CORRESPONDENCE
The “Separation Factor”
One can conclude from Table I that because the four values for D are no more constant than those for A, the homogeneous distribution equation used by Weaver is no more valid for his ovalate SIR: I n the March 1954 issue of ANALYTICAL CHEUIGTRY there system than is the logarithmic distribution equation. appear three papers (12-14) by Boyd Weaver, in which he introill1 the data of Table I were included by Weaver in a previous duces the “separation factor” as a criterion for the evaluation of report (16). with a conclusion that there is apparently no correlafractional separation processes. The undersigned believe that tion between separation factor and degree of precipitation. the general application of the separation factor, as proposed by However, in the subsequent publication (14) in ASALYTICAL Weaver, can lead to completely erroneous conclusions. CHEMISTRY, he concluded, on the basis of only part of the data of First, one might infer from these papers that the term “separaTable I, that there appeared to be a slight trend for the separation tion factor” is new so far as precipitation processes are concerned. to improve as the degree of precipitation is increased; with However, Weaver’s equation (12) utilizing this factor is matherespect to this latter statement, it is possible to select data from matically identical with that proposed by Henderson and Kracek ( 1 5 ) for an opposite conclusion. The undersigned do not understand why any of the data were discarded in order to arrive at a (6) D = (Ra/Ba)oryltsle different conclusion. I n either case, a trend in the separation (Ra/Ba)Boiution factor indicates that the homogeneous distribution law is not completely valid for this system. It should be noted for the record that Henderson and Kracek I n two of Weaver’s papers (12, 1 3 ) separation factors have been were criticized by Chlopin (a) because the latter author (1)had calculated for a praseodymium-cerium mixture from data by previously stated an identical expression, as follows: Gordon, Brandt, Quill, and Salutsky (4). The latter paper contains no data for praseodymium-cerium mixtures, in den Kristallen enthaltendes Ra in Prozenten der Gesamt-Ra-Xenge but Only data for praseodymium-1anthanum and cerium-lanthanum mixtures. R e wonder, therein den Kristallen enthaltendes Ba in Prozenten der Ges amt-~a-Menge Kf fore, how these data were used to calculate separain d. Mutterlauge verbliebenes Ra in Proaenten d. Ges,amt-Ra-Menge tion factors for praseodymium-cerium mixtures. in d. Mutterlauge verbliebenes Ba in Prozenten d. Gasamt-Ba-lfenge -4s another example, we cite the text by Kolthoff and Sandell (8) which shows the following equation:
Table I.
Fractionation of Samarium-Seodymium >fixtures
Degree of Precipitation,
gr,
D
1 H4b 1 H6b
16 8 b 36.3b 65.7b 75.16 2.8 6 5 7.0 16.2 36.7 44 8
Secondly, and more important, Weaver apparently overlooks another aspect of precipitation processes. This is concerned with the mode of distribution within the crystal of a substance coprecipitated with another as in a fractional precipitation procese. The separation factor-commonly known as the homogeneous, distribution coefficient (Il)-is valid for a system in which one component is homogeneously distributed throughout the precipitate. In another mode of distribution, one component is logarithmically distributed. Doerner and Hoskins ( 3 ) describe such a system by the following equation:
Separation b’actors,
1,706 1.83b
\=
p9 52 44
38
1 56 1 46 1 i4 1 .55
1. ii3
1 66 1.78 1 . ti7 2.14 1.54 2.12 1.42
45.1
52.4 54 2 74.3 83.5 89.2 a h values calculated by us. (16). b D a t a by Weaver ( 1 4 ) .
Remaining data taken froin ORNL-1629
Ra++initial = h log Ba++initial log Ra++fin.l Ba++ri,,i ~
In the paper describing the use of mandelic acid ( I S ) , separation factors are reported in Tables V, VI, and VI1 for pairs of rare earths in complex systems containing from four to seven rare earths. I t is our belief that it may be incorrect to apply a distribution law describing a binary system to such a complicated mixture of rare earths. When we calculated separation factors for those instances where there are blank spaces in the tables, we obtained several values less than 1.0. In these cases the order of precipitation of the elements would be the reverse of that reported by Weaver.
