Vapor Pressures of Water Over Aqueous Solutions of Strong Electrolytes Charles 1. Kusikl Arthur D. Little, Inc., Cambridge, Mass. 02140 Herman P. Meissner Chemical Engineering Department, M I T , Cambridge, Mass. 02139
Vapor pressures of water a t any temperature and pressure over a solution of a single strong electrolyte involving ions 1 and 2 can b e estimated by knowing a t least onevalue of I'12n, the reduced activity coefficient a t some specified temperature and pressure. The quantity I ' 1 Z n is defined as y121'r1z2where 7 1 2 is the mean activity coefficient of this electrolyte and z1 and 2 2 are the charge numbers on the ions. For solutions of 1 : 1 electrolytes, water activities are presented graphically as a function of J? and the ionic strength. Values of water activities read from this figure can b e easily corrected for higher electrolytes. It is shown that data on water vapor pressure lowering or boiling point rise can b e used for estimating reduced activity coefficients for electrolytes a t any desired temperature.
Activity of Water in Electrolyte Solutions
W h e n we deal with aqueous solutions of strong electrolytes, it is often necessary to evaluate the vapor pressures (activities) of the water as \vel1 as the activities of the electrolytes present. The object here is to present a generalized procedure for estimating such vapor pressures, applicable when experimental data are not available. Activity Coefficients of Strong Electrolytes
The magnitude of ylZo, the mean activit'y coefficient of a single strong electrolyte 12 composed of ions 1 and 2 in aqueous solution depends upon its molality m12 (moles per kilogram of ivater), upon the charges on the electrolyte's cation and anion, namely zl and zZ,respectively, and upon the t'emperature. Except a t very low concentrations, activity coefficients for different electrolytes in their pure solutions a t any given temperature and concentration are usually far from being equal. However, the general isothermal behavior of these activity coefficients a t any temperature between 0 and 150°C is conveniently represented by the curves of Figure 1 showing the variation of the reduced activity coefficient ri2O [namely (yO)l/zlz*]with the ionic strength p (Xeissner and Tester 1972). Each curve may be viewed as representing a solution of a different electrolyte. Inspection shows that all curves start a t a value for of unity a t zero concentration, and then diverge without crossover as concent,ration increases. Obviously, an entire isothermal curve for a particular electrolyte can be located on Figure I,knowing a single value of y12O a t a n ionic strength of 2 or higher. and a t the temperature of interest. Thus, when we knokv that log YlZ0 for X a S 0 3 a t a p of 2 is -0.32 a t 25"C, then its value a t 25OC and a p of 6 is determined from Figure 1 as -0.44 or rl20is 0.363, compared bo a n esperimental value of 0.371. For electrolytes on which no experimental data are available a method of predict'ing an approximate value for ylno a t 25°C and a n ionic strength of 2 has been proposed (Meissner arid Tester 1972). 1
T o whom correspondence should be addressed.
