A Graphic Method of Studying the Separation of Mixtures bv Immiscible Solvents J
LILA F. KNUDSEN AND DONALD C. GROVE Food and Drug Administration, Federal Security Agency, Washington, D. C. U/V FOR ERGOMETRINE
A graphical procedure is described by which it is possible to predict the ratio of
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the volumes of the solvents and the number of funnels and separations required to give the best separation of the components of a mixture by the use of immiscible solvents.
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1
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U/V FOR ERGOMETRININE N*(D
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HE separation of mixtures by means of immiscible solvents is customarily based on the insolubility of one of the components in one of the solvents. For some mixtures, however, it is not possible to find a pair of solvents which will fulfill this condition. If the distribution coefficients of the components of such a mixture between two solvents differ sufficiently, a separation may be made by passing a solution of the mixture in one solvent through a series of separatory funnels containing the other solvent and repeatedly washing the solution remaining in the funnels with portions of the first solvent. Calculating the proper volume ratio of the solvents, and the number of funnels and washings to give a satisfactorily quantitative separation, is so laborious as to be almost prohibitive. The Bame results may be obtained rather quickly by a graphical procedure. The distribution of any solute between two immiscible solvents, where the molecular weight of the solute is the same in both solvents, is expressed by the formula: X = k -U
-
1--2
(1)
u
FRACTION IN WATER- (XI
where, considering the amount of solute as unity: x fraction of solute dissolved in solvent 1 1 - x = fraction of solute dissolved in solvent 2 u = volume of solvent 1 u = volumeofsolvent2 k = distribution coefficient Solving Equation 1 for 2, k! X=-
U
FIGURE1. SEPARATION OF ERGOMETRINE AND ERGOMETRININE Using two separatory funnels and one to seven eeparations
The specific problem used in the development of this method was the separation of the stereoisomeric ergot alkaloids, ergometrine and ergometrinine, wherein i t was desired to obtain the ergometrine as free as possible from its stereoisomer. This was accomplished by their distribution between water and ether, and is here used as an example of the general application of the method. For the purposes of this presentation, the term “separation” indicates the passing of a given volume of one solvent
(2)
lfk; Thus, the fraction present in solvent 1 may be calculated for any ratio of volumes of solvents.
TABLE I. DISTRIBUTION OF A SOLUTE BETWEEN Two IMMISCIBLE SOLVENTS Separation 1st 2nd 3rd 4th 5th nth
Total solute 1
First Funnel Fraction in water
Fraction in ether
Total solute
Second Funnel Fraction in water
-
1--2
(1 (1 (1
(1
Fraction in ether z(l 2)
- z)l - =): z) -- =)*-I a=- r(r
+ 1)
2!
2!, 3!, etc. = factorial 2, factorial 3, etc.
556
Total solute
rth Funnel Fraction in water
Frootion in ether 2‘-1(1 z)
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ANALYTICAL EDITION
July 15, 1942
557
successively through each of the entire series of funnels conTABLE11. SEPARATION OF ERGOMETRINE AND ERGOMETRININE taining the other solvent. Let us assume a series of funnels u/c 1 Separation 3 Separations 5 Separations 7 Separations containing equal volumes of ether through which a water A B A B A B A B solution of the alkaloids is shaken successively. This is % % % % % % % % followed by successive portions of water, each equal to the Using Two Funnels volume of water used as the original solvent for the alkaloids. 6 3 93 1s 0 57 1 82 0.1 The distribution of the alkaloids in the various layers in the 56 19 100 28 2 94 9 99 0.4 99 55 100 72 78 8 32 100 1.0 separatory funnels is shown in Table I. 100 93 100 28 99 74 100 3.0 93 From the data in this table, a series of curves are prepared Using Four Funnels as illustrated for two funnels (Figure 1) and four funnels 70 0 0 0 22 0 48 0.1 3 (Figure 2). Since we are concerned only with the total 100 5 97 2 0 83 0 0.4 33 amount of solute in the combined water extracts, which is 17 100 30 0 97 5 100 1.0 60 100 89 72 84 9 100 43 100 3.0 expressed as per cent of the original amount of solute and called “y”, the curve for one separation, Figure 1, represents a graph of the values of y = 100 z2 (see column 6, Table I, first separation), that for two separations represents the values of y = 100 [z2 2z2(1-2)] (sum of first and second these values of k independently in Equation 2, together with separations, column 6, Table I),that for three separationsrepa volume ratio (u/v = water to ether) of 0.3, the values of x resents the values of y = 100 [%* 2r2(1-z) 3 ~ ~ ( 1 - % ) ~ ] for , ergometrine and ergometrinine are calculated to be e t a Only two sets of curves are illustrated, but similar 0.694 and 0.105, respectively. The values of z thus obgraphs may be prepared for any number of funnels and tained are marked off on the z scale above the graph, each separations required. Since these values are independent mark being identified by its appropriate u/v ratio as indicated of the nature of the solute and solvents, they can be applied by the figures above the scale. to any combination. The intersection of a vertical line projected from these For the application of these curves to any specific problem, points and each of the curves gives the per cent of the oria scale, as shown above the curves in Figures 1 and 2, must ginal amount of these alkaloids which has been carried into be constructed for the two substances to be separated. This the combined water extracts for the number of separations scale consists of the values of z for various ratios of the solindicated. Table I1 gives a tabulation of some of these vents as calculated from Equation 2. For example, the values obtained from Figures 1 and 2, where A and B repdistribution coefficients, k, for ergometrine and ergometresent the amount of ergometrine and ergometrinine, rinine between water and ether were determined experirespectively, in the water extracts from two and four mentally to be 7.55 and 0.39, respectively. By substituting funnels with varying numbers of separations. It is obvious that an optimum separation calls for the highest possible recovery of A and a t the same time the lowest possible contamination with B. An inspection of Table I1 shows that no separation of U/V FOR ERGOMETRINE these alkaloids approaching quantitative proportions can be 2 obtained with only two funnels. I n Table 11, however, r ? ” ? ? ? a t a u/v ratio of 0.4, five and seven separations, using four 0 2 0 0 0 - N I I I L I I I I I I I funnels, give practically complete recoveries of ergometrine with only slight amounts of ergometrinine. A more de> U/V F O R ERGOMETRININE tailed survey of the points in this region on Figure 2 reveals N t a 0 that, a t a u/v ratio of 0.3, seven separations give a 99 per cent recovery of ergometrine and 2 per cent of ergometrinine. It is possible that the use of more funnels would give an even more quantitative separation. The accuracy of the separation to be desired will be dictated by the nature of the problem, and with a set of curves, as illustrated here, it is possible, knowing only the distribution coefficients of the components of a mixture, to determine the optimum ratio of solvents and the least number of funnels and separations required to give the desired results. In practice, these curves, which are applicable to any P situation and need be prepared only once, should be plotted W z on a fairly large scale to facilitate their use. The single x a scale prepared for the specific mixture, if plotted on the same z ,scale on a strip of graph paper, may be applied to all the 0 series of graphs. 0 To assure sufficient shaking time for the various extractions, it is usually well to determine experimentally the W time required for the distribution of the solutes between the Isolvents to reach equilibrium. 3
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+
+
::2
d
-
-I
g
-0
0.2
0.4 FRACTION
0.6
0.8
I N WATER-00
1.0
FIGURE2. SEPARATION OF ERGOMETRINE AND ERGOMETRININE Using four separatory funnels and one to seven separations
Acknowledgment The authors are indebted to F. H. Wiley for continued encouragement and assistance and to P. A. Clifford also for helpful suggestions and criticisms.
