Distribution of Isomorphous Salts Between Aqueous and Solid Phases in Fractional Crystallization Effect of Varying Concentration of Less Soluble Salt on Distribution A. Srinivasamurthy Ananda Murthy and D. Siddalingiah Mahadevappa Department os Post-Graduate Studies and Research in Chemistry, C-niversity of Jf ysore, Jlanasa Gangotri, Mysore-6, India
Distribution of isomorphaus salts between aqueous and solid phases in fractional crystallization was studied at different concentrations of less soluble salt in the ternary systems nickel-magnesium-ammonium sulfatewuter and barium-lead nitrate-water systems. The applicability cf theoretical equation developed by Abu Elamayem was investigated. Experimental results were explained by a proper choice of values for the parameters in Abu Elamayem's equation. These parameters characterize a given system over a wide range of concentrations and can be effectively used in predicting the amount of less soluble salt crystallizing out of a ternary system.
Fractional crystallization in ternary systems is a nonequilibrium process. Several theoretical equations have been developed (Henderaoii and Kracek, 1927; Chlopin, 1925; Doerner and Hoskins, 1925) for systems in equilibrium, some of which could as well be employed for studying the nonequilibrium states encountered in fractional crystallization. Recently, d b u Elamayem (1964) has derived Equation 1 for fractional crystallization of isomorphous salts in a noiiequilibrium system:
-
-
-~ dy -
dw
where
w
= fraction by lveight of original mixture separated as
crystals fraction by weight of less soluble salt in crystals a = fraction by weight of less soluble salt in the initial mixture y
=
K and v i are constants from the semiempirical equation formulated by Hill et al. (1940) for the distribution of a pair of isomorphous salts having a common ion, between solid and aqueous phases:
Here R Zand R, are the mole ratios of salts d and B in the liquid and solid pha$es, respectively, n~ is emliirical while K is a distribution coefficient. The authors (1970) have reported previously on the application of Equation 1 to two ternary systems: 1. iiickel-iiiagiirsiunI--ammollium sulfate-Ivater 2 . barium-lead nitrate-water
Crystallization experiments were carried out at a = 0.333 and the fraction by weight of the less soluble salt was determined (yexDt,).Equation 1 was then used for theoretically computing the fraction by weight of the lesh soluble salt ( y t h e o r ) crystalliziiig out of the ternary systems. This was done by choobiiig appropriate values fur the parameters K aiid rn and adopting Euler's method of successive approxiThe values clioseii were ten1 2 , K = 4.2, vi = !vas good agreement between yeXptiand Y t h e o r a t low w values. In his studies on alums, Abu Elamayem (1964) has shown t h a t values of K and m can be fixed for each alum pair, such that they can be employed for predicting g t h e o r over a wide range of a values: (0.909-0.333). Since there !vas good agreement between y t h e o r and y e r v t l , it was theii assumed that these values of K and ~n are characteristic of the given alum system. K e have a similar objective in our present studies with systems 1 and 2. It was of iriterest to investigate whether these system3 could be characterized with definite values of K and m. Hence crystallization experiments were carried out over a broad spectrum of a varying from 0.909-0.0476. Materials and Methods
Preparation of material., experimental procedure, and method of applying correction for the salt>held by the mother liquor adhering to the crystals are the m n e as reported in the earlier communication. (Xnanda Murthy and Mahadevappa, 1970). 'The :iniouiitb of the two salts in the initial mixture were adjusted to give a = 0.909, 0.666, 0.200, 0.111, and 0.0476, respectively. -111 crystallization experiments are carried out a t 30°('. The analytical techniques are reported earlier, but for a = 0.0476, spectrophotoinetric methods had to be used for estimating nickel and barium in the ti70 systems. In systeni 1 in a11 aliquot of the solution of moist crystals, S i was converted into Si-dimethyl glyoxime and estimated at 445 nip (Snell and h e l l , 1959). Xagnesium does not interfere. Barium iii system 2 waa estimated as BaCr04 at' 356 nip (Scott, 1961), after removing lead electrolytically. Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
201
Results and Discussion
SYSTEM (1)
I
I
1
0 1
0.1
0.3
0.2
0.4
0.5
W Figure 1 . Ni-Mg system, K = 3.6 and m = 0.8 for a = 0.909, 0.666,and 0.333;K = 3.6 and m = 1 for a = 0.200,O.l 1 1 ,and 0.0476
SYSTEM (2) a=o.909
