Supplementation of the medium with casein hydrolyzate, vitamins, purines, and pyrimidines eliminated this effect. Hydrolysis with 3 ml. of 0.1Nsodium hydroxide usually gave complete cleavage of panthenol to pantoic .a&d. However, incomplete hydrolysis may occur a t this concentration of alkali with some samples of low potency. Because of the large sample aliquot that would then be required, sufficient buffering capacity may be developed within the system to neutralize the alkali. With samples of low potency, this difficulty can be avoided by doubling the amount of 0.1N sodium hydroxide used for hydrolysis (6 ml. used in place of 3 ml.). I n tests with pharmaceutical preparations, the E. coli method compared favorably with the inhibition assay as to stability of response, precision, and reproducibility. Both methods were simpler to use and more suitable for
routine analysis than the Acetobacter assay. The E . coli 99-4 method was more sensitive than the inhibition assay and seemed particularly suitable for the routine estimation of panthenol in pharmaceutical preparations. ACKNOWLEDGMENT
The culture of Escherichia coli 99-4 used in this study was obtained through the kindness of Werner K. Maas, Bellevue Medical Center, New York University, New York. The authors acknowledge the technical assistance of Fernand J. Noel. LITERATURE CITED
(1) Bird, 0. D.,McCready, L., ANAL. CHEM.30, 2045 (1958). (2) Davis, B. D.,Proc. Natl. Acad. Sci. U . S. 35, 1 (1949). (3) Davis, B. D.,Mingioli, E. S., J. B a o terzol. 60, 17 (1950).
(4) De Ritter, E., Rubin, S. H., ANAL.
CHEM.21, 823 (1949). (5) Maas, W. K.,Bellevue Medical Center, New York, personal communication. 1956. (6) Maas, W. K., Davis, B. D., J . Bacteriol. 60, 733 (1950). (7) Maas, W.K.,Vogel, H. J., Zbid., 65, 388 (1953). (8) Schmall; M., Wollisch, E. G., ANAL. CHEM.29, 1509 (1957). (9) Szalkowski, C: R., .Davidson, J. H., Jr., Ibid., 25, 1192 (1953). (10) United States Pharmacopeia, 15th Rev., Mack Publ. Co., Easton, Pa., 1956. (11) Weiss, M. S., Sonnenfeld, I., De Ritter, E., Rubin, S. H., ANAL.CHEM. 23, 1689 (1951). (12) Williams, W. L., Broquist, H. P., Snell, E. E., J . Biol. Chem. 170, 619 (1947). (13) Wollisch, E. G.,Schmall, M., ANAL. CHEM.22, 1033 (1950). RECEIVED for review March 2, 1960. Accepted August 10, 1960.
Repeated Extractions A Method of Analyzing a Mixture of Labeled Co m pounds GOSTA RUDSTAM CERN, European Organization for Nuclear Research, Geneva, Switzerland
b A method of analyzing a solution containing a mixture of labeled compounds is presented. It can b e used when the compounds at hand are extractable with different partition coefficients into the same solvent (even after addition of complex-forming reagents). The method is of greatest value when the different compounds depend on each other and interchange at a rate which is not negligible in comparison with the time required for the analysis. By following a fixed time schedule during the experiment it i s often possible to correct accurately for interchange between the constituents of the solution during the analysis, and to determine their concentrations a t the beginning of the experiment.
