505
V O L U M E 26, N O . 3, M A R C H 1 9 5 4 This instrument has proved to be very sensitive and the values observed were readily reproducible. The densitometer is adjusted to 0% transmittance density against the edge of each filter paper strip and readjusted as readings are made progreseively up the paper strip. Figure 2 shows curves of the various amino acid standards Then color density units are plotted against micrograms of a-amino nitrogen. RESULTS
Block (3)has published data for thr analysis of samples of brain neurokeratin and also determination of the amino acids present in casein ( 2 ) by the use of paper chromatograms. He has reported an over-all accuracy of & l o % by his procedure.. Stein and Moore have analyzed crystalline bovine serum albumin (BSA) by the use of starch column chromatography ( I S ) . Likewise, Redfield and Guzman Barron ( 1 2 ) have analyzed bovine serum albumin and alro a partial synthetic amino acid mixture by paper chromatographic procedures with excellent results. A similar studywasundertakenat thislaboratory, in which a mixture of 15 amino acids designed to reproduce the composition of amino acids as found in crystalline bovine serum albumin were carried through an acid hydrolytic procedure ( I S ) and analyzed by the paper chromatographic procedure described above. Table I shows the comparative results obtained from this experiment. The individual estimations of the composition of the amino acid mixture are in reasonably good agreement with the actual composition of the synthetic mixture. The assay data and the actual composition for each of the amino acids are presented in Table I. The computation of the standard errors was used as a measuie of the accuracy of the assays. All of the constituents, 15ith the exception of lyqine, glutamic acid, and glycine, were within thc experimental confidence limits ( P = 0.95). The differences between actual composition and the experimental mean, howevcr,
are only -7.84% for the glutamic acid, +9.21% for lysine, and +8.24% for glycine. Analytical data on the amino acid cornposition of crystalline proteins such as p-lactoglobulin (Table 11) and bovine serum albumin when determined by this method have been in good agreement with previously published (12, I S ) values. In general, the procedurrs which have been described provide a less tedious, more rapid, and reasonably accurate approach to the analysis of protein hydrolyzates than has previously been available. ACKNOWLEDGMENT
The authors wish to acknowledge the technical assistance of John RoPevear in the early stages of this work and to express thanks to C. F. Marquardt for the statistical evaluations and also to Jean Hogan and .Janet Dunlevy for photographic apsistanre. LITERATURE CITED
(1) .kcher, R., Fromageot, C., and Justia, l l . , Biochini. et B i o p h y s . Acta, 5 , 81 (1950). ( 2 ) Block. R. J.. A s a ~ CHEY.. . 22. 1327 (1950). (3) Block, R . J., Arch. Biochem. a n d Bibphys.. 31, 266 (1951). (4) Block, R. J . , Proc. SOC.Exptl. Bid. M e d . , 72, 337 (1949). (5) Block, R . J., Science, 108, 608 (1948).
(6) Block, R. J., and Bolling, D., “.-imino .kcid Composition of Proteins and Foods,” 2nd ed., Springfield, Ill., C. C Thomas, 1950.
(7) Fowden. L., Biochetn. J . (Londorc),4 8 , 3 2 7 (1951). (8) I b i d . , 50, 355 (1952). ANAL.C H E W ,24, 650 (1952). (9) JIcFarren, E. F., and llills, J. d., (10) Niettinen, J. K., and T’irtanen, d. I., Acta Chem. Scand., 3, 459 (1949). (11) Patton. il. R., and Chism. P., ..~N.AI.. CHEM.,23, 1683 (1951). (12) Redficld, R. R., and Guzman Barron, E. P.,Arch Biochem. anti BiophZjs., 3 5 , 4 4 3 (1952). (13) Stein, 15‘. H., and JIoore. S., J . B i d . Chem., 178, 79 (1949). (14) Toennies, G., and Kolb, J. J., AN.AL.C H E x , 23, 823 (1951).
RECEIVED for review July 3, 1952. Accepted December 28,
1953.
Behavior of the Condensed Phosphates in Ani on-Exc hange Chromat ography JOHN BEUKENKAMP, WILLIAM RIEMAN 111, and SIEGFRIED LINDENBAUM School o f Chemistry, Rutgers University, N e w Brunswick, N. 1. There is need of a rapid and more accurate method for the analysis of mixtures of the lower condensed phosphates, ortho-, pyro-, tri-, trimeta-, and tetrametaphosphates. The successful application of ion-exchange chromatography to numerous difficult analytical separations suggests the possibility of developing an ionexchange procedure for the analysis of mixtures of the polymeric phosphates. A s an approach to this problem, equations were developed to describe the elution graphs of the various phosphoric acids as functions of the pH and concentration of the eluant solutions. Several dozen elutions were performed which indicate the reliability of these equations. This work advances the theory of ion-exchange chromatography and points the way to the development of an accurate procedure for the analysis of mixtures of the polymeric phosphates.
T
HE objectives of this investigation are: (1) to develop equations, based on the plate theory of Martin and Synge ( 6 ) , for describing the elution graphs of polyprotic acids as functions of the concentration of potassium chloride and the pH; (2) to derive an equation by means of whirh it vi11 be possible to calculate the column height required for a given separation; (3) to test the
reliability of these equations by elutions of ortho-, P>TO-, tri-, trimeta-, and tetrametaphosphoric acids; and (4) to use these equations for the development of an ion-exchange procedure for the analysis of a mixture of these acids or their salts. The first, second, and third of these points are described in this paper. The fourth will be reported in a later paper. DERIVATION OF EQUATIONS
Notation. The following notation is used in this paper. a = a parameter in the Gaussian equation, No. 2. -4= chemical s~7mbolfor an acid radical. C = the distribution ratio of an acid-i.e., the total quantity of its anions in the resin of any given plate divided by the total quantity of the acid (both ionized and nonionized) in the solution of the same plate. e = base of the natural system of logarithms. E l , E,, E a , etc. = apparent equilibrium constants for the,exchange of a primary (secondary, tertiary) anion. See Equations 7 to 9. F = fraction of solute eluted between any two given U values. G I R , G ? R , G 3 R = quantity of the primary (secondary, tertiary) anion in the resin phase of any given plate, millimoles. GoS = quantity of nonionized acid in the solution of the same plate, millimoles. GIs, G2S, G3S = quantity of the primary (secondary, tertiary) anion in the solution of the same plate, millimoles.
