November, 1945
695
ANALYTICAL EDITION
up to 4%, which corresponds to a vitamin A potency of approximately 50,000 units per gram. The compound will probably not be used as an adulterant because an absorption band in the blue region makes it easily recognizable by its yellow color even when highly diluted. The best method of using 2-phenylazo-p-cresol, especially in laboratories which periodically standardize instruments, is to prepare a solution in maize oil in the concentration range of the fish oils encountered, and dilute it in the same manner as the fish oils for spectrophotometric determinations. A fresh dilution may be made for each calibration or the dilutions may be kept indefinitely in stoppered bottles and reused. This procedure will give a standard which is stable at room temperature, is easily
handled, and can be used routinely to standardize or calibrate instruments in United States Pharmacopoeia units or micrograms of vitamin A. LITERATURE CITED
(1) Baxter, J. G., and Robeson, C. D., J. Am. Chem. SOC.,64, 2407 (1942).
(2) Ibid., p. 2411; and personal communication. (3)
McFarlan, R. L., Bates, P. K., and Merrill, E. C., IND. ENQ. CHEM., ANAL.ED.,12, 645 (1940).
Taylor, R.J., Nature, 149, 474 (1942). (5) Zscheile, F. P., and Henry, R. L., IND.ENO.CHEM.,ANAL.ED., (4)
1 6 , 4 3 6 (1944). (6)
Zsoheile, F. P., Nash, H. A., Henry, R. L., and Green, L. F., I b i d . , 16, 83 (1944).
Simultaneous Spectrophotometric Determination of Titanium, Vanadium, and Molybdenum ALFRED WEISSLER Naval Research Laboratory, Washington, D. C.
* Measurements have been made of the absorption spectra of the hydrogen peroxide complexes of titanium, vanadium, and molybdenum in perchloric acid solution. Inasmuch as the optical densities at various wave lengths are additive, it has been found possible
M
ODERATELY small amounts of titanium are most often determined by the yellow color produced by hydrogen peroxide in acid solution (11). Effects of acid concentrations, temperature, and bleaching agents have been studied (6, 6) and Beer's law has been found to hold for titanium concentrations up 50 p.p.m. (4). The color is stable over a period of 2 years (1). Vanadium under the same conditions gives a reddish-yellow color which has been studied spectrophotometrically (12); molybdenum gives a pale yellow color ( 2 ) which is intensified in phosphoric acid ( I O ) . The titanium-peroxide color is bleached quantitatively by hydrofluoric acid, while the vanadium is not affected (8), so interference betxeen these two may be avoided, even if at the cost of etched optical cells. Another scheme ( 7 ) permits simultaneous determination of titanium and vanadium, using two different spectral filters, one transmitting at 420 to 440 mG and the other at 550 to 580 mg. However, in both cases molybdenum interferes. It therefore seemed desirable to investigate the absorption spectra of the peroxide complexes of titanium, vanadium, and molybdenum with a view to determining these ions simultaneously in a given solution, by the use of monochromatic light of various wave lengths. THEORETICAL ASPECTS
A molecule of a colored substance in solution acts as if it contains a damped simple harmonic oscillator-for example, an electron-which has a natural frequency corresponding to that of the peak absorption (9). The oscillator is impelled toward the equilibrium position by an elastic restoring force, and is also subject to a frictional d a m p ing resistance proportional to the velocity. An external light wave exerts a sinusoidal force, F , cos ut (alternatively, the real part of F o e i w t ) , which causes the oscillator to undergo forced vibration. Let x be the dsplacement of the particle of mass m, mk the frictional damping constant, wo the natural angular frequency, and w the impressed angular frequency; then the familiar differential equation of motion is:
to determine these three ions simultaneously in mixtures b y using the monochromatic light available in a spectrophotometer. A considerable saving of time is involved in the use of a single color reaction to determine three constituents.