1 12 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
As is customary, t'he activity of water (u,)~~,, is expressed as namely the ratio of the vapor pressures over the single electrolyte solution and over pure water, all a t the temperature of interest. For a solution of a single strong electrolyte, the isothermal relationship between (a,),,,,, y12O, and concentration is expressed by the familiar Gibbs-Duhem equation, conveniently written as follows in standard texts (e.g., Pitzer and Brewer equation 22-27) :
p,/p,",
55.5 d In (a,jzIz, =
-v12rn12
d In m12 -
v12rn12
d In
y120
(1)
Here v12 represents the moles of ions formed upon dissociation of one mole of electrolyte. The ionic strength p12 of a single electrolyte is related to its molality as follows: p12 =
0.5
(2)
2122~12rn12
[ r o t e : This equation is readily derived, in that p equals 0.5 m v2zZ2),or 0.5 m(v12z12/v1 Y ~ ~ P ~ Since ~ ~ Y vlzl ~ ) equals . v 2 z 2 , p 1 2 equals 0.5 m l z ~ 1 z 1 ~ 2 z 2 (u~21 ) / v 1 v z . If we recognize that (vl up) equals v12, Equation 2 results upon canceling common terms in numerator and denominator.] in Equation I, combining with Substituting ro for Equation 2 , and simplifying, we get (v1z12
+
+
+ +
Equation 3 can now be integrated between molality limits of zero and m, equivalent to limits for the ionic strength of zero and the final ionic strength of the solut,ion112; the corresponding limits for the reduced activity coefficient are unity and r1zo. Performing the integration gives us rl?Q p d log rlZo log ( ~ w ) 2 , , , = -0.0156 p 1 2 / ( ~ 1 ~ 2) (0.036)
s,
(4)
When we know zl, z2, and plz, the first term on the right side of Equation 4 can be evaluated directly, while the second
r20 t16
r12
.oa
-
r04 0
-34 -08 -1 2
C
40
120
80
160
203
fi
Figure 1 . Generalized plot of reduced activity coefficient vs. ionic strength p over ionic strength range 1 .O-20
r
Table I. Comparison of Water Activities from Figure 2 and literature Values for Selected Saturated Solutions a t 2 5 ° C Experimental value Log
Solid phase, 1 : 1 electrolytes
KIT03 KC1 KBr LiN03.3 H z 0 LiCl. HzO NH4Cl XH4N03 KaBr . 2 H z 0 NaN03 NaOH. HzO
ro
3.79 4.80 5.75 12.35 19.6 7.75 27.5 9.14 10.80 27.5
-0.62 -0.22 -0.21 +0.48 +1.78 -0.19 -0.87 +0.30 -0.46 +1.5
0.92 0.84 0.81 0.47 0.11 0.77 0.62 0.58 0.74 0.07
Values from Fig. 2 and Eq. 6 Log
-0.03 -0.065 -0.085 -0.35 -0.96 -0.12 -0.22. -0.24 -0.13 -1.030
0.93 0.86 0.82 0.45 0.11 0.76 0.60 0.58 0.74 0.09
2 : l and 1 : 2 Electrolytes*
BaC12.2 H 2 0 CaClp
5 . 4 -0.174 0.90 -0.08 0.92 6 . 3 5 +0.02 0.85 - 0 . 1 2 0.85 IIg(K03)za t 25°C and at' p = 15.1, ylzo equals (2.12)* or 4.6 vs. a reported value of 4.9 (extrapolated from Robinson and Stokes, p 497). T o determine ionic strengths a t any other concentration and/or temperature, t,he methods outlined elsewhere (lleissner et al., 1972) can be followed. It has already been shown (1Ieissner et al., 1972) that the activity coefficients of electrolytes falling above the dotted line of Figure 1 teiid to decrease with t'emperature, while those below t,he dotted line increase, as dictated by Equation 7 . A t a given concentration, the activity of water does not vary with temperature for those pure electrolyte solutions, such as KaCl, whose activity coefficients fall close to the dott'ed line of Figure 1. Thus for NaC1, am is almost constant a t 0.7 for a 3-m solut,ion a t temperatures of from O-lOO°C. Boiling Point Elevation
When appropriate data on a strong elect'rolyte are completely lacking, the simplest experimental procedure for approximating such information is probably to measure the boiling point, rise of a solution. For example, the boiling point elevation, a t 760 mm I l g ambient pressure of a 5-?nsolution of sodium chloride is 5.92"C (Int. Crit. Tables, 1928, p 329). At 105.9OC, the vapor pressure of pure water is 930 m m Hg, making a, equal to 760/930, and log a, equal to -0.090. K h e n log a, is -0.09 and p is 5, then from Figure 2, log
rNaCl is -0.06. When we correct for temperature by methods previously discussed, using Figure 1 and Equation 7, (log r)saC1 a t p = 5 and 25OC is -0.03. Thus, y is 0.94 compared to a reported value of 0.874 (Robinson and Stokes, App. 8.10, 1959). Obviously, the above procedure can be reversed to predict (by a trial and error procedure) the boiling point elevation from a k n o m activity coefficient or water vapor pressure above the electrolyte a t some other temperature. Osmotic Coefficient
The osmotic coefficient is given for a single electrolyte, by Robinson and Stokes, p 29 (1959). (9) which with Equations 2 and 6 can be transformed to
Thus at a given ionic strength, # I 2 can be easily derived from values of log awl from Figure 2 and substituted in Equation 10. Precision
Errors in estimating vapor pressure of water for various electrolyte solutions are generally within 20%. Further errors call be introduced when F values are predicted from vapor pressure lowering, extrapolated over large ranges of ionic strength in Figure 1 or large temperature ranges by Equation 7 . Thus the relat,ionships proposed here should be used only when direct experimental evidence is not available.
