DISTRIBUTION OF ISOMORPHOUS SALTS BETWEEN AQUEOUS AND SOLID PHASES IN FRACTIONAL CRYSTALLIZATION Nickel Ammonium Sulfate-Magnesium Ammonium Sulfate- Water and Barium Nitrate-Lead Nitrate- Water Systems A .
S .
A N A N D A
M U R T H Y
A N D
D .
5 . M A H A D E V A P P A
Department of Postgraduate Studies and Research in Chemistry, University of Mysore, Manasa Gangotri, Mysore-6, India The distribution of isomorphous salts between aqueous and solid phases in fractional crystallization was determined. The results were examined from the standpoint of theoretical equations developed by Doerner and Hoskins, Berthelot and Nernst, and Abu Elamayem. Calculations of the distribution constants, X and D, employed in the Doerner and Hoskins and Berthelot and Nernst equations, respectively, show that these equations are not strictly applicable to the systems studied. Experimental results can be quantitatively explained, however, by Abu Elamayem’s equation. The less soluble salt is separated more effectively by allowing a small weight fraction of the crystals to separate from a ternary system.
WHEN a pair of isomorphous salts is rapidly crystallized from an aqueous solution, the resulting solid solution changes in composition continuously. A study of the distribution of the salts in the resulting system is of considerable theoretical and practical interest. Although fractional crystallization normally affords nonequilibrium states, the final distribution can be studied with the aid of equations developed for systems a t equilibrium. The Berthelot-Nernst law (Chlopin, 1925) may be written as
where a and b are the initial amounts and y and n are the final amounts of radium and barium chlorides in solution; is a constant. These equations have been employed by several workers (Callow, 1962; Chlopin, 1927, 1929, 1930; Marques, 1936; Polessitskii, 1933; Riehl and Kading, 1930) t o explain the results of their studies on equilibrium and nonequilibrium systems. Recently Klein and Fontal (1965) studied the kinetics of coprecipitation of lead and barium ions as their sulfates, in the reaction hi
Pb2- (as) + BaS04 (crystal) 2 Ba2+ (aq) + k?
where a and b are the total amounts (grams) of original salts, x and y are the amounts (grams) in the solid phase, (a - x) and ( b - y ) are the amounts in the liquid phase, and D is the distribution constant. A logarithmic relation was developed by Doerner and Hoskins (1925) for the coprecipitation of radium and barium chlorides with sulfuric acid in the form:
Y n In- = h l n a b 260
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
(2)
PbS04 (crystal)
(3)
k l and h2 are the rate constants involved. By thermodynamic treatment they showed that the total precipitation rate, I , and in the logarithmic equation of Doerner and Hoskins (1925) are related to the specific rate constants, kl and h2, and the number of active sites, M , on the solid particles as represented by the equation A =
I J M - kl I / M - kz
(4)
Hill et al. (1940) put forward a semiempirical relation governing the distribution of a pair of isomorphous salts having a common ion, between solid and aqueous phases:
R1 -=K R," where RI and R, are the mole ratios of salts A and B in the liquid and solid phases, respectively, m is an empirical constant, and K is the distribution constant. On the basis of ideas developed by Sugden, Abu Elamayem (1964) worked out Equations 6 and 7 for fractional crystallization of isomorphous salts in equilibrium and nonequilibrium systems, respectively:
y2u ( K - 1) - -dy = -1f du
u .
1
where u'=
y =
a = M q a n d MB = K and m =
fraction by weight of original mixture separated as crystals fraction by weight of less soluble salt in crystals fraction by weight of less soluble salt in initial mixture the molecular weights of the two salts constants in the equation of Hill et al. (1940)
As a special case, when m = 1, Equation 7 reduces to
I C - - l - - - I I
"I
Equations 1, 2, 5, and 6 have been proposed for systems in equilibrium, while Equation 7 is applicable to a nonequilibrium system. The object of the present investigation was t o study experimentally the distribution of a pair of isomorphous salts between aqueous and solid phases and examine the results from the standpoint of available theoretical equations. Two pairs of isomorphous salts were selected: nickel ~_.__ ammonium sulfate- water magnesium
1,
--
2.