The logarithmic distribution coefficient, A, is valid for the case xhere equilibrium exists a t all times between each infinitesimal layer of the crystal, during the process of its formation, and the solution. This is in contrast with the homogeneous distribution concept which demands that the whole crystal must a t all times be in equilibrium with its solution. Systems, such as Weaver’s (13, 1 4 ) , which utilize precipitation from homogeneous solution, would normally be characterized by a logarithmic distribution because of the gradual formation of the precipitate and the concomitant equilibrium state between the successive crystal surfaces and the solution (3, 6 , 7, 9, 10). On the other hand, a long contact time between crystal and solution, with possible resulting resolution, might partially disrupt the system so that it is characterized by neither mode of distribution. We believe that this is the case with the data of Table I1 of the third Weaver paper ( I d ) , as is shorn-n by the first four values in Table I.
LITERATURE CITED
(1) Chlopin, V., 2. anal. allgem. Chem. 143, 97 (1925). (2) Chlopin, V., 2. anorg. Chem. 172, 318 (1928). (3) Doerner, H. A., and Hoskins, W. M., J . A m . Chem. SOC.47, 622 (1925). (4) Gordon, L., Brandt. R . A., Quill, L. L., and Saiutsky, XI. L., A N A L . C H E M . 23, 1811 (1951). (5) Gordon, L., Reimer, C . C . , and Burtt, B. P., Ibid., 26,842 (1954).
138
139
L U M E 28, N O . 1, J A N U A R Y 1 9 5 6 Hendenon, L. M., and Kracek, F. C., J . Am. Chem. SOC.49, 738 (1927). Hermann, J. rl., “Separation of Americium from Lanthanum by
Fractional Oxalate Precipitation from Homogeneous Solution,” U. S. rltomic Energy Commission, AECD-3637 (July
less error in these analyses. This minimizes the error in X factors for small degrees of precipitation, but leaves considerable possibility of error in extensive precipitations, where the compositions of the total precipitate and original are similar.
22, 1954).
Kolthoff, I. hl., and Sandell, E. B., “Textbook of Quantitative Inorganic Analysis,” 3rd ed., p. 123, llacmillan, New York, 1952.
Table I.
Salutsky, M. L., Stites, J. G., and Martin, A . W., ANALCHEM. 25, 1677 (1953).
Shaver, K., Division of Physical and Inorganic Chemistry, 125th Meeting, AM.CHEM.SOC., Kansas City, Mo., 1954. Wahl, A. C., and Bonner, N. -4.,”Radioactivity Applied to Chemistry,” p. 106, Wiley, New York, 1951. Weaver, B., ANAL.CHEM.26, 474 (1954). Ibid., p. 476. Ibid., p. 479.
(Yariation in degree of urecipitntion) Ratios of SmnOa t o iFd20P St-Paration Factor Degree of P p t n , Filtrate ~~7% Precipitate (calcd.) D h 1 59 0 988 1.61 2 8 1.55 1 . 53 1 49 0.973 6 6 1,32
MURRELL L. SALUTSKY LOUISGORDOS
SIR: I n an article published in ANALYTIC.4L CHEMISTRY[26, 474 (1954)l I pointed out that most workers engaged in difficult separations, such as between the rare earths, have failed to publish any standards by which the efficiency of their separations can be measured I n m y own separations, and I assumed in those of most other M orkers, there was a schematic arrangement of pairs of fractions. The two fractions of a pair !yere usually of nearly equal quantity. .is I was interested in the difference between the members of a pair, I expressed the degree of separation of two elements as the ratio of the relative abundances of these elements in the two fractions and called this the separation factor. I applied this rrlationship to the measurement of the efficiency of the few other vparations published with adequate data, and in tTvo concuriently published articles applied it t o m) own work on two methods of separating rare earth. Subsequently L Gordon and 11 L. Salutsky have pointed out that this homogeneous distribution factor, D , applies strictly only t o separations in vhich the two fractions are in complete equilibrium throughout the process of separation, as in liquidliquid extractions. In pi ecipitations or crystallization8, espec~:dly those made from homogeneous solutions, the solution is in equilibrium only with the surfaces of the solids. The separation efficiency here can be iheasui ed more accurately by the logarithmic distribution coefficient,
1 68
7 0 I6 2 16 8 35 7 36 2 44 8 45 1 52.4 54 2 55 7 74 3 75 1 83 5 89 2
Weaver, B., “Fractional Separation of Rare Earths by Oxalate Precipitation from Homogeneous Solution,” U. S. Atomic Energy Commission, ORNL-1629 (Dee. 4, 1953). Nonsanto Chemical Co. Dayton, Ohio Syracuse University Syracuse, N. Y.