SO6
ANALYTICAL CHEMISTRY
H = height of resin bed, cm. J = total amount of solute added, meq. K = classical ionization constant (in terms of concentration). K = thermodvnamic ionization constant (in terms of activities). L = the fraction of the total solute in the interstitial volume of the last plate. L* = the maximum value of L. M = concentration of solute in the eluate, millimoles per milliliter. AI* = maximum value of M . p = total number of plates in column. P = plates per centimeter. Q = capacity of the resin, meq. per gram. R + = chemical symbol for cation of resin. t = parameter in probability equations. II = volume eluted, ml. C* = U when . I [= M*. M* U , = U when AI = -. U', C" = values of L'between which 99.9% of the given solute will be eluted. v = interstitial volume of one plate, ml. V = interstitial volume of the column, ml w = weight of resin per plate, grams. IV = weight of resin in column, grams. p = ionic strength. u = standard deviation. [ ] = concentration in moles per liter for a constituent in the solution phase, or concentration in mole fraction for a constituent in the resin phase.
Jf
U* = CV
+v
(1)
'M* L*J V
Since v = V/p
llayer and Tompkins ( 7 1 have shown that
Therefore
Combination of this equation with Equation 3 yields
v
A1f*e-4U-u*)2
2C(C
+ 1)
Elimination of V from this equation with the aid of Equation 1 yields
a = -US
tipw
Substitution of this value in Equation 2 yields the general elution equation
This equation is more convenient in its logarithmic form log M = log M *
;
- 0 . 2 1 7 ~(C"()I
Equation for the Evaluation of
___ ;*U*)2
p . From the definition of
(5) Ca,
it follows that
In previous publications ( 2 , 9, 11) the authors used the equation U* = CV because of a misinterpretation of the work of Mayer and Tompkins. Data from elutions of sodium and potassium with hydrochloric acid (cation exchange) and data from elutions of primary orthophosphate with potassium nitrate (anion exchange) show that Equation 1 is valid, and is more accurate than Equation 1 of a previous publication ( 2 ) . M as a Function of M * , p , C, U*, and U. Mayer and Tompkins have also derived an equation, number 5 of ( 7 ) , which describes the elution graph of almost all properly performed ion-exchange elutions. They present a graph to indicate the close conformance of one actual elution to this equation, Unfortunately, the equation with its large fractional exponents is awkward to use. I t is well known that this and most other ion-exchange elution graphs resemble very closely the Gaussian equation ( 7 , 14). I t is possible, therefore, to develop a semiempirical equation of the Gaussian type to describe the elution graphs. The Gaussian equation may be written
'U =
LJ -
Therefore
U * as a Function of C and V . I n an extension of the plate
theory of Martin and Synge (e),Mayer and Tompkins ( 7 ) have shown that CV ml. of eluant have passed through the column when the solute undergoing elution is a t its maximum concentration in the last plate, and hence also in the effluent. If the collection of the effluent is started immediately after the addition of the sample (as is done in all of the work in this laboratory), an additional V ml. of effluent (the liquid in the resin bed before the sample is added) have been collected when the solute concentration in the effluent is a maximum. Therefore
=
(2)
Since all of the solute added to the column for elution is eventually recovered in the eluate, it follows that
Values of U* and U,can be read from an experimentally determined elution graph. C can be evaluated from Equation 1. The experimental procedure for the determination of V has been published (9). Thus Equation 6 can be used to evaluate p . Erroneous equations, differing slightly from Equations 5 and 6, have been published previously (2,9, 11 ). C as a Function of the pH and Concentration of the Eluant. Consider the elution of a weak triprotic acid, HSA, through a column of RCI with a buffered chloride solution as eluant. Whatever the pH, there will be a t least a small concentration of each of its ions in solution. Therefore three exchange reactions occur RC1 H2ARH2.4 C1-
+ + + + 2C12RC1 + HA-- + 3RC1 + A - - RIA + 3C1$
for which the equilibrium constants are [RHzA][Cl-1 [RCI][HZA-] The concentration of solute in the interstitial volume of the last plate, or in the eluate, is
[R?H.4][Cl-]'
E2
= [RC1I2[HA--]
507
V O L U M E 2 6 , NO. 3, M A R C H 1 9 5 4
The quantity of Ha.\ (or its salt) taken for an elution should be so small that the resin in any plate remains almost entirely in the chloride form during the entire elution. Therefore [RCI] is essentially equal to unity in these three equations. The quantity of RH, 1 in the resin of any given plate is
G:
=
QIU
[RHAI
Combination of this ~ i t Equation h 7 yields (10) Analogously
Equations 19 and 20 are less troublesome to use than would appear a t first sight .4t any given pI1, several terms are negligible so that it is never necessary to consider more than two terms in the numerator and the same number of terms in the denominator. This followvs from the fact that a t any pH only two of t h e ions can exist in appreciable concentration. Column Height Required for a Given Separation. If two solutes, designated by the subscripts 1 and 2, give overlapping elution graphs and hence a poor separation, as illustrated in Figure 3,A, it is generally possible to change their C values by changing the pH or the concentration of the eluant or by adding a complex
