20 Reverse-Osmosis Separations of Alkali Metal Halides in Methanol Solutions Using Cellulose Acetate Membranes B R I A N A . F A R N A N D and F . D . F . T A L B O T Department of Chemical Engineering, University of Ottawa, Ottawa T A K E S H I M A T S U U R A and S. S O U R I R A J A N Downloaded by GEORGETOWN UNIV on February 19, 2015 | http://pubs.acs.org Publication Date: May 27, 1981 | doi: 10.1021/bk-1981-0154.ch020
Division of Chemistry, National Research Council of Canada, Ottawa
Virtually all reverse osmosis separations have been made w i t h water as the major component, and the general case of aqueous salt s o l u t i o n s has been well documented in t h e literature (1, 2 ) . While separations in nonaqueous s o l u t i o n systems have been i n v e s t i g a t e d (3, 4, 5 ) , no organized study o f such systems has been made and there are no r e p o r t s in t h e literature of u s i n g reverse osmosis t o separate i n o r g a n i c s a l t s in nonaqueous s o l u t i o n s . F o r these reasons, the reverse osmosis s e p a r a t i o n of alkali metal h a l i d e s in methanol s o l u t i o n s u s i n g porous c e l l u l o s e acetate membranes has been s t u d i e d in this work. Previous work w i t h aqueous s o l u t i o n systems has been s u c c e s s f u l in t r e a t i n g both completely i o n i z e d salts as well as incompletely i o n i z e d salts (2, 6 ) . T h i s work i n c o r p o r a t e s both of these cases in methanol s o l u t i o n s and uses the KimuraSourirajan a n a l y s i s f o r t h e treatment of reverse osmosis data (7). The surface excess f r e e energy parameters (-ΔΔ/RT) for t h e ions and ion p a i r s i n v o l v e d were determined by the methods e s t a b l i s h e d earlier ( 8 ) . The predictability of membrane performance by the use o f data on f r e e energy parameters obtained in this work has been t e s t e d . Removal of d i s s o l v e d i n o r g a n i c i m p u r i t i e s from methanol is of i n t e r e s t from the p o i n t of view of utilization of methanol as an a l t e r n a t i v e t o conventional fuels. Reports show that t h e c o r r o s i o n r a t e of metal alloys used f o r t u r b i n e s and fuel t r a n s p o r t a t i o n is g r e a t e r in methanol than in water in t h e presence of t r a c e s of c h l o r i n e and sodium ions (9, 1 0 ) . F u r t h e r , i o n complexes in t r a c e q u a n t i t i e s have been observed in methanol and there is concern that they could alter the r e a c t i o n kinetics f o r processes which use methanol as a feedstock o r r e a c t i o n medium (11). Methanol t h a t is used as a feedstockinthe p r o d u c t i o n o f s i n g l e cell p r o t e i n could be sterilized as well as purified of heavy metals by reverse osmosis which can be i n t e g r a t e d in the d e s i g n of these processes. 0097-6156/81/0154-0339$05.25/0 © 1981 American Chemical Society
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
340
SYNTHETIC
Table I .
mol
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x
fraction 10 3
a
from
(14)
from
(15)
Table I .
fraction 10 3
from
^AB
b
2
m /s
x
10
1 0
mol f r a c t i o n
basis
1.000 .496 .384 .333 .304 .285 .273 .265 .259 .254 .251 .250 .248
12.07 7.74 7.65 8.02 8.47 8.93 9.37 9.79 10.20 10.59 10.95 11.29 11.68
- Cont'd P h y s i c a l P r o p e r t i e s of L i B r - M e t h a n o l S o l u t i o n s
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0
a
TT
kPa 0 71 155 235 318 403 495 592 675 755 839 925 993
b
x
H F A N D U F USES
P h y s i c a l P r o p e r t i e s of L i C l - M e t h a n o l S o l u t i o n s
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0
mol
MEMBRANES:
kPa 0 71 155 235 318 403 495 592 675 755 839 925 993
Y ±
^AB
7T 2
m /s
x
12.56 8.05 7.96 8.35 8.81 9.29 9.75 10.19 10.61 11.02 11.39 11.75 12.15
10
1 0
a
mol f r a c t i o n
basis
1.000 .496 .384 .333 .304 .285 .273 .265 .259 .254 .251 .250 .248
(16)
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
20.
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RO Separations of Alkali Metal Halides
ET AL.