Fractionation of Samarium-Neodymium Mixtures
a
1.44 1 RR 1 35 1 48 1 33 1.35 1.32 1.30 1.33 1.24 1.22 1 13 1.03
0 962 0.931 0.904 0.848 0,800 0.792 0.782 0.737 0.735 0 700 0.530 0.537 0.528 0.770
1,73 1.55 1.84 1.59 1,85 1 08 1.73 1 i9 1.77 1.90 2.34 2.27 2 14 134
Originally 1: 1.
The data in Table I show the X factor t o be considerably more nearly constant than the D factor. However, its use does leave one rvithout a simple relationship betveen the products of a separation. I do not know why the X values calculated solely on the basis of analyses of precipitates are more nearly constant than if calculated from filtrates, but this is a fact in this instance. As D values involve both fractions, they are not so greatly affect,ed by analytical inaccuracies in only one fraction. I can understand the critics’ puzzlement regarding the difference in ORSL-1629 and the published article. The embarrassing fact ip that, while the article was not submitted until after ORXL1629 had been written, the copy submitted was an earlier version written some time before the additional work given in the larger table had been done. There was no selection of items. The enlarged table had been given at Chicago, and I intended to publish it. While all analyses of rare earths are subject t o some error, the most obviously inaccurate analyses were obtained in the case of 16.8% precipitation, the case which Gordon and Salutsky continually point out as typical example. I should prefer to omit it from the table. BOYDWEAVER
Union Carbide Xuclear C o . Oak Ridge, Tenn. Both factors have appeared in previous publications. The applicability of each expression can be tested by calculating it for different degrees of precipitation. I n my article on separation of rare earths by oxalate precipitation I applied the D factor t o a few varying degrees of precipitation of samarium-neodymium mixtures consisting initially of equal amounts of the oxides of these elements. Subsequently the data n e r e extended hv more euperiments. I have now calcuh t e d both D and X factors for the full set of experiments. Littention must be called t o the fact that when the extent of precipitation iq small, the composition of the final fraction is only slightly different from that of the initial material. A slight error in malysis, easily made in the case of rare earths, can make a great difference in the logarithmic ratio. I n the present case the compositions of the final fractions have been calculated from those of the original mixtureP and the p i wipitates, as there appeared to be
1.73 1.51 1.75 1.22 1.65 1.48 1.51 1.51 1.50 1.55 1.50 1.55 1.42 1.12
“Standard Addition” Method of Polarographic Analysis SIR: One of the most valuable technique3 of quantitative polarographic analysis is the standard addition method devised by Ilohn ( 1 ) and discussed by KolthofT and Iingane ( d ) , Taylor ( 4 ) ,and Meites (3). Startingwith a known volume of the sample, the diffusion current, il, of the desired wave is measured; then a known volume of a known solution of the sulxtance being determined is added, and the diffusion current, il, is measured again. The calculation of the concentration of the substance in question in the original solution follom from an equation of the form C, = ilcCs/ [i2(1-
+ v) - i I V ]
(1)