From the experimental results, y e x p t l can be calculated for the several trials associated with each value of a. The t m parameters K and m have to be fixed for each syst'ern, before we can calculate Ytheor from Equation 1. hlt'hough there is no clear-cut method for evaluating these parameters, an approximate estimate of these values can be obtained from the equilibrium values of K and m (Hill et al., 1940).K is analogous to a distribution constant and hence is a function of temperature. The slope, m, is a plot of log R, vs. log R Zin Equation 2 . Similarity between Equation 2 and the general la^^ governing the distribution of a solut'e between two immiscible solvents s h o m t,hat the value of m could indicate a kind of iimolecular complexity" in the solid phase. However, a theoretical int,erpretation of this parameter a t this stage may prove to be difficult. An examination of Equation 1 shows that y is a complex function of w and, as such, this differenbial equation has no regular solution. It has to be solved only by numerical methods, such as Euler's method (Ross, 1964) of successive approximations. This requires a proper choice of the values for K and m. If one of the parameters can be fixed, ther;. will be a unique value of the other parameter which 6atisfit.s the approximate solution of the differential equation. In the present case, we intend to fix the values of K by inspection such that m is around unit'y for the two systems. Xi11 et al. (1940) have shown that m = 1 for alums and that' it is less than unity for picromerites. We have chosen K to be 3.6 and 4.2, respectively, for systems 1 and 2. By applying Euler's method of successive approximations, we have cal-. culat,ed Y t h e a r v i t h the above values of K and for a series of values of m around unit'y. Then a statistical method (t test method, Hogg and Craig. 1969) was employed to test for the best fit between Ytheor and yeXptl. In this method a quantity, t , was calculated and is given by
0.8 2 =
IGexptl d(S.e),,,t12
-tI 0.4
I
0
- ;theor
+
z/ac,Tj
(S.e)theorz
where @.e)* is the square of the standard error, n is the number of trials, and y i s the mean of y values in a given trial. As t is a measure of the fit between y e X p t 1 and &heor the smaller the value of t the bett'er is the fit between y t h e o r and y e x p t l . The best fit between y e x p t l and Ytheor is found when m = 0.8, for a = 0.909, 0.666, 0.333 and VI = 1.0 for a = 0.200, 0,111, 0.0476 in system 1; in system 2 , the best fit is obt'ained 1%-henm = 0.8 for a = 0.909, 0.666, 0.333, 0.200, and m = 0.7 when a = 0.111 and 0.0476. Summarizing
w Figure 2. Bo-Pb system, K = 4.2 and m = 0.8 for a = 0.909, 0.666,0.333, and 0.200;K = 4.2 and rn = 0.7 f o r a = 0.1 1 1 and 0.0476
Optical density measurements were carried out on a Beckman D B spectrophotometer. The correction factors (6mAlnz) and (GmB/m) for the salts held by the mother liquor adhering to crystals (Ananda hlurthy and Mahadevappa, 1970) are exact. These range between 0.001-0.085 and 0.003-0.277, respectively, for the Tu'i-lIg system and 0.001-0.070 and 0.005-0.362, respectively, for the Ba-Pb system. 202
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1 9 7 2
System 1: less soluble salt-nickel ammonium sulfate K = 3.6, m = 0.8, a = 0.909, 0.666, 0.333 K = 3.6, V L = 1.0, a = 0.200, 0.111, 0.0476 System 2. lesb soluble salt-barium nitrate K = 4.2, m = 0.8, a = 0.909, 0.666, 0 333, 0.200 K = 4.2, m = 0.7, a = 0.111, 0.0476 The results are shoir n in Figures 1 and 2, n here y is plotted againit w. The solid lines indicate theoretlcal curves TT hile the points show experimental values (yexptl). There 15 good agreement betn een y t h e o r and yeXp,la t all a values. From the above results, we can conclude that nlthuugh our objective of characterizing systems 1 and 2 nlth unique values of K and ,n was not completely successful, the valuts obtained for these parameters could be sufficient for pre-
dicting ytheor in the appropriate range of a values. If a n approsimate estimate of a can be made in any industrial separation involving these systems, the reported values of K and m are quite adequate for theoretically computing the amount of nickel or barium salt crystallizing out of the ternary systems. literature Cited
Abu Elamayem, 11. A,, J . Inorg. .\-ucl. Chenz., 26, 2159-64 (1964). hnanda lInrthy, A . S.,Mahadevappa, D. S., Znd. Eng. Chrm. Process Dcs. Dcw/op.,9, 260-3 (1970). Chlopin, V., Z. Anorg. Allgem. Chcm., 143, 97-117 (192,;). Doerner, H. A , , Hoskins, IT. lI.,J . dnaer. Chem. SOC.,47, G62-7.5 ( 192.5 ) .
Henderson, L., Kracek, F., ibid., 49, 738-49 (1927). Hill, A. E., Ihrham, G. S.,Ricci, E., ibid., 62, 2723-32 (1940). Hogg, I
