1451
V O L U M E 28, NO. 9, S E P T E M B E R 1 9 5 6 The data presented point to the possibility that the copreripitntion of iron by metastannic acid is governed by the Freundlioli cqliation, I = Kc’’% ( I ) , There rrL
5
in fostering the utilization of radioisotopes in the naval matcrial development program, from which this paper is derived
is milligrams of adsorhate
(iron), 111 is milligrams of stannic oxide, and c is concentration of iwn (mg. per ml.) remaining iinadsorbed a t equilibrium. The constaiits K and l / n are particular to the system. A plot of
LITERATURE CITED
ACKLYOWLEDGMENT
(1) Freundlich, I€.,Schucht, H., 2. p h y y i k . Che7n. 85, GGO (1913). (2) Gates, O., Silverman, L., ISD.ENG.CHEY., -1s.~~. En. 11, 3iO (1939). (3) Goldberg, C., Iron Age 166, 84 (1950). (4) Hillebrand, \I-, F., Lundell, G. E. F., “Applied Inorgnnic Analysis,” p. 236, TYiley, Xew York, 1944. (6) Kolthoff, I. M.,ZIoltzan, D. K., Chem. Revs. 17, 293 (1935). (6) Kolthoff, I. l I . , Sandell, E. B., “Textbook of Qusntitative Inorganic Analysis,“ p. 698, llacmillan, Xeiv Tork, 1948. (71 Lundell, G. E. F., Hoffman, J. I.,“Outlinesof blethodsof Clieinpp. 4 i , 210, Wiley, Xew Tork, 1945. (8) bleyer, A, C‘hem.-Ztg. 46, 209 (1922). (9) Sorwitr, C., Boyd, T.F.. Bacht.iger, F,, A s x r . CHF.>r. 21, 1291 (1949). (IO) Powis, F., Z . phi/si/:. C‘hem. 89, 91-110 (1911). (11) Rodden, C. J., “Analytical Chemhry of the blanliattan Project,” vol. VIII-1, p. 375, ilIcGraw-Hill. S e w Tork, 1950. (12) Weiser, H., J . Phys. Chem. 26, 681 (1922). (13) Willard, H. H., Furman, S . H., “Elementary Quantitative .-inalysis,” p. 486, \-an Nostrand, Ken. York. 1940. (14) Zaigmondy, I fi and a concave gradient when f l < fi. Case 11, B. The mixing chamber contains a buffer as before. The reservoir contains a solution of the weak acid which provides a decreasing gradient. Because A; = 0, the second term in Equation 5 becomes 0 and the numerator within the log term of Equation 6 becomes 1. The situation is identical to Case 11, A (Equation 9 ) except that the p H change is negative and the ratio
v/
vo
Figure 4. Effect of different ratios of flow-rates on pH gradient obtained by addition of a salt of a weak acid to a buffer at equal salt concentrations Plot of Equation 11
ANALYTICAL CHEMISTRY
1454 2 .o
I
I
I
I
Figure 6. Effect of different ratios of flow rates on pH gradient obtained by addition of strong base to a buffer at equal concentrations of buffer salt and strong base
Figure 5. Effect of different ratios of base to hutfer salt on pH gradient obtained by addition of strong base to a buffer at equal flow rates Plot of Equation 1.5
Case 111, B . The mixing chamber contains a buffer as before. The ieservoir contains a solution of a strong acid to provide a derieasing pH gradient. I n a manner similar to Case 111, A , an e-qression similar to Equation 14 is obtained. The p H change is negative and the concentration of arid in the reservoir, rather than base, becomes a controlling fnctor. The same considerations apply as in Case 111, A . DI SCUSSIOS
Inasmuch as a buffer composed of a monobasic acid and its salt has a buffering range of onlj- 2 pH units, it is often advantageous to use a polybasic acid and salt or a mixed buffer system. The equations derived above do not describe such situations quantitatively, but the same general considerations apply. For esample, with a citrate buffer in the mixing chamber and sodium citrate in the reservoir the gradients predicted in Case 11, A , are realized except that the rate of change of p H is approximately doubled. I n any case, it is usually necessary to work out the final details by trial and error because it is seldom possible to predict accurately the behavior of the compounds to be chromatographed. Lakshmanan and Lieberman (11, 1 2 ) have shown that a concentration gradient that is concave upwards is most desirable to minimize tailing. On the basis of the limited material now in the literature, particularly with regard to ion exchange chromatography, it