~-
barium lead
nitratewater
System 1 consists of salts belonging to the picromerite group for which Equation 5 has been shown t o apply. System 2 was chosen to see how far the theoretical equations were applicable to a pair of isomorphous salts other than alums and picromerites. Materials and Methods
Nickel ammonium sulfate was prepared by mixing hot equimolar solutions of nickel sulfate and ammonium sul-
fate. The product was recrystallized, then analyzed for nickel, sulfate, and water. Magnesium ammonium sulfate was similarly prepared by using magnesium sulfate and ammonium sulfate. Lead nitrate (British Drug Houses) was recrystallized; reagent grade barium nitrate was used without further purification. Appropriate amounts of the two salts were weighed in a flask. hfter the addition of a suitable amount of water, the flask was reweighed. The salts were dissolved in water by gently heating the stoppered flask. T h e flask was then kept in a thermostat maintained a t 30.0" =t 0.05" C. Crystallization was generally initiated within 15 minutes. When it did not start spontaneously, the solution was seeded with a tiny crystal of one of the salts. The flask was thermostated for 6 hours, shaken a t frequent intervals, then removed and wiped dry with a piece of cloth. The mother liquor was quickly decanted into a weighed flask; the crystals were retained in the original flask. After both flasks were reweighed, the crystals were analyzed. The entire experiment was repeated with the same amounts of the two salts but varying amounts of water. For the analysis of the crystals from the Ni-Mg salt system, the moist crystals were dissolved in water. Ni was separated and estimated by electrolytic deposition (Scott, 1961d) on a previously weighed cylindrical Pt gauze electrode (surface area 125.0 cm?) a t a current density of 6 to 8 ma. per cm? The nickel-free solution was then made up to a known volume and magnesium was determined on an aliquot by weighing as the oxinate, Mg(CsHsON)n (Scott, 1 9 6 1 ~ ) . I n the case of the lead-barium nitrate system, the moist crystals were dissolved in water and made up to a known volume. From a suitable aliquot, lead was determined by separation as PbO, by anodic deposition (Scott, 1961b) from a nitric acid solution a t a current density of 10.0 ma. per cm? The lead-free solution was evaporated nearly to dryness. The residue was dissolved in water and barium was determined as its carbonate (Scott, 1961a). The conventional method of estimating barium as its sulfate was not adopted on account of the errors that would arise from adsorption of nitrate on the precipitate. The analyses so made yield the amounts of the two salts in the solid phase, which also contains a small amount of adhering mother liquor. A correction was applied in all analyses for the amount of salts present in the adhering mother liquor. The method employed is identical with Schreinmaker's method (Glasstone, 1953) in so far as the wet residue from the system is taken for analysis. But the method of correcting for the salts held in mother liquor is different; the weight of water present in the moist crystals and the amount of salts held by this water are calculated. From the weight of mother liquor and the amount of the salts present in it, it is possible to calculate the weight of water in the moist crystals and of the salts held by the water. The calculations can be summarized as follows: Let, 1. Weight of water taken 2 . Weight of mother liquor 3. Weight of salt A (less soluble salt) in mother liquor 4. Weight of salt B in mother liquor
ml grams m2 grams m3 grams m4 grams
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 2, 1970
261
5. Weight of water in mother liquor m2 - (ms+ m4) = m5 grams 6. Weight of water present in form of mother liquor adhering t o moist crystals (ml - m5)grams Weight of salt A in adhering mother liquor = [ m 3 ( n l- m , ) / m 5 ]= 6mA Weight of salt B in adhering mother liquor = [m4(ml- m s ) / m s = ] 6mB The correction factors expressed in terms of 6 m A / m and 6mB/m,where m is the corrected weight of crystals, range between 0.03 t o 0.007 and 0.069 to 0.041, respectively, for the Ni-Mg system and 0.053 to 0.021 and 0.197 to 0.064, respectively, for the Ra-Pb system. The corrections thus made are exact, as they are based on accurate experimental data. Although the analysis of the aqueous phase is not required, it was carried out in a few experiments, to check the results of analysis of the solid phase. Results and Discussion
