Liimatta and Spain (3) state that the rings of metal precipitate form in the order of increasing solubility. In their data, however, they show the intersec- tion of the lines representing the rela- tionship between the area of the spot and the concentration of copper and ferric ion solutions. This would indi- cate the solubility of cupric ferrocyanide in relationship to ferric ferrocyanide changes with increasing concentration. Since these authors do not maintain a constant pH but work with solutions whose pH lies below 5 , it would seem this factor might be an important one in interpreting these results.

Furthermore, the solubility series given by Liimatta and Spain (3) is not in agreement with that given by Wilson (4) . The former list copper before iron in their solubility series for the order of increasing solubility; the latter shows the reverse order. Since Liimatta and Spain show the order of solubilities to be reversed a t higher concentrations, it is questioned as to whether the hydrolysis factor should have been con- sidered. According to Hunt (2) iron hydrolyzes to a greater extent than does copper. The pKh values are 2.17 for ferric iron and 7 .5 for copper. If this factor is significant, then the concentra-

52 -

5.0 -

- 4,5- 6 P - 4.0 -

ZO 7.2 7.4 7.6 0.0 Capillary Discharge (sec.)

Figure 4. Area in sq. cm. as func- tion of time of capillary discharge Constant concentration of Cdll) of 5.58 mg./ml. pH varies between 3.04 and 4.82

tion of ferric ions would actually be greater than indicated because the vol- ume of water would be less. With this adjustment there would be a direct proportion between area of the precipi- tated spot and concentration of metal ions, and the two lines reported by Liimatta and Spain (3) would not inter-

sect. Also, it would indicate the order of solubility for the two precipitated salts to be in agreement with the solubil- ity scale given l ~ y Wilson (4) .

Although the method of precipita- tion chromatography is relatively simple, it would seem that some con- sideration should be given to the factor of pH in order to accept the data as being reliable from a quantitative point of view.

Private communication from J. D. Spain suggests that discrepancies might be dependent on ranges of concentration and capillary discharge time. Further investigation is under way.

LITERATURE CITED

(I) Bjerrum, N., Chem. Rev. 46, 381 (1900).

( 2 ) Hunt, J. P., “1Ietal Ions in Aqueous Solution,” W. A. Benjamin Co., New York, 1963.

(3) Liimatta, A. >I., Spain, J. D., ANAL. CHEM. 35, 1898 (1963).

(4) Wilson, C. L., “Comprehensive An- alytical Chemistry,” T’ol. I-B, Elsevier, New York, 1960.

SISTER HELENE YEN HORST ~ I A R Y FRANCES ROGERS

HELEN TANG SIWGH hlarycrest College Department of Physical Science Davenport, Iowa

Accuracy in Determination of Chromatographic Mobility and Its Significance in Identification of Compounds

SIR: In the identification of an un- known compound by chromatographic means, two options confront the inves- tigator. He may first subject the com- pound to a series of class separation processes which, taken as a whole, de- fine the functional groups in the mole- cule and then by chromatographic means select from the small number of possibilities which remain. Alterna- tively, he may rely directly on an accu- rate determination of the compound’s retention value in a known chromato- graphic system to eliminate all but a few possibilities. To date, most efforts to improve the second option have been concerned with increasing the accuracy with which a retention value or mobility can be determined. It is worthwhile to inquire if there is, in the abstract, any difference between deciding between two alternatives and between twenty choices; in other words, how is the accuracy with which a retention value can be determined related to the num- ber of compounds which can be distin- guished?

Suppose we have a fractionation system which effects a separation be- tween various types of molecules such that they appear in some sequential

array. We characterize (physically) a compound by measuring some intensive property (mass, radioactivity, electron capture, etc.) as a function of the dis- placement from the origin, be it in time, volume, or centimeters. From the midpoint of such a distribution, the identifying mobility, elution volume, or retention value of the substance is computed. (We note in passing that in any real system, the compound under- goes a dispersion in the separation process which results in an elution curve of approximately Gaussian shape. This curve reflects processes occurring during the separation, but their contribution will be disregarded since they are, to a first approximation, without specific effect on particular members of the class being fractionated.)

Measurement of the mobility in- volves a certain degree of uncertainty generated by instrumental and opera- tional variations of temperature, eluent flow, chart speed, recorder response, etc. These can be minimized, but not eliminated, by the use of comparisons- e.g., using compounds of bracketing mobility to obtain a close reference point. For purposes of discussing iden- tity determinations, we shall disregard

the actual dispersion of the peak and consider that the compound occupies an interval on the retention scale 6 IM centered about the retention value Jf itself. The quantity 6 -If is taken as 4(s.e.M) where (s.e.x) is the standard error of the replicate measurements of the mobility or retention value. This interval represents the inherent instru- mental limitations on the recognition of two different compounds-i.e., we spec- ify that two compounds are different if the interval separating them is greater than 6 Jf and indistinguishable if this interval is less than or equal to 6 -If. The quantity 6 ;If is appropriately re- garded as the ‘‘mesh size” and may be determined experimentally.

