Simultaneous Spectrophotometric
John T. MacQueen, Samuel 0. Knight, and Charles N. Reilley
The Universitv of North Carolina Chopel Hill
I
Determination of Cobalt and Chromium A student experiment
M a n y undergraduate courses in quantitative analysis now include an experiment to present spectrophotometric analysis for one component. An extension of such experiments to two-component analyses introduces the student to the problems encountered in the general case of multi-component analyses, and serves as an illustration of the ideas of linear dependence of several variables applied to the description of a physical system, a concept in quantitative analysis often encountered only in textbook problems. This paper presents a summary of the theory and procedure appiicable to two-component spectrophotometric analysis and describes a system which has been found very convenient for student instruction in this laboratory. The necessary stock solutions are easy to prepare (no buffers are required) and are quite stable for long periods of time. The unknowns as issued are ready for direct absorbance measurements and, though this is somewhat artificial from an analytical point of view, the experiment serves to present the essential spectrophotometric features of the problem as distinct from the preparation of the sample as such. Other systems have been described, such as the analysis of steel for Cr and Mn ( I ) , which differ in these respects. A student experiment using the two-component method for the determination of the dissociation constant of methyl red and a two-component analysis in the ultraviolet region have previously been described in THIS JOURNAL (2, 3). The student should be familiar Gith the general procedures of one-component spectrophotometric analysis based on the Boguer-Beer equation A = abc, where A is the ahsorbancy, a is the absorbancy index, b is the length of the light path through the cell, and c is the concentration of the ahsorbine substance. Since for most applications the value of b is held constant throughout an experiment, we shall define and use the quantity lz = ab throughout this paper. Row in the suhseqnent discussion we shall consider only systems for which the total absorhancy of a mixture for a given wave length is the sum of the absorbancies which would he measured for each of the components separately at the same concentrations present in the mixture. That is, for a mixture of n components the ahsorbancy at the ith wavelength is
-
where the i's refer to wavelengths and the j's to components. This linear relationship must be checked
experimentally, and when it is found to exist for a twocomponent system the unknowns cl and cr are completely defined by the two equations A, A,
kncs ++ k>,cx
= kuc~ = kns
(2)
The experimental task then is to check for linearity, make an appropriate choice of wavelengths a t which to measure A , and A%,and to evaluate the k,,'s. The Experiment
Solutions. Stock solutions of cobalt (11) nitrate, 0.188 M, and chromium(II1) nitrate, 0.0500 M, are provided in the laboratory. By reason of the method of preparing unknowns, it is not necessary for the solutions to be standardized, but they should he as close to the stated molarity as they can be prepared with graduated cylinder and laboratory trip scales. From the stock solutions the following are prepared by appropriate dilutions: 0.0376 M, 0.0752 M, 0.1501 M, cobalt; 0.0100 M, 0.0200 If, 0.0400 M chromium; and one mixture that is 0.0752 M in cobalt and 0.0200 M in chromium. Absorption Spectra. The absorption ~pectraof the 0.0752 M cobalt solution, of the 0.0200 M chromium solution, and of the mixture prepared above are taken. Adequate spectra can he obtained by making measurcments at 375, 400, 425, 440, 455, 470, 490, 500, 510, 520, 530, 540, 550, 575, 580. 600, and 625 mp. The values of absorbancy are required although on many instruments it may be desirable to read O/oT and convert these for plotting. The spectra for the 0.0752 M cobalt and for the 0.0200 M chromium solutions are plotted on one graph. A curve representing the graphical
Curve A, 0.0752 M cobaltllll nitrate; c v n e B, 0.0200 M chromiumlllll rum of A and B point.-experimental nitrote; curve C, curve only-the point. for the mixture.