The extension of these developments to multicomponent solutions is to be the subject of a subsequent paper. Nomenclature
azo
activity of water = activity of water in pure electrolyte 12 = activity of water in a pure 1: 1 electrolyte m12 = molal concentration of electrolyte (mol/kg of water) ml, m2 = molal concentration of ions 1 and 2 z+, z= cationic and anionic charge numbers =
GREEKLETTERS = mean activity coefficient in a solution containing pure electrolyte 12 rlzo = reduced activity coefficient (y0)1’~1~2 + = osmotic coefficient (Equation 9) plz = ionic strength of electrolyte 12 (0.5 m1zI2 0.5 m&) u l , u p , uI2 = number of ions 1, of ions 2, and ions 1 plus ions 2 found in dissolving 1 mole of electrolyte 12 y120
+
Literature Cited
International Critical Tables, 1st ed., Vol. 111, McGraw-Hill, New York, N.Y., 1928. hleissner, H. P., et al., AIChE J.,18(3), 661 (1972). hleissner, H. P., Kusik, C. L., ibid., (2), 294 (1972). Meissner. H. P.. Tester. J. W.. Ind. Ena. Chem. Process Des. Develop., 11, I28 (1972). Pitaer, K. S., Brewer, L., “Thermodynamics,” McGraw-Hill, Sew York, N.Y., 1961. Robinson, R. A,, Stokes, R. H., “Electrolyte Solutions,” 2nd ed., Appendix 8.1, ilcademic Press, New York, N.Y., 1959. Stokes, It. H., Robinson, R. A,, Ind. Eng. Chem., 41, 2013 (1949). Smithsonian Physical Tables, Smithsonian Inst. Publ., pp 373-4, 9th rev. ed., Washington, D.C., 1954. RECEIVED for review July 3, 1972 ACCEPTED September 1, 1972
Performance of Screen-Packed Liquid-Liquid Extraction Tower Bih H. Chen Department of Chemical Engineering, Y o v a Scotia Technical College, Halifax, S . S . , Canada
The screen cylinder was tested for its effectiveness as a column packing in a liquid extraction tower using benzene-acetic acid-water system. The mass transfer performance was determined as a function of size and mesh opening of the screen cylinder, tower height, direction of mass transfer, and flow rate of the dispersed and the continuous phases. Holdup of the dispersed phase and flooding characteristics were also determined. Data show that operating throughputs of the screen cylinder are two to three times higher than those achieved with Raschig rings a t the same time that equally high rates of extraction are maintained.
P a c k e d towers frequently have been used as interfacial cont’actiiigdevices iii chemical engineering operations. In addition to providing a larger surface area for interphase contact, the packing serves to reduce the axial mixing and also to jostle and distort the gaseous bubbles or the liquid droplets of the diaIiersed phase, in this way improving the rate of mass transfer. However, depending on the type of packing material used, the flow capacity of a packed column could be severely re-
duced by comparison with a n unpacked column. Recently, a novel type of packing has been developed a t the Applied Chemistry Division of the Sational Research Council of Canada, which could retain the advantage of a packed tower without adversely affecting its flow capacity. This packing is made from wire cloth, 3-14 meshes, in. which is first cut into rectangular pieces of desired dimensions and then rolled to form open-ended cylinders. Thus, the porosity Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1, 1973
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