341
Table I . - Cont'd P h y s i c a l P r o p e r t i e s of NaCl-Methanol S o l u t i o n s
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mol f r a c t i o n x 103
kPa
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
0 74 155 241 327 406 488 558 648 725 803
a
from (17)
b
from (18)
c
from (19)
d
from (15)
Y
^AB
TT 2
m /s
x 10
1 0
3
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 12.0 14.0 16.0 18.0
0 86 181 282 385 488 594 690 795 898 1001 1203 1408 1613 1818
Solutions
0AB
TT
kPa
b
1.000 .428 .332 .285 .257 .239 .226 .217 .210 .205 .202
13.17 7.25 7.17 7.33 7.51 7.68 7.89 8.09 8.29 8.48 8.69
b
>
mol f r a c t i o n b a s i s
Table I . - Cont'd P h y s i c a l P r o p e r t i e s of NaBr-Methanol
mol f r a c t i o n x IO
a +
m2/
s
x 10
13.37 12.09 11.31 10.98 10.73 10.54 10.39 10.27 10.17 10.09
-
1 0
mol f r a c t i o n b a s i s 1.000 .658 .581 .536 .504 .479 .459 .442 .427 .414 .403 .382 .365 .350 .337
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
342
SYNTHETIC
MEMBRANES:
HF
AND
UF
from (18) b
from (19)
Table I . - Cont'd P h y s i c a l P r o p e r t i e s of KI-Methanol S o l u t i o n s
10
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x
kPa
3
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
2
m /s
0 74 150 230 306 394 466 538 613 696 780
a
from (14)
b
from (20)
Y±
^AB
mol f r a c t i o n
x iolO
A
mol f r a c t i o n b a s i s 1.000 .545 .472 .428 .398 .374 .355 .338 .324 .311 .300
15.20 13.02 11.95 11.40 11.18 10.87 10.64 10.34 10.14 9.85 9.59
Table I . - Cont'd P h y s i c a l P r o p e r t i e s of CsCl-Methanol S o l u t i o n s
mol f r a c t i o n x
10
3
0 1.0 2.0 3.0 4.0 5.0
a
from (21)
b
from (15)
b kPa 0 74 155 241 327 406
Y+
^AB
TT 2
m /s
x
10
14.98 7.89 7.81 7.98 8.18 8.36
1 0
A
mol f r a c t i o n b a s i s 1.000 .428 .332 .285 .257 .239
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
USES
20.
FARNAND
ET AL.
343
RO Separations of Alkali Metal Halides
Table I . - Cont'd L i m i t i n g D i f f u s i o n C o e f f i c i e n t s of A l k a l i M e t a l H a l i d e s i n Methanol Solute 2
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m /s
Table I I .
Ion
^AB x 10l0
LiCl LiBr
12.07 12.56
NaCl NaBr Nal
13.17 13.37 14.03
KF KC1 KBr KI
11.88 14.24 14.41 15.20
RbCl
14.33
CsCl CsBr
14.98 15.16
Bulk S o l u t i o n Free Energy of S o l v a t i o n f o r A l k a l i M e t a l and H a l i d e Ions i n Methanol Solutions Crystallographic radius nm
kJ/mol
Li Na+ K+ Rb+ Cs+
+
6.0 9.5 13.3 14.8 16.9
481.9 385.5 314.3 289.1 249.3
F" CI" Br" I-
13.6 18.1 19.5 21.6
_
_
305.9 282.8 253.5
-
a
from (22)
b
from (23)
a
481.9 385.5 314.3 289.0 247.2
—
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
b
344
SYNTHETIC
MEMBRANES:
H F A N D U F USES
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Experimental Twelve a l k a l i metal h a l i d e s were used i n s i n g l e s o l u t e methanol s o l u t i o n systems with c e l l u l o s e acetate batch 316 (10/30) membranes at pressures of 1725 kPa gauge (250 psig) and 3450 kPa gauge (500 p s i g ) ( 1 ) . The membranes were heat t r e a t e d i n water and then solvent exchanged to methanol by immersion i n s u c c e s s i v e l y concentrated methanol-water s o l u t i o n s . A f t e r a pure methanol immersion had been completed, the membranes were loaded i n t o c e l l s and subjected to pressures of 120% of the subsequent operating pressures f o r one h o u r . The apparatus used was the same as reported e a r l i e r with the a d d i t i o n of a temperature c o n t r o l l e r to keep the temperature of the feed s o l u t i o n at 25 ± 0 . 