A
COMMON analytical problem in radiochemistry is to analyze a solution containing a mixture of compounds labeled with radioactive tracers. If the different compounds are labeled with different tracer atoms, the radiation characteristics of these may be sufficiently different to allow a direct determination by differential countingfor instance, 7-spectroscopy or absorption methods. However, when the game tracer atom is used to label several
1664
ANALYTICAL CHEMISTRY
compounds, a chemical separation must precede the activity measurement. The method of analysis proposed here is intended primarily for a solution containing a mixture of compounds labeled with the same tracer atom. The solution is extracted repeatedly with fresh portions of a suitable solvent into which the compounds are extractable with different partition coefficients, and the activities of the successive portions are measured. From an analysis of these activity data the composition of the solution can be determined. EXPERIMENTAL
Apparatus. The apparatus required is simple. For extractions with a heavier solvent a simple separation funnel is adequate. As many partition coefficients change rapidly with temperature, the funnel should be thermostated. Furthermore, i t is advisable to use some means for facilitating the addition of measured portions of the solvent. Figure 1, A , shows a suitable arrangement. If the solvent is lighter than the solution t o be extracted, an apparatus similar to the one of Figure 1, B, can be used. The upper phase is easily removed after the extraction. Procedure. Add a measured amount of the solvent to the solution
and stir for a certain time. When the phases have separated, the solvent is removed and a fresh portion is added. The whole procedure is repeated a suitable number of times. It is important to keep a fixed time schedule for the procedure if the constituents of the solution depend on each other. By doing so, it is possible t o correct for interchange between the components during the experiment. The activity of the successive portions of the solvent is measured with any suitable device, such as a scintillation counter. ANALYSIS OF EXTRACTION DATA
Independent Constituents. Consider a case where a liquid phase A containing i independent solutes of concentrations c i is extracted repeatedly with equal volumes (equal to the volume of phase A ) of another phase B. The coefficients for the partition of the solutes between the second phase and the first one are denoted by gi. I n order t o simplify the formulas, the symbols p i are introduced by the relation :
The nth portion of phase B will contain the ith component in concentration (ci)n:
Figure 1 .
Apparatus for repeated extractions A. 6.
( ~ 8 ) "
= C, q b (1 - pi)"
lighter phase Heavier phase
The total concentration of all the solutes can evidently be written as follo\vs : 1
For large values of n the constituent with the smallest partition coefficient (here assumed to be PI) will dominate, as the factor q , ( l - p , ) " of all other components will ultimately become negligible in comparison with pl(1 pi)". Thus. if log (CB),,is plotted us. n, a straight line results for sufficiently large valuw of n. log
(CB)n
-+
log
CiQi
+
?L
log (1 - pi) ( 4 )
This line has the slope log(1 - p l ) , and its intercept for n = 0 is equal to log clql. From these data both q, and c1 can be determined. The term clql (1 p l ) " is then subtracted from (CB)" to yield a second function (CB'),. By plotting this function us. n on a semilogarithmic scale the partition coefficient and concentration of the component with next lowest partition coefficient are obtained. The same procedure is repeated to yield the partition coefficients and concentrations of the remaining components of the solution. The method outlined above is analogous to the resolution of a complex decay curve of a number of radioactive isotopes into its components, and the same graphical technique is conveniently applied. Difficulties may arise if the smallest partition coefficient is very small, or if the largest one is very large. If PI is very small. the line corresponding to Equation 4 will have a small slope, and the determination of pi (but not of el) is difficult. For large values of n, however, the following relation is valid
-
(CB)"
(2)
(C'4)"
(5)
Thus ql is obtained by plotting the concentration ratio ( C B ) J ( C A ) ~us. n. On the other hand, if one of the components has a very large distribution coefficient, the slope of the corresponding line will be too steep to make a reliable determination of the partition coefficient possible. This difficulty is avoided easily by repeatedly extracting phase B with equal portions of phase A . I n this case the components will be determined in the reverse order with the partition coefficients qz eschanged for l/'qi.