The quantities D (Equation l), A (Equation 2), and u: and y (Equation 7) can be readily calculated from experimental dat,a. Typical results are presented in Tables I and 11. Table I contains the results in the form required for testing Equations 1 and 2; the results in Table I1 are expressed in the form necessary for verifying Equation 7. I t is seen from Table I that the values of the distribution constant, A, of Equation 2 vary gradually from 3.15 to 4.08 for the nickel-magnesium system and from 3.98 to 5.18 for the lead-barium system. The values of D of Equation 1 vary from 5.82 to 4.55 for the nickelmagnesium salt system and 6.98 to 5.64 for the bariumlead nitrate system. I t is evident that neither of the distribution laws is obeyed a t the concentrations investigated in the present studies. An explanation of this behavior might lie in the nonequilibrium nature of the process of crystallization encountered in the present studies. Feibush et al. (1958) rederived Equation 2 for a pair of salts coprecipitating essentially in the same form
by assuming the activity coefficients of the salts to be unity. This assumption can be justified for a pair of sparingly soluble salts. I n the present systems, the ionic strength of the aqueous phase being fairly high, one can expect the deviation of activity coefficients from unity to be considerable. I n addition, it is probable that the rate of crystallization plays a prominent role. Feibush et al. (1958) showed that the equilibrium model used for deriving the homogeneous and heterogeneous distribution laws is not strictly valid, as it cannot explain the variation in A. They propose a new approach in the form of a nonequilibrium kinetic model which can be used for deriving Equation 2. I n this model, the distribution constant, A, is related to the rates of precipitation. This argument has been rationalized by Klein and Fontal (1965) who relate A to the total precipitation rate and the number of active sites available for precipitation. In view of these considerations, study of the rates of crystallization is required for a theoretical interpretation of the processes taking place during crystallization of the systems employed in the current investigations. A purely quantitative approach to the actual separation of the two salts in the systems can be made, however, through the use of Equation 7, which seems to be of practical importance. Abu Elamayem's Equations 6 and 7 have been deduced for systems which are in a state of equilibrium and nonequilibrium, respectively. The systems in the present investigation are in a state of nonequilibrium, since the duration of crystallization is only 6 hours, during which period equilibrium may not have been attained. Hence, we feel that Equation 7 can be employed to explain our experimental results. 'rhe importance of Equation 7 lies in the fact that it is possible to calculate theoretically the amount of the less soluble salt (nickel and barium salts, respectively, in the two systems, expressed as weight fraction y ) that will be present in a given weight of crystals (expressed as
Table II. Typical Results
Table I. Typical Results
No.
Weight of Water. Grams
Corrected Weight of Crystals. Grams
Corrected Weight of Salts in Cnstals ivi salt k f g salt
N O
X
1 2 3 4 5 6 7
30.049 35.194 40.639 45.051 50.045 55.197 60.279
7.809 6.805 5,566 4.703 3.390 2.488 1.4189
3.932 3.600 3.070 2.728 2.067 1593 0.9235
3.877 3.205 2.496 1.975 1.323 0.8951 0.4954
3.15 3.30 3.32 3.59 3.76 4.08 4.01
5.82 5.45 4.78 4.88 4.62 4.78 4.55
1 2 3 4 5 6 7
262
20.010 25.122 35.030 40.116 45.041
6.351 4.474 3.086 2.249 1.354
3.606 2.815 2.046 1.542 0.953
2.745 1.559 1.020 0.707 0.401
3.98 4.89 4.90 5.02 5.18
6.84 6.98 6.10 5.86 5.64
Ind. Eng. Chem. Process Des. Develop., Vol. 9 , No. 2, 1970
U'
Expti.
Theoret.
