Differential Analysis with a Beckman Spectrophotometer ROBERT BASTIAN, RICHARD WEBERLING, A N D FRANK PALILLA Sylvania Electric Products, Inc., Kew Gardens, 3’. Y. The differential method of colorimetric analysis as applied to the Beckman RIodel DU spectrophotometer is discussed. The maximum increases in accuracy of this method over the normal one are computed for the instrument. Taking special precautions, experimental accuracies and precisions in the range of about *0.5 to + l part per thousand are obtained on potassium dichromate and potassium permanganate solutions.
T
HL priiiciples of differential colorimetry have been re-
cently discussed ( I , 2, 6). Utilizing the differential method a Beckman spectrophotometer, Bastian ( 2 ) obtained conwrltration accuracies and precisions of 1 to 3 parts per thousand in the determination of copper. As indicated in his paper, however, these results cannot be expected to represent the maximum precision obtainable on this instrument. To the important 6ources of error considered there may be added those due to the various analytical manipulations as well as fluctuations in final acidity which might have affected the color intensities. This paper discusses the differential method more thoroughly, computes the maximum accuracy (compared to the normal procedure) which can be obtained a t various wave lengths on the Model DU Beckman spectrophotometer utilizing the method, anti gives a better notion of the experimental accuracy and precision that can be obtained under carefully controlled conditions. In order to keep errors due to the formation of the colored product at a minimum, this work was conducted on aqueous solutions of potassium dichromate and potassium permanganate. To minimize volumetric errors aliquots were taken by weight wherever advisable. To eliminate errors due to calibration of volumetric equipment the same volumetric flask was used for diluting all standards and unknowns. As previously described ( Z ) , in the differential method one sets the optical density scale zero (or the transmittancy for 100yG) with a solution of a highly colored or light-absorbing substance in a place of a reagent blank. Higher concentrations of the given substance are then read against this zero point in the usual way. The optical density scale readings thus obtained represent the differences in absorbancy between the zero point sample5 and the samples in question. (In the new nomenclature, 9, “absorbancy of the sample,” il,, replaces the term “optical 1 Tsolution density.” A , = loglo -, where T. = _ _ The authors [in
T,
Tsoirent ‘
will use these newer terms but, because their Beckman instrument is marked in accordance n i t h the older nomenclature, the) will continue to use the term “optical densitj- scale.”) I n order to obtain the increased light needed to set the scale zero by this procedure, the spectrophotometer slit is used a t nider aperture? than normal. The effect of the procedure is sho\\n in Figure 1. Here varying concentration ranges of permanganate, expressed in grams of a standard solution per indicated volume, were plotted against optical density scale readings.
100 GRAMS OF 0 1054 N K Mn 04
90
84
Figure 1.
110
Effect of Spectrophotometric Procedure
the indicated volumes to permit an easier visual comparison from the standpoint of relative accuracies. For curve 3 