Another difficulty arises when some of the solutes have similar partition coefficients. In order to apply the present method of analysis the partition coefficients must be sufficiently different by a factor of at least 2. By an appropriate choice of solvents suitable partition coefficients can often be found. It is not necessary that the two phases be completely immiscible. If the solvents dissolve each other to some extent, however, they must be brought into equilibrium with each other before the experiment. I n the extraction esperiment nothing should be changed except the concentration of the solutes, and these concentrations should be kept low in order not to influence the partition coefficients. The method cannot be used if the partition coefficients depend on the concentrations of the solutes (this obviously excludes certain solvents). A pre-equilibration is also necessary if a chelating reagent, which distributes itself between the phases, is used for the extraction of the compounds of interest. For the application of the method'of repeated extractions the total concentration (CB)"should be readily meas-
urable. For labeled compounds the activity is proportional to the concentration. The analysis gives the product k,c,. I n the special case where all solutes are labeled with the same tracer and radioactive equilibrium is attained, all proportionality constants ki are equal. The analysis of the extraction data yields the relative concentrations of the solutes. If different tracers are used the constants k, will be different. The partition coefficients are still obtained correctly, but the determination of concentrations requires additional calibration experiments. Other methods of total concentration determination (spectrophotometric methods, etc.) may sometimes be useful. In general, however, activity measurements are to be preferred because of their simplicity and rapidity, especially if the number of samples to be determined is large. Dependent Constituents. If t h e solutes are not independent of each other, and t h e interchange between them is appreciable during the experiment, this has t o be taken into account in the interpretation of the extraction d a t a in terms of concentrations and partition coefficients. To make this possible the reaction rates have to be known. The solutes will be found in both phases during the extractions. For this reason effective rate constants are used, determined from the rate constants in both phases, the partition coefficients, and the time schedule followed in the experiment (extraction time and time for separation of the phases). Immediately after the nth extraction the total concentration of the solutes in the two phases may be written: (CA)n
=
(Yi)n
(1 - pi)
i
(6)
(Cip),
(Yi)npi i
The (Y;),'S will be complicated functions of the type of reaction, the rate constants, and the initial concentrations of all components. A special casenamely, unimolecular reactions-is considered here. The reactions are assumed to take place according to the scheme :
-
+zi-1
Ki-1.i
Ki.i*l
2, Ki.i-1
z,+1
Ki+l,i
where K i etc., are rate constants and 2, the compounds of interest. If the time for a complete extraction step is short in comparison to the halftime of the reactions, a first approximation can be used neglecting all terms which contain more than one rate constant as a factor. The following expression is then found for (Yi)": VOL. 32, NO. 12, NOVEMBER 1960
1665
- Ki.i-1.-
+
the rapid interchange between the complexes. ci+iKi+i,i Qi+i - Qi Determination of Ferrous-Ferric Ratios. Another application of the Qi-in - Qi" ci- iKi- t,i (7) method is the determination of the Qi-1 - Qi APPLICATIONS ratio of ferrous to ferric iron. Such The method described above is of where an analysis is of interest since ferrous special value for the analysis of a solusulfate solutions are widely used as Qi = ( 1 - Ki.i-1 - Ki.i+l)(l - Pi) a number of so~uks tion radiation dosimeters (1). The amount which fulfill the following conditions: Thus, of trivalent iron formed, which .is proAll solutes must contain the same portional to the radiation dose,' has to (cI), = (yi)n p i = xi (8) tracer isotope, which must be in radiobe measured. In this case the comactive equilibrium with respect to the ponents can be regarded as independent i i different solutes. of each other. Furthermore, many A solvent must be found, into which with methods of analysis-for instance, titrations and spectrophotometric methods-are available, a t least if the amount of iron is not too small. NeverQi Qi Qi theless, the method of repeated exci p c l K , . c l c i ~ i Ki.i+, + ~ ci-ipi Ki-1.i Qi+i - Qi Qi-1 - Qi Qci- Q i tractions might be used to advantage, since it is accurate and very simple to the compounds are extractable, even carry