seems likely that this is also true with buffered pH gradients. At the same time, it is often desirable to maintain a constant cation concentration in the eluent, when using a cation exchange resin, to minimize volume changes of the resin. This can be done in Cases I1 (Figure 4) or I11 (Figure 6 ) while the pH gradient is controlled by the flow rates. At other times, a superimposed concentrabion gradient is desirable t o speed up the chromatographic process or to supplement a p H gradient. This can be attained most easily in Case I11 (Figure 5 ) while still maintaining a concave p H gradient. These same considerations apply to the anion concentrntion u-ith anion exchange resins. 4 constant volume miser can conveniently produce a concave p H gradient only in Case I11 (Figure 5 ) . If concentration differences exist the concentration gradient will be convex. An equal level arrangement employing identical vessels (fl/f2 = I/'?) provides a concave pH gradient in either Case I1 (Figure 4) or Case 111 (Figures 5 and B), arid if a concentration gradient exist,s i t is linear. It seems likply that this arrangement should Iw of considerable general use. A convex pH gradient, p:irtir~iInrlywhen used with a concentr:rtion gradient, may be u v f i i l for the wparation of one group
I
/ / I
Plot of Equation 16
of compounds from another, or in cases where the stability of the compounds does not alloa large p H changes. Case I (Figure I ) and Case I1 (Figures 3 and 4 ) provide gradients of the type. I n ion exchange chromatography, it is probably never desirable to have a negative concentration gradient, because this would work against the p H gradient. This situation would exist in Case 11, for example, if a concave p H gradient was produced at equal flow rates by employing a low concentration of salt in the reservoir (Figure 3). Neutral salt could be added to the reservoir but a decrease in buffer strength would occur. ThiP decrease in strength magnifies the retarding effect of the ion exchange resin on the p H gradient, a result of the buffering capacity of the resin. Partly for the same reason, it is not always possible to realize very steep gradients. It is made more difficult by the fact that a t values of fl/fi of less than 1, which give the most rapidlj. changing gradients, the volume of the mixing chamber becomes very small. Technical difficulties, primarily the holdup volume of the column, prevent all of the volume from being used. Although sorption gradients cannot increase the resolution of compounds that have a linear sorption isotherm ( 2 ) ,the technique is of more general value in that it speeds up the chromatographic process in an automatic manner (IS) and sharpens the peak;. This allows smaller amounts to be chromatographed n ithout loss of precision. LITERATURE CITED
Alm, R. S., Acta Chem. Scand. 6, 1186 (1952). dlm, R. S., Williams, R. J. P., Tiselius, d.,Ibid., 6,826 (19521. Bock, R. M,, Ling, Ii.,ANAL.CHEM.26, 1543 (1954). (4) Bowman, H. G., Biochem. et Bwphgs. Acta 16, 245 (1955). ( 5 ) Busch, H., Hurlbert, R. B., Potter, V.R., J . B i d . Chem. 196, 717 (1952). (6)
Cherkz, A., Martinez, F. E., Dunn, hI. S., J . Am. Chem. Soc.
75, 1244 (1953). (7) Clauser, H., Li, C. H., Ibid.,76, 4337 (1954). (81 Donaldson. K. 0.. Tulane, V. J., Marshall. L. M., Ax.4~.C H E ~ I . 24, 185 (1952). (9) Drake, B., Arkia K e m i 8 , 1 (1955). (10) Huisman, T. H. J., Schaaf. P. C. van der, Chem. Weekblad 51, 2 (1955). (11) Lakshmanan, T. K., Lieberman, S., Arch. Biochem. Biophus. 45, 235 (1953). (12) Ibid., 53, 258 (1954). (13) 1Ioore. S., Stein, W. H., J . B i d . Chem. 211, 893 (1954). (14) Parr, C. W., Biochem. J . 56, xxvii (1954). (15) Sober, H. A . , Gutter, F. J., Ryckoff, 11.A l . , Peterson, E. I., J . Am. Chem. SOC.77, 756 (1956). (16) Strain, H. H., ANAL.CHEW23, 25 (1951). (17) Synge. R. L. M.,Discussions Farudug SOC.7, 167 (1949). (18) Thompson, A. R., Biochem. J . 61, 253 (1955). R E C E I I E Dfor review January 26, 1956. Accepted M a y 24, 1950