1.419 2.488 3.390 4.703 5,566 6.806 7.809
0.924 1.593 2.067 2.728 3.070 3.600 3.932
0.095 0.166 0.226 0.313 0.372 0.453 0.520
0.651 0.640 0.610 0.580 0.552 0.529 0.504
0.650 0.632 0.616 0.590 0.570 0.543 0.518
Barium 'lead nitrate-water. Initial weight of barium nitrate. 5.000 grams Initial weight of lead nitrate. 10.000 grams K = 4.2. m = 0.8
Barium/ lead nitrate-water. Initial weight of barium nitrate. 5,000 grams Initial weight of lead nitrate. 10.000 grams 1 2 3 4 5
Grams
Nickel/ magnesium ammonium sulfate-water. Initial weight of Ni salt taken. 5.000 grams Initial weight of Mg salt taken. 10.000 grams K = 3.6, m = 0.8
D
Nicke1,'magnesium ammonium sulfate-water. Initial weight of nickel salt. 5.000 grams Initial weight of magnesium salt. 10.000 grams
Grams
1 2 3 4 7
1.354 2.249 3.086 4.474 6.351
0.953 1.542 2.046 2,815 3.606
0.090 0.150 0.206 0.298 0.424
0.704 0.686 0.663 0.629 0.568
0.693 0.684 0.671 0.639 0.602
weight fraction w) that separate during crystallization. This calculation involves the numerical integration of Equation 7 by the modified Euler method (Ross, 1964). Values for parameters K and m can be chosen and the K and m values approach those given by Equation 5 as the limit when the system approaches equilibrium. The theoretical values so obtained with the assumed values for K and m of 3.6 and 0.8 for the nickel-magnesium salt system and 4.2 and 0.8 for the lead--barium nitrate-~ water system are given in column 6 of Table 11. The theoretical values are in good agreement with the experimental values (column 5 of Table 11). Thus Equation 7 clearly explains the experimental results and is applicable except a t high values of u,when deviations from the experimental values begin (Table 11). The values of y increase with decrease in u’ and hence it is possible to make the separation of the less soluble salt more effective by allowing a small weight fraction of the crystals to separate out of the ternary system. This value of u: can be obtained from Abu Elamayem’s equation. The selection of the values of K and m employed for the systems investigated looks arbitrary, but a comparison of ytheorand yexprshows good agreement between theory and experiment. One might hope that these values of K and m would be characteristic of’ the system and hold good for various values of a, the fraction of the less soluble salt in the initial mixture. Abu Elamayem (1964) has shown that this is true in the case of alum pairs. Acknowledgment
The authors thank G. Narayan, emeritus professor of chemistry, LJniversity of Mysore, Mysore, India, for suggesting the problem and for his keen interest and constructive criticism throughout, these investigations. One of lis (A.S.A.) acknowledges financial assistance in the form of a research scholarship from the University Grants Commission, Government of India, New Delhi, India.
Literature Cited
Abu Elamayem, M. A., J . Inorg. Nucl. Chem. 26, 215964 (1964). Callow, R . J., J . Chem. SOC.1962, 4353-71. Chlopin, V., 2.anurg. allgem. Chem. 143, 97-117 (1925). Chlopin, V., Nikitin, B., 2.anorg. allgem. Chem. 166, 31138 (1927). Chlopin, V., Polessitskii, A., 2. Physik. Chem. A 145, 67-8 (1929). Chlopin, V., Ratner, P., Compt. rend. acad. sci. [IRSS, No. 27, 723-30 (1930). Doerner, H. A., Hoskins, W. M., J . A m . Chem. SOC. 47, 662-75 (1925). Feibush, A. M., Rowley, K., Gordon, L., A n d . Chem. 30, 1605-9 (1958). Glasstone, S . , “Textbook of Physical Chemistry,” p. 802, Macmillan, London, 1953. Hill, A. E., Durham, G. S., Ricci, E., J . A m . Chem. SOC.62, 2723-32 (1940). Klein, D. H., Fontal, B., Tularzta 12, 35-41 (1965). Marques, B.-E., J . Chim. Phys. 33, 1-40 (19363; CA 30, 3318 (1936). Polessitskii, A., Z . Physik. Chem. A 161, 325-35 (1932); CA 27, 20 (1933). Riehl, N., Kading, H., Z . Physik. Chem. A 149, 180-94 (1930); CA 24, 4985 (1930). Ross, S. L., “Differential Equations,” p. 282, Blaisdel, Ginn and Co., London, 1964. “Scott’s Standard Methods of Chemical Analysis,” 5th ed., Vol. I , p. 126, Van Kostrand, S e w York, 1961a. “Scott’s Standard Methods of Chemical Analysis,” 5th ed., Vol. I , p. 507, Van Nostrand, New York, 1961b. “Scott’s Standard Methods of Chemical Analysis,” 5th ed., Vol. I , p. 535, Van S o s t r a n d , New York, 1 9 6 1 ~ . “Scott’s Standard Methods of Chemical Analysis,” 5th ed., Vol. I , p. 620, Van Nostrand, New York, 196ld. RECEIVED for review March 17, 1969 ACCEPTED October 9, 1969
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