m
d2x
+ mk a x + mwXx =
Neglecting transients, this has a solution of the form x = Aeiwl. Since the am litude, A , may be a complex quantity consisting of a real part, and an imaginary part, Ai, the real part of the solution is:
I,,
5
= A, cos wt
+ iAi sin ut
It can be shown that the oscillator continually absorbs energy from the light wave, the absorbed energy going into the frictional resistance; also that the rate of absorption is proportional to the component of amplitude out of phase with the impressed force, This component is the negative of the imaginary part of the amplitude, found from the solution of the differential equation to be:
Plotting this absorption component against the impressed frequency (or wave length) gives the characteristic absorption curve, such as was obtained experimentally in Figures 1 and 2. The shape of the experimental curves is partly due also to the distribution of vibrational and rotational frequencies and the varying solvation of the absorbing molecules. The combined effect of many colored molecules in solution may be considered next. It can be shown (3) by the Beer-Lambert law that the intensity of monochromatic light transmitted by an absorbing solution decreases with the concentration, c, and length of optical path, L: Z = Zoe-k'cL. Using Briggsian Z logarithms, this is more conveniently expressed as -log - = 10 kcL = D where Illo is the transmittancy, the negative log of which equals the optical density, D (also called the extinction). The specific extinction, k , is characteristic of the nature of the colored molecule and it becomes numerically equal to the density when L i s 1 cm. and cis also unity. If the length of optical path is kept constant,
696
INDUSTRIAL AND ENGINEERING CHEMISTRY 1.
Influence of Perchloric A c i d Concentration on TitaniumPeroxide Color (1 mg. of titanium plus varying amounts of 70% HC104,diluted to 50 ml.) HC104, Optical Density Position of MI. a t 410 mp Absorption Peak, mp 410 0
Table
410 410 410 410 415 420 425 430
1 3 5 10 15 25 40 49
This is the aspect of greatest interest to analytical chemistry: the concentration of a colored molecule in solution may be determined by measuring the optical density, provided that the optical density of a solution of known concentration has been previously measured. The use of a spectrophotometer provides a much closer approximation to monochromaticity than is possible with a filter photometer, and therefore gives experimental results closer to ideality.
In the abBnce of chemical interaction between two types of colored molecules, the optical densities would be expected to be additive. Therefore, it is possible to determine the concentrations of several components in a mixture by measuring the optical density of the mixture at various wase lengths, a8 explained below. Other useful examples of the additive nature of the densities are the analysis of mixtures of dyes, and the infrared analysis of hydrocarbon mixtures.
Vol. 17, No. 11
Standard titanium solution containing 1.00 mg. of titanium er ml. was prepared from N.B.S.standard sample 154, 98.7% $io*, by heating 1.691 grams with 10 grams of ammonium sulfate and 50 ml. of sulfuric acid until dissolved, then cooling and diluting to 1 liter. Standard vanadium solution containing 1.00 mg. of vanadium per ml. was prepared by dissolving 2.43 grams of C.P. ammonium metmanadate in 100 ml. of 1 to 1sulfuric acid, diluting to 1liter, and adjusting the volume after standardization by potentiometric titration with ferrous ammonium sulfate. Standard molybdenum solution containing 1.00 mg. of molybdenum per ml. was prepared by dissolving 0.630 gram of sodium molybdate dihydrate in water, and diluting to 250 ml. Each solution examined contained 10 ml. of 70% perchloric acid (unless specifically noted otherwise) and was diluted to 50 ml. in a volumetric flask. Then a portion of the solution was poured into each of two identical cells, which were filled to the same height each time. One drop of water was added to one cell, one drop of 30% hydrogen peroxide to the other, and each solution was stirred with a little glass rod. The instrument was set to read zero optical density for the unperoxidized portion, against which the density of the peroxidized portion was then measured.
Table 11.
Influence of Phosphoric A c i d Concentration on TitaniumPeroxide Color (1 mg. of titanium plur 10 ml. of 70% HC104, varying smounta of 1 t o I phosphoric acid, diluted to 50 ml.) HsPOs Optical Density (1 to l),MI. At 400 mp At 410 mp At 460 mp 0 0.288 0.303 0.205 2 4
6 8 10
0.290 0.287 0.287 0.286 0.285
0.292 0.285 0.283 0.281 0.277
0.160 0.149 0.148 0.147 0.145
APPARATUS AND REAGENTS
The Beckman spectrophotometer was used in this work, with 1.000-cm. Corex covered cells: direct readings of both per cent transmimion and optical density are obtainable. The slit width was usually less than 0.02 mm., corresponding to spectral band widths of less than 5 mp.