out ( 5 to 6 extractions.are suffiEvidently this case can be treated as after the addition of some reagent, with cient). The method is also independent before. Log (C& is plotted us. n, different partition coefficients. of the amount of iron, which can be and all values of Qiand Xi are deterThe components must depend on each extremely small. A suitable extraction mined by a subtraction procedure. other, but the reaction rates should be system would be to extract isoamyl Now, for a determination of partition neither too great nor too small. A alcohol containing thiocyanate with coefficients and concentrations from suitable range of rate constants might 0.8N sulfuric acid (the iron originally these data, the rate constants for the be from about 0.01 to 0.2 minute-'. contained in the first water phase) Higher values of the rate constants mean interchange between the solutes have experimental difEculties because the using Fe59as tracer. It is important to to be determined. If they are known, experiment has to be carried out very keep the thiocyanate concentration in Qi will give the partition coefficients fast. If the rate constants are lower, the water phases constant and in directly. The concentrations are then other separation methods can usually equilibrium with the thiocyanate conobtained by solving a system of linear be applied. The method of repeated centration in the organic phase since equations. The rate constants are extractions is still of great value, howthe partition coefficients depend strongly determined from kinetic experiments. ever, because it is simple to carry out, on the thiocyanate concentration. They have to be evaluated by successive and furthermore, because other chemical The method should be useful also for approximations. A convenient starting separation methods might introduce other branches of chemistry-eg., for harmful changes into the system. point might be to assume all components the analysis of a mixture of labeled to be independent and to calculate the Nitrosylruthenium Complexes. Niorganic compounds. concentrations as functions of time trosylruthenium forms several difusing this assumption. The rate conLITERATURE CITED ferent nitrato complexes in nitric acid stants are then calculated from the time(1) Bildstein, H., Atompuzis 4, 164 solutions (2'). Since these complexes dependence of the concentrations. These (1958). interchange with reaction half-times rate constants are used for the deter(2) Fletcher, J. M., Brown, P. G. M., Gardner, E. R., Hard C . J., Wain, of the order of 10 minutes or longer, mination of effective rate constants to A. G., Woodhead, J. J : Inorg. & they can conveniently be analyzed by be introduced into Qiand X,. The conNuclear Chern. 12,.154 (1959). the method of repeated extractions centrations and rate constants are then (3) Rudstam, G., Acta Ghem. Scund. 13, (9). A suitable solvent is tributyl re-evaluated until further approxima1481 (1959). phosphate. I n this case other methtions do not change the results. RECEIVED June 16, 1960, Accepted Auiust 23, 1960. ods of analysis are difficult owing to It is not always possible to neglect (Yi). = ci (1
Ki.i+i)Qi"-' Qi+l" - Qi +
terms containing two (or more) rate constants as factors. A calculation to the second approximation is given in a previous paper (3).
c
~
~
~
E.,
Colorimetric Determination of Chlorates in Well Waters PAUL URONE and ERIK BONDE Department of Chemistry, University of Colorado, Boulder, Colo.
b Chlorates react with o-tolidine in strong hydrochloric acid solutions to give a sensitive colorimetric method for their determination in waters used for drinking or irrigation purposes. The method is simple, rapid, and relatively free from interferences. Using a 4ml. sample, the proposed method quantitatively measures from 0.05 to 10 p.p.m. chlorate ion with an average deviation of 0.02 p.p.m. Higher or lower concentrations may be measured 1666
a
ANALYllCAL CHEMISTRY
with smaller samples or longer path length spectrophotometer cells. Except for very low concentrations, Beer's law is followed closely. Quantitative measurements are made with a spectrophotometer, but visual comparisons may be made in the absence of strongly interfering colors. Nitrite ion interferes while residual chlorine and ferric ion give additive effects that can be corrected. Chlorides and nitrates do not interfere.
D
a recent study, it became necessary to measure small concentrations of chlorate ion in well waters used for irrigation and household purposes. The commonly used iodide-thiosulfate method (1, 5) waa not sensitive enough to apply it directly to the waters. Concentrating the samples by boiling involved the possible high temperature reduction of chlorate by trace impurities. At first, a modification of the polarographic URING