5 ° C ( 2 ) . The concentrations of the feed s o l u t i o n s i n v o l v e d were i n the range of 0.005 m to 0.45 m and the o p e r a t i n g pressure was e i t h e r 1725 kPa gauge (250 psig) or 3450 kPa gauge (500 p s i g ) . A l l experiments were performed at 25°C with a feed flow r a t e of 490 c m / m i n . For each experiment, pure solvent permeation r a t e s (PSP) and product r a t e s (PR) as w e l l as s o l u t e s e p a r a t i o n (f) defined as: 3
f - feed m o l a l i t y - permeate m o l a l i t y ^ feed m o l a l i t y were determined. A n a l y s i s of the c o n c e n t r a t i o n of the v a r i o u s s a l t s i n both the feed and the permeate s o l u t i o n s was by e i t h e r e l e c t r i c a l conductance or atomic a b s o r p t i o n spectroscopy. Results and D i s c u s s i o n P h y s i c a l P r o p e r t i e s . The c a l c u l a t i o n of osmotic pressure r e q u i r e s values of the s o l v e n t ' s thermodynamic a c t i v i t y f o r each solution. The s o l u t e mean a c t i v i t y c o e f f i c i e n t s , y are reported i n the l i t e r a t u r e and t h e i r transformation"to solvent a c t i v i t i e s was made by use of the Gibbs-Duhem r e l a t i o n (12). The d i f f u s i o n c o e f f i c i e n t , ^^g* was determined f o r each s o l u t e by the Nernst-Haskel equation (13). These are presented i n Table I along with osmotic p r e s s u r e s . The f r e e energy of s o l v a t i o n f o r the b u l k s o l u t i o n (Ac7g) f o r each i o n considered and the d i s s o c i a t i o n constant ( i £ ) of r e l e v a n t s a l t s are given i n Tables I I and I I I r e s p e c t i v e l y . +9
D
Basic Transport E q u a t i o n s . The Kimura-Sourirajan a n a l y s i s of experimental reverse osmosis data leads to the f o l l o w i n g b a s i c t r a n s p o r t equations (2, 1_, 8) :
A
=
nm
Methanol
6.0 9.5 13.3 14.8 16.9 13.6 18.1 19.5 21.6
-1.36 -0.427 0.033 0.138 0.244 -2.34 -1.71 -1.58 -1.41
r
a from
Water (-AAG/RT)i 5.77 5.79 5.91 5.86 5.72 -4.91 -4.42 -4.25 -3.98
(2)
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
20.
FARNAND
ET
RO
AL.
Separations of Alkali Metal Halides
351
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5.0
r., Figure 3.
nm
Born Equation for alkali metal and halide ions—bulk-phase free energy of solvation in methanol solutions
Table V I I . Values of
Ion P a i r
NaCl NaBr KI CsCl LiCia LiBr a
Average a, f o r 0.15 m feed, determined at 0.73 0.80 0.85 0.82 =a.o ^1.0
-1.295 -0.343 5.175 1.706
-
Kj) i s so l a r g e that a i s considered as u n i t y f o r the c o n c e n t r a t i o n ranges used i n t h i s work.
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
352
SYNTHETIC MEMBRANES:
HF AND U F
USES
Reverse osmosis experiments were performed w i t h the same membranes that were used p r e v i o u s l y a t concentrations where t h e formation of i o n p a i r s was s i g n i f i c a n t . The values of (-AAG/RT)^ f o r the unassociated ions t h a t were determined p r e v i o u s l y were used i n eq. (10) w i t h the values of ln(^AM/#6) f o r the a s s o c i a t e d i o n experiments t o o b t a i n the values of (-AAG/R2)-j-p presented i n Table V I I .