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sum of these two spectra is then drawn. Finally the experimental values for the mixture are plotted and, if the measurements have been carefully made, these points will fall closely on the graphical sum of the other spectra. This fact shows that the linearity relationship holds. (Though strictly this is only demonstrated for a mixture of this particular composition, this is usually taken as being sufficient.) It is now seen that the cobalt spectrum has a reasonnhly flat maximum near 510 mp and that the chromium epectrum has one near 575 mp which may be used for analysis. These wavelengths will hereinafter be referred to as XI and X2, respectively. "Beer's Law Plots" and the Evaluation of the k,,'s. Plots of the ahsorbancy as a functionof concentration (A versus C) are now obtained for cobalt and for chromium both a t XI and X2. The stock solutions are included in these measurements. The slopes of the straight lines obtained are evaluated graphically to obtain the values of the k i s . Inspection of equations (2) shows that the slope of the line for cobalt (component 1) measured at A1 is just equal to kll, and the slope a t X p is ktl, whereas klz and kn are obtained similarly from the plots for chromium at XI and X*, respectively. It is true that these constants might he calculated from single experimental measurements, hut their evaluation from the slopes is more accurate. Analysis of Unknowns and Calculations. I t only remains to measure the absorbancy of the unknown solutions at XI and Xz, and the desired concentrations may be calculated. If we solve equations (2) for the concentrations, we obtain
where
Thus, once the p's are obtained from the experimental values of the k's, one has direct iiquations from the c's with known coefficients. The use ofnmatrix methods in obtaining solutions such as these may be described to the student and the near-necessity for such methods pointed out in cases such as multi-component infrared analysis (4) and mass spectrometry (5) where the number of components, and equations, may be as large as ten to twenty.
Results
Results obtained by one of the authors (J. T. M.) using a Bausch and Lomb "Spectronic 20" spectrophotometer with the standard round cuvettes supplied are given in Table 1. Absorption spectra obtained are displayed in the figure. PI, = 0.155,~= -0.0960*1 = -O.O1lO,u
Table 1
Substance
Found (moles/liter)
% Error
Cobalt Chromium
0.0673 0.0179
0.0675 0.0180
0.3 0.6
Students were issued unknowns, consisting of accurately measured volumes of the stock solutions delivered into 25-ml glass stoppered volumetric flasks, yielding on dilution easily calculated apparent concentrations, unaffected by any small errors in the real concentrations of the stock solutions. A summary of the results for 70 analyses obt,ained by students, also using the "Spectronic 20" is given in Table 2. Table 2.
0-2 Cob& Chromium
15 24
Number of Results with error in range 0 4 4-6 6-3 8-10 >10 7
13
12 9
5 9
lournal o f Chemical Education
6 2
25 13
Limits of concentration given: cobalt 0.0400 M to 0.1300
M; obromium 0.0075 M to 0.0200 M.
Of the 25 cobalt analyses with relative error greater than lo%, there were 14 where the molar ratio of cobalt to chromium was less than 3.5; and of the 13 chromium analyses with similar relative error, 9 contained a molar ratio of cobalt to chromium greater than 8. This gives indication of the reasonable limits of corcentration ratios for unknowns. With the equipment used it was found to be important to use great care in aligning the cuvettes and to make repeated readings to insure accuracy of 0 and 100% reference settings. Literature Cited (1) LINOANE, J . J., AND COLLAT, J. W., Anal. Chem., 22, 166 f1S.WI~ ,- - - - ,. (2) TOBY,S. W., J. CHEM.EDUC.,35, 515 (1958). FITZPATRICK J. D., AND ORCHIN, M., (3) MOSHEIBH-SHALOM, J . CHEM.EDUC.,34, 496 (1957). (4) KING,W. H., AND PRIESTLY, W., Anal. Chem., 23, 1418 (1951). R.,Anal. Chem., 30,877(1958). (5) HOPP,H.F., AND WERTZLER,
ALBERT EINSTEIN
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0.0601
Taken (moles/liter)
Many times a day I realixe how much my own outer and inner life is built upon the lobors of my fellow-men, both living and &ad, and how earnestly Imust emrt myself in order to give in return as much as I have received. My peace of mind is often troubled by the depressing sense that I have borrowed too heavily from the work of other men.
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