On the one hand, to be of use in the definitive identification of a compound, an instrument must have a 6 -11 small enough to resolve any pair of compounds likely to occur in the same class of compounds. Ostensibly it would not appear possible to forecast the actual separation in retention values between all known (and, as yet, unknown) com- pounds of a given class. Under such circumstances it would not seem feasible to contemplate identifying any com- pound by chromatographic means until

1280 ANALYTICAL CHEMISTRY

II . .&u + 4 1 411 u

all members of the class had been pre- pared and their mobilities determined.

On the other hand, there is the intui- tive realization that the smaller the value for 6 M , the greater is the resolv- ing power of the system. It is errone- ous, however, to regard this as a linear relationship. In a recent discussion, Keulemans (1) points out that the num- ber of compounds to be differentiated from the unknown compound decreases in direct proportion to the accuracy with which a given mobility or retention value can be measured. The implica- tion (not made by Keulemans) that follows is that when there are N com- pounds in an interval x, and 6 M is small enough to satisfy the requirement:

N(6 X) = x

(Le., that one can divide the interval into as many units as there are com- pounds) identity determinations for each and every compound may be achieved.

The error in both of the foregoing considerations, complete impossibility us. complete possibility of identification, lies in the confusion of the term average as opposed to uniform. If there are 1000 compounds in an interval of 100 divisions, the number within one divi- sion of one another will fluctuate about an average of 10 with rather surprising variations. (The contrary contention is that the retention values for a variety of compounds will occur a t uniform in- tervals from each other-i.e., different functional groups will be separated from one another by a simple repetitive spacing. For any appreciable portion of a scale, this contention can be re- jected, as can be seen from most tables of retention values.) As a consequence, when the density of points in an interval is determined by random factors, the requirements for resolution capability take on a markedly different aspect.

To use Keulemans' example, suppose an instrument has a 6 M of 1 unit in the retention index region between 1000 and 1100. Let the density p of reten- tion values in this interval be defined as the fractional occupancy of 6 M aver- aged over the entire interval, in this instance :

N 100 6 M P = -

where N is the total number of com- pounds whose retention values fall within this interval. We are interested in finding out how many randomly placed retention values can be selected before two values are encountered which differ by less than 6 M . This may be examined in two ways, the first of which is as follows: Successive 3 digit numbers in the interval 000 to 999 are drawn from a table of random numbers until 5, 10, 20, 30, or 40 such numbers have been obtained. Each group is arranged in numerical order and ex- amined for pairs which differ by less than 10-i.e., 1 part in 100, or the ratio of 6 M to the interval; occurrence of such pairs marks a potential identifica- tion failure of the system. Figure 1 illustrates the consequences of one such group of trials.

Second, the more general solution can be obtained by considering the situation as an occupancy problem. The proba- bility of finding n values in the interval 6 M is given by :

e-p.pn p(n, 6 M ) = ~

n!

In this instance, we wish to determine the density which results in an overlap no more frequently than, say, once in 20 instances. The easiest solution is to require tha t the probability of finding an interval with no compound or only one compound be 0.95. Then,

1.6 1 1.2 i- 1.0 c

P I I I

o.e 0.6 t I i I

PROBABILITY OF COINCIDENT RETENTION VALUES

Figure 2. Retention value density and probability of coincident retention values

0.95 = (1 + p)e-p

which may be solved by interpolation to obtain the required density p = 0,362- i.e., about 36 compounds in an interval of 100 6 M . Similarly, density values for probabilities from 0.001 to 0.5 may be obtained by appropriate solution of Equation 3 and are shown in Figure 2.

Figures 1 and 2 provide striking dem- onstrations of the effect of the compound or sample density in an interval on the resolution capability of a given 6 M . They indicate that the requirement for accuracy in the determination of reten- tion values is much higher than one might suspect on an intuitive basis. In this instance, to identify a given compound in a region where there were an average of 10 compounds per unit with a certainty of 0.995 would require a 6 1l.I of 0.010 or 0.001%. Clearly, an attempt to increase resolution capability indefinitely is a prohibitively difficult practice when the density of retention values is high. Class separations ap- plied in preceding steps of the identifica- tion procedure are therefore effective in improving the resolution capability of the system if they do no more than reduce the density of points to be con- sidered.

LITERATURE CITED

(1) Ettre, L. S., ANAL. CHEM. 36, No.

PETER D. KLEIN SYLVANUS A. TYLER

8, 31A (1964).

Division of Biological and

Argonne National Laboratory Argonne, Ill. WORK supported by the U. S. Atomic Energy Commission.

Medical Research

VOL. 37, NO. 10, SEPTEMBER 1965 0 1281