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7
P r e d i c t a b i l i t y o f Membrane Performance. New membranes were placed i n the c e l l s as before and an experiment was done w i t h a reference s o l u t e (NaCl). With the use of the t r a n s p o r t equations (eq. (2), (3), (6), and (7)) and the c o r r e l a t i o n of k w i t h A, eq. (14), ( ^ A M / Z 6 ) was determined. The a p p r o p r i a t e (AAc7/RZ ) s were used from Table VI t o determine C$ ci f o r each membrane. C a l c u l a t i o n s o f (Pi?) and / f o r s e v e r a l s a l t s a t v a r i o u s concentrations and pressures were made and compared t o the experimental r e s u l t s w i t h the new membranes and these a r e summarized i n F i g u r e 4 and Tables V I I I , and IX. The s a t i s f a c t o r y agreement between p r e d i c t e d and experimental r e s u l t s obtained i n d i c a t e s the p r a c t i c a l u t i l i t y o f the c o r r e l a t i o n s and parameters generated i n t h i s work. NaC1
7
f
a
i
Comparison of Water and Methanol S o l u t i o n s . Comparison of (-AAG/R2 ) i f o r i o n s i n both water and methanol s o l u t i o n s can be made by u s i n g (-AAG/R20 + and (-AA&/R2 ) as references f o r the a l k a l i metal c a t i o n s and h a l i d e anions r e s p e c t i v e l y . These have been p l o t t e d i n F i g u r e 5 w i t h the l y o t r o p i c numbers f o r each i o n . Figure 5 shows that w i t h respect to h a l i d e ions the c o r r e l a t i o n of l y o t r o p i c number w i t h [ (-AAG /R2 ) -(-AA6 /R5 ) -] i s both l i n e a r and i d e n t i c a l f o r both s o l v e n t s , whereas t h e corresponding c o r r e l a t i o n s w i t h respect t o a l k a l i metal c a t i o n s are d i f f e r e n t . I n p a r t i c u l a r , w i t h respect t o these l a t t e r i o n s , the change of [ (-AA6^/R!Z ) -(-AA6 /R5 ) +] w i t h l y o t r o p i c number i s g r e a t e r i n methanol s o l u t i o n s than i n aqueous s o l u t i o n s . T h i s means that f o r a given membrane, the v a r i a t i o n s i n s o l u t e s e p a r a t i o n f o r a l k a l i metal h a l i d e s a l t s w i t h common anions i s much l e s s i n aqueous s o l u t i o n s than i n methanol s o l u t i o n s , which i s c o n s i s t e n t w i t h experimental r e s u l t s . F u r t h e r , i n the case of methanol s o l u t i o n s , t h e s o l u t e s e p a r a t i o n i n c r e a s e s w i t h i n c r e a s e i n l y o t r o p i c number f o r the a l k a l i metal c a t i o n s e r i e s and decreases w i t h an i n c r e a s e i n l y o t r o p i c number f o r the halide series. The l y t o r o p i c number f o r an i o n i s a fundamental physicochemical parameter which expresses i t s r e l a t i v e tendency f o r e l e c t r o n t r a n s f e r (30) which i s a l s o the b a s i s f o r p r e f e r e n t i a l s o r p t i o n a t i n t e r f a c e s f o r aqueous s o l u t i o n s i n v o l v i n g p o l a r s o l u t e s (31). Since t h e l y o t r o p i c s e r i e s i s v a l i d i n many f i e l d s of p h y s i c a l chemistry i n c l u d i n g s o l v a t i o n , 7
7
Na
!
T
!
i
7
!
i
7
Na
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
7
cl
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FARNAND
ET AL.
RO Separations of Alkali Metal Halides
E i
Figure 4.
353
(-AAG/RT),
Separation in methanol solutions with surface excess free energy of solvation at 0.005m and 1725 kPa
LYOTROPIC NUMBER Figure 5.
Comparison of the surface excess free energies for alkali metal and halide ions for aqueous and methanol solutions
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
354
SYNTHETIC
Table V I I I .
MEMBRANES:
Experimental and Product Rates, ( P i ? ) , at 0.15 m and 1725 kPa
(PR)
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HF AND U F
Membrane
Run
Solute
7
32 38 40 41 42 47
8
Exptl
Calcd
Exptl
Calcd
NaCl CsCl LiCl LiBr NaBr KI
.605 .351 .817 .780 .605 .323
.606 .361 .813 .792 .590 .304
6.32 6.87 5.65 5.75 6.04 5.94
5.90 6.90 5.52 5.50 5.77 6.89
.74 .83 1.00 1.00 .80 .87
32 38 40 41 42 47
NaCl CsCl LiCl LiBr NaBr KI
.658 .471 .848 .817 .639 .361
.636 .392 .831 .812 .619 .330
4.61 4.99 4.08 4.17 4.37 4.39
4.31 5.03 4.06 4.05 4.22 5.02
.74 .83 1.00 1.00 .80 .87
9
32 38 40 41 42 47
NaCl CsCl LiCl LiBr NaBr KI
.639 .417 .836 .805 .625 .349
.641 .407 .835 .816 .623 .335
3.65 3.94 3.22 3 .30 3.47 3.43
3.41 3.95 3.22 3.21 3.33 3.95
.74 .83 1.00 1.00 .80 .87
11
32 38 40 41 42 47
NaCl CsCl LiCl LiBr NaBr KI
.655 .431 .850 .822 .649 .381
.673 .434 .853 .835 .655 .367
3.60 3.97 3.20 3.31 3.47 3.48
3.40 3.98 3.24 3.22 3.32 3.95
.74 .84 1.00 1.00 .80 .87
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
a
USES
20.
FARNAND
Table I X .
ET AL.
Experimental and C a l c u l a t e d Separation, and Product Rate, (PR), at 3450 kPa
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Membrane Run
355
RO Separations of Alkali Metal Halides
/,
(PR)
Solute
Concn m
Exptl
Calcd
Exptl
Calcd
a
7
16 22 14 24 11 26
LiCl LiCl LiBr LiBr NaBr NaBr
.4586 .4930 .4093 .2617 .3853 .2686
.801 .790 .768 .821 .554 .583
.816 .796 .802 .816 .551 .552
9.17 8.25 9.88 11.10 11.48 11.04
7.61 7.34 8.49 10.20 12.12 10.90
1.00 1.00 1.00 1.00 .73 .75
8
16 22 14 24 11 26
LiCl LiCl LiBr LiBr NaBr NaBr
.4586 .4930 .4093 .2617 .3853 .2686
.835 .828 .814 .856 .616 .676
.852 .838 .841 .853 .615 .613
6.71 6.10 7.29 8.21 8.50 8.15
5.64 5.40 6.30 7.59 8.65 7.95
1.00 1.00 1.00 1.00 .73 .75
9
16 22 14 24 11 26
LiCl LiCl LiBr LiBr NaBr NaBr
.4586 .4930 .4093 .2617 .3853 .2686
.820 .815 .800 .840 .600 .661
.839 .819 .836 .842 .591 .590
5.38 4.86 5.79 6.53 6.73 6.45
4.57 4.40 5.01 6.07 7.04 6.17
1.00 1.00 1.00 1.00 .73 .75
11
16 22 14 24 11 26
LiCl LiCl LiBr LiBr NaBr NaBr
.4586 .4930 .4093 .2617 .3853 .2686
.839 .835 .816 .861 .617 .684
.854 .832 .846 .853 .621 .619
5.51 5.05 5.99 6.71 6.91 6.72
4.73 4.49 5.24 6.27 7.18 6.51
1.00 1.00 1.00 1.00 .73 .75
12
16 22 14 24 11 26
LiCl LiCl LiBr LiBr NaBr NaBr
.4586 .4930 .4093 .2617 .3853 .2686
.748 .737 .729 .771 .515 .571
.792 .766 .887 .790 .517 .517
4.54 4.16 4.84 5.47 5.42 5.34
3.95 3.85 3.78 5.11 6.10 5.51
1.00 1.00 1.00 1.00 .73 .75
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
356
SYNTHETIC
MEMBRANES:
HF
AND
UF
USES
7
s o r b a b i l i t y , and s u r f a c e t e n s i o n , the c o r r e l a t i o n of (-AA&/R2 )^ w i t h l y o t r o p i c number r e f l e c t s the s e p a r a t i o n of ions i n reverse osmosis.
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Conclusions The physicochemical c r i t e r i a approach t o reverse osmosis separations i n v o l v i n g the surface excess f r e e energy of s o l v a t i o n f o r i o n i z e d and nonionized s o l u t e s has been demonstrated by t h i s work t o i n c l u d e nonaqueous s o l u t i o n s . The parameters and c o r r e l a t i o n s presented i n t h i s work permit the p r e d i c t i o n of reverse osmosis separations and permeation r a t e s f o r d i f f e r e n t a l k a l i metal h a l i d e s f o r c e l l u l o s e acetate OEastman E-398) membranes of d i f f e r e n t s u r f a c e p o r o s i t i e s from only a s i n g l e s e t of experimental data f o r a sodium c h l o r i d e methanol reference feed s o l u t i o n system. Abstract Reverse osmosis separations of 12 alkali metal h a l i d e s in methanol s o l u t i o n s have been s t u d i e d u s i n g c e l l u l o s e acetate membranes of different s u r f a c e porosities. Data f o r s u r f a c e excess f r e e energy parameters for the ions and ion pairs i n v o l v e d have been generated for the above membrane m a t e r i a l - s o l u t i o n systems. These data o f f e r a means of p r e d i c t i n g the performance of c e l l u l o s e acetate membranes in the reverse osmosis treatment of methanol s o l u t i o n s i n v o l v i n g the above ions from only a s i n g l e s e t of experimental data. Nomenclature A
= pure s o l v e n t p e r m e a b i l i t y constant (mol s o l v e n t ) • m'^s'l-kPa" -. d e f i n e d i n eq. ( 8 ) , m/s. = molar c o n c e n t r a t i o n of s o l u t i o n , mol/nr*. d i f f u s i v i t y o f s o l u t e A i n s o l v e n t B, m /s. = s o l u t e t r a n s p o r t parameter, t r e a t e d as a s i n g l e v a r i a b l e , m/s. = constant i n m o d i f i e d Born equation, kJ*nm*mol~-'-. = f r a c t i o n of s o l u t e s e p a r a t i o n , defined i n eq. ( 1 ) . = f r e e energy of s o l v a t i o n , kJ/mol. = s u r f a c e excess f r e e energy of s o l v a t i o n , kJ/mol. = i o n i c d i s s o c i a t i o n e q u i l i b r i u m constant based on mol f r a c t i o n . = mass t r a n s f e r c o e f f i c i e n t on the high pressure s i d e of the membrane, m/s. = molecular weight of s o l v e n t B. = s o l v e n t f l u x through membrane, mol-nT . - l . - o p e r a t i n g pressure, kPa. 1
^NaCl o AAB ^AM/X6 E / AG AAG Kj) k
Nft P
=
=
c o n s t a n t
2
2
s
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
20.
FARNAND
ET AL.
(PR) (PSP)
RO Separations of Alkali Metal Halides
= product permeation r a t e through a given membrane area, g/h. = pure solvent permeation r a t e through a g i v e n membrane area, g/h. = gas constant, 8.314 x 1 0 " J - K ^ M H O I " . = P a u l i n g c r y s t a l l o g r a p h i c r a d i u s of i o n i , nm. = e f f e c t i v e membrane s u r f a c e area, m . = system temperature, K. ° l f r a c t i o n of t o t a l ( d i s s o c i a t e d and u n d i s s o c i a t e d ) s o l u t e A. 3
R S T ZA
357
1
2
=
m
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Greek L e t t e r s a 3 Y A ^
= = = = =
+
degree of i o n i c d i s s o c i a t i o n . d e f i n e d i n eq. (13). mean i o n i c a c t i v i t y c o e f f i c i e n t (mol f r a c t i o n ) . constant i n m o d i f i e d Born equation, nm. osmotic pressure of s o l u t i o n , kPa.
Subscripts 1 2 3 A B I i IP +, -
= bulk s o l u t i o n or feed s o l u t i o n , i . e . 3^1• = concentrated boundary s o l u t i o n on the high pressure s i d e of the membrane, i . e . ^A2« = membrane permeated s o l u t i o n on the low pressure s i d e o f the membrane, i . e . ^A3= p e r t a i n i n g t o the s o l u t e . = p e r t a i n i n g t o the solvent or bulk s o l u t i o n phase. = membrane-solution i n t e r f a c e , = i o n of type i . = ion pair. = c a t i o n i c and a n i o n i c , r e s p e c t i v e l y .
Acknowledgement The authors are t h a n k f u l f o r the t e c h n i c a l a s s i s t a n c e o f A. Baxter and f o r the a n a l y t i c a l work of V. Clancy, G. Gardner, and H. MacPherson. T h i s work r e c e i v e d f i n a n c i a l support from the N a t i o n a l Science and Engineering Research C o u n c i l of Canada and from a research c o n t r a c t with the N a t i o n a l Research C o u n c i l of Canada. One of the authors (B.F.) thanks the Province of Ontario f o r the award of a s c h o l a r s h i p . Literature Cited
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Pageau, L.; S o u r i r a j a n , S. J. A p p l . Polym. S c i . , 1972, 16, 3185. Matsuura, T.; Pageau, L.; S o u r i r a j a n , S. J. Appl. Polym. S c i . , 1975, 19, 179.
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9.
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14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
SYNTHETIC
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HF
AND
UF
USES
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Matsuura, T.; S o u r i r a j a n , S. J. A p p l . Polym.Sci.,1973, 17, 1043. McBain, J.W. "Colloid Science"; Heath Co.: Boston, 1950; p. 131. S o u r i r a j a n , S.; Matsuura, T. "Reverse Osmosis and S y n t h e t i c Membranes", S o u r i r a j a n , S., Ed.; N.R.C. Canada: Ottawa, 1977; p. 11.
Issued as NRC No. 18591
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RECEIVED December 4, 1980.
In Synthetic Membranes: Volume II; Turbak, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.