EXPERIMENTAL WORK
Amounts of standard titanium solution varying from 0.1 to 7.0 ml. were added to 10.0 ml. of perchloric acid, and diluted
WRYELENGTH-mp
Figure I. Transminion Spectra of Titanium-Peroxide Complex in Perchloric A c i d Solution
Figure 2.
Optical Denrit Spectra of Titanium-Peroxide Complex in Perclloric A c i d Solution
ANALYTICAL EDITION
November, 1945
697
460 mp; therefore, phosphoric acid possesses the additional advantage of narrowing the absorption band. To investigate the extent of interference by vanadium, the adsorption of the vanadium-peroxide complex in perchloric acid solution was determined. Figure 4 shows that the color is less intense than that of titanium, and that peak absorption is at 460 mp. Figure 5 demonstrates the validity of Beer's law at 410 and 460 mp. To investigate the extent of interference by the pale yellow molybdenum-peroxide complex, measurements were made of its spectra in perchloric acid solution. Surprisingly, Figure 6 shows an intense absorption peak at 330 mp, which seems not to have been mentioned in the literature. Figure 7 shows the linearity between concentrat,ion and optical density at 330 and 410 mp.
Figure 3.
!
Linearity of Titanium Concentration-Density Relation
0.2
to 50.0 ml. The per cent transmission and optical density of a
a0/
peroxidieed portion were measured against an unperoxidized portion of each, in 1.000-cm. cells, over the range 300 to 020 mp.
Figure 1 s h o w the absorption spectra, plotted as per cent transmission against wave length. Figure 2 represents the same eolutions, plotted in terms of optical density. It was found more convenient t o use optical density in this work, because of its linear relation to concentration. Peak absorption occurs at 410 mp. Figure 3 affords experimental verification of the validity of Beer's law for this system a t 410 mp, and indicates approximate validity a t some other wave length such as 460 mp. The effect of variation in perchloric acid concentration was studied, using 1.0 me. of titanium. Table I shows that no significant variation occurs in the range from 0 up to 15 ml., beyond which the color bleaches slightly and the absorption peak moves toward the longer wave lengths. The usefulness of phosphoric acid in eliminating extraneous color due to iron prompted investigation of its effect on the peroxide-titanium color. Table I1 shows that bleaching is negligible at 400 mp but considerable at
Simultaneous Determination OF Titanium, Vanadium, and Molybdenum b y Peroxide Color Reaction (Standard solutions of metals plus 10 ml. of 70% HC104, diluted t o 50 ml.) Ti V &lo V MO Ti Bample Added Added Added Daao D41m Del Found Found Found Ma. Mo. MQ. MQ. Mg. Mg. Table 111.
1 2 3 4 5 6 7
1.00 1.00 1.00 0.245 2.00 2.00 2.00 0.488 3.00 1 . 0 0 1.00 0.356 2.00 4.00 2.00 0.429 1.00 2.00 2.00 0.426 3.00 3.00 3.00 0.710 2.00 3.00 1.00 0.248
0.403 0.798 0.997 0.944 0.500 1.20
0.309 0.614 0.711 0.818
1.00 1.96 2.90 1.92 0.408 1.03 0.917 3.00 0 . 8 5 7 0.718 1.95
1.01 2.06 1.01 4.10 1.97 2.93 3.00
*
WAVELENGTH mp
Figure 4. Optical Density Spectra of Vanadium-Peroxide Complex in Perchloric A c i d Solution
08
07
3 O,3-
?
% 0.c 0.3
0.2
0.1
0.95 1.91 0.87 1.82 1.90 2.78 0.86
/,O
2.0
3.0
q.0
9.VANADIUM Figure 5.
3.0
6.0
70
8
/N 5 O m L
Linearity OF Vanadium Concentration-Density Relation
698
Vol. 17, No. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
dium, and z of molybdenum, these simultaneous equations can be set up: 0.065 z
- 0.020 y
+ 0.205 Z + 0.304 L
+ + +
0.208 z = Dat~ 0.074 y 0.024 z = Dam 0.100 y 0.001 z = D w
Solving by determinants gives :
x = 7.01 Dao -
0.57 D83o
y = 20.7 Dim
-
z = 5.12 Da3o
-
14.3 Dlle
- 5.46 Daw
+ 1.55
0300
+
3.57 D ~ I Q 3.67 Ddw
To test the above equations, several known solutions containing the three ions in varying proportions were made up, and analyzed by measuring the optical densities of a peroxidized portion at 330, 410, and 460 mp. Table I11 shows that the results are fairly accurate. This method is not intended to replace other methods for vanadium and Figure 7. Linearit of M o l bdenum Conmolybdenum, but rather to Figure 6. 0 tical Density Spectra of centration-bensity Reration furnish an interesting exMolybdenum-feroxide Complex in Perample of the possibilities of chloric A c i d Solution the spectrophotometer. I t is probable that increased accuracy could be attained by a careful search for more favorable condiIt was believed po&sibleto determine titanium, vanadium, and tions-for example, the absorption of titanium and vanadium molybdenum simultaneously in solution, by the single color reat 330 mp is not strictly linear. action of adding hydrogen peroxide, if the optical densities of the solution were measured at three different wave lengths, corresponding to the absorption peaks of the three complexes. A comLITERATURE CITED parison of the spectra of the three complexes is shown in Figure 8. (1) Ayres, G. H., and Vienneau, E. M., IND.ENO.CHEW,ANAL. ED., 12,96 (1940). Under the given conditions, 1 mg. of titanium causes a density (2) Funck, A. D.,Z . a d . Chem., 68,283(1926). of 0.065 a t 330 m p , 0.304 a t 410 mw, and 0.205 a t 460 mp; 1 mg. ( 3 ) Gibb, T. R. P., “Optical Methods of Chemical Analysis”, of vanadium gives a density of -0.020 at 330 mp, 0.074 a t 410 Chapter 11, New York, McGraw-Hill Book Co., 1942. mp,and 0.100 a t 460 mp; 1 mg. of molybdenum results in a den(4) Ginsberg, H., Z . amrg. allgem. Chem., 211,401 (1933). mty of 0.208 at 330 mp 0.024 at 410 mp, and 0.001 at 460 mp. (5) Klinger, P., and Koch, W., Arch. Ekenhiittenw., 13,127 (1939). If 2 represents the number of milligrams of titanium, y of vana(6) Merwin, H. E., Am. J. Sei., 28, 119 (1909). (7) Pinsl, H., Angew. Chem., 50, 115 (1937). (8) Sandell, E. B., “Colorimetric Metal Analysis”, p. 443, New York, Interscience Publishers, 1944. (9) Slater, J. C., and Frank, N. H., “Introduction to Theoretical Physics”, Chapters IV and V, New York, McGraw-Hill Book Co., 1933. (10) Thanheiser, G., and Goebbels, P., Mitt. Kaiser Wilhelm Inst. Eisenjorechung Diisseldorj, 23, 187 (1941). (11) Weller, A., Ber., 15B,2593 (1882). (12) Wright, E. R.,with Mellon, M. G., IND. ENG.CHEM.,ANAL. ED.,9,375 (1937).
Benzotriazole
Figure 8.
Comparison of Spectra of Peroxide Complexes of Molybdenum, Titanium, and Vanadium
The article “Quantitative Determination and Separation of Copper with Benzotriazole” by J. Alfred Curtis [IND. ENG. CHEM.,ANAL. ED.,13, 349 (1941)] describes favorable results obtained with benzotriazole, but quotes as a disadvantage that the reagent is an expensive one, 100 grams costing approximately $25. Benzotriazole in good purity is now manufactured for use as a photographic chemical. The current quotation for 4 ounces is $4 and for 1 pound $12.50, making the 1-gram quantities used in the determination inexpensive.
