85 " 2 5 Methocel HG-90d- Anion exchangee 0 . 6 2 1 .5y0decrease 2 . 39AVHC1 17cSeparan NP-108Anion exchangec 0.50 2 , OyOincrease 1 04.lrHNO1 Table I.
Sulfonated polyvinyltolurne. iVa@lm 0-30. c A M F IOIA. d Hydroxymethylpropylcellulose. e Polyacrylamide.
a b
HG-90) containing HC1 was dialyzed against water. With steady-state conditions giving 62% dialysis of HC1, the polymeric solution was increased in concentration by 1.5y0, Under similar conditions, the dialysis of a solution of H N 0 3 and polyacrylamide (Separan NP-10) was studied. 115th flow the polymer rates adjusted to give 50% removal of "03, solution concentration was increased by 2%. Initial solute concentrations for these two experiments are given in Table I. T h e decreases in volume of the polymeric solutions here are not inconsistent with the results in Figure 3 showing transport of water from the dilute to concentrated solutions for both HC1 and H N 0 3 systems. While Figure 3 shows only the transport of water, the volume changes noted in these experiments with the polymeric solutions consist of both water and acid transport. Since the anion exchange membranes allow very little transport of salts, they can also be used for acid-salt separations. Here again. the essentially nondiffusible salt is not diluted by water as the acid is removed by dialysis. As shown in Table 11, a 2 . 4 5 FeS04-1.3,V HzS04 solution was dialyzed in a plate and frame dialyzer, with an increase of about 1.5% in FeS04 concentration when 65% of the HzS04 was removed. T h e same solution was dialyzed with a nonionic membrane to achieve the same extent of acid removal. Table I1 shows the dilution of the salt solution and the dialysis of a portion of the salt along with the acid. Similarly, dialysis of a 0.64N Mg(N03)z solution containing 1 . 5 5 5 H N 0 3 with an anion exchange membrane resulted in about a 5% increase in concentration of the M g ( N 0 3 ) ~with 90% removal of " 0 3 . I n a comparable experiment with a nonionic membrane, the salt was diluted 55% and considerable salt was dialyzed along with the acid. Thus, anomalous negative osmosis is beneficial in a system where a valuable salt is being recovered from an acid solution, where dilution and loss of salt would be appreciably lower than in conventional dialysis. Discussion
T h e requirements outlined by Schlogl (1955) for the occurrence of anomalous osmosis-Le., a charged membrane and a diffusible solute having ions of significantly differing mobilities-are met in the case of the acids dialyzed through a n anion exchange membrane in the dilatometric cell. Anomalous negative osmosis was clearly demonstrated with HsP04 and H2S04, in which cases the net flow of solvent was toward the dilute solution. That anomalous negative osmosis occurred with H N 0 3 and HC1 is not obvious, but can be implied by comparing the water transport rates found \+ith the anion exchange membrane with water transport rates for NaC1 through a nonionic membrane of comparable porosity. Examination of the conductance of solutions of these acids allows one to estimate the relative effect predicted by Schlogl's theory. T h e equivalent conductances (Handbook of Chemistry and Physics, 1956) for these acids in 0.1-V solutions a t 18' C. are shown inTable 111. These values for the conductance would indicate that the HZP04- ions (the principal species present at this concentration) would diffuse more slowly than the other anions, leading to the largest difference in mobility betbveen H + and H2P04-, compared to the other acid species, and thereby creating the largest membrane potential and hence the largest anomalous negative osmotic effect. Similarly, HC1 and " 0 3 would be expected to show the smallest difference in mobility between the H + ion and anion, leading to the smallest anomalous negative osmotic effect. Thus, the observed results are in qualitative agreement with predictions based on Schlogl's theory. Although the conductance of HC1 is about 1% VOL. 6
NO. 4
NOVEMBER 1 9 6 7
545
Table II. Dialysis of Acids from Salts
Solution Dialyzed 2 . 4 N FeS04-1.3N HzSOa
0.64N M g ( N 0 a ) r 1.55~\'"03
Table 111. Acid
Fraction Dialyzed Acid Salt 0.65 0.023 0.59 0.28
Membrane Tyke Anion exchange0 Nonionic*
Anion exchangeC Nonionicb
0.008 0.50
0.90
0.88
Change in Volume of Concentrated Solution 1 . 5 yo decrease 70y0 increase
5y0 decrease 55y0increase
by the addition of SPVT to a sulfuric acid solution (Figure 2) can be explained in the light of Schlogl's theory also. SPVT is strongly ionized into protons and the negatively charged polymer molecule. The protons from SPVT partially satisfy the electrical neutrality requirement of the diffusing HzSO4 species, thereby lessening the attraction between the diffusing protons and bisulfate ions and thus increasing the membrane potential which gives rise to the anomalous negative osmosis.
Conductance of Acids Equivalent Concentration, Conductance, 1V Ohms-' 0.1 350.6 346,4 0.1 0.1 233.3 0.1 95.7
literature Cited
greater than for "03, the observed anomalous negative osmosis for H N O , is less than that for HCl. This difference may be due to membrane interactions, as the attraction of the anion exchange membranes is greater for NOa- than for C1-, as reflected in the greater selectivity for N O S - than for C1-. The selectivity of strong base anion exchange resins for N 0 3 over C1- is 3.80 (Wheaton and Bauman, 1951). T h e increase in anomalous negative osmosis brought about
Grim, E., Sollner, K., J. Gen. Physzol. 40, No. 6, 887-99 (1957). "Handbook of Chemistry and Physics," 38th ed., Chemical Rubber Co., Cleveland, Ohio, 1956. Mindick, M., Oda, R., Symposium on Innovations in Separation Processes, North Jersey Section, ACS, 1958. Schlogl, R., 2. Physik. Chem. (Frankfurt) 3, 73 (1955). Wheaton, R. M., Bauman, W. C., Znd. Eng. Chem. 43, 1088-93 (1951). RECEIVED for review January 19, 1967 ACCEPTEDJuly 13, 1967
ADSORPTION EQUILIBRIA IN THE METHANE-PROPANE-SILICA
GEL SYSTEM
A T HIGH PRESSURES JOHN J. H A Y D E L ' A N D R l K l KOBAYASHI Defartment of Chemical Engineering, William Marsh Rice University, Houston, Tex.
Further improvements and application of the chrorriatographic technique for obtaining adsorption equilibrium data have been made. Adsorption data have been obtained a t high pressure for methane, propane, and several of their mixfures on silica gel, by using radioactive tracer pulsing. A method of obtaining adsorbedphase volumes is introduced. The data are represented analytically using a two-dimensional virial equation of state truncated after the third virial coefficients.
general chromatographic method for determining the adsorption of gases on adsorbents was recently introduced by Gilmer and Kobayashi (1965), who presented the theory by which component and total adsorption of gases from mixtures on an absorbent could be determined by a per-
A
1
546
RATHER
Present address, Shell Oil Co., Houston, Tex. I&EC FUNDAMENTALS
turbation or chromatographic technique. Experimental adsorption data were obtained on the methane-propane-silica gel system to verify the proposed method. The present work was undertaken to extend the application of the method over a wider range of compositions, temperatures, and pressures and to make other modifications that would further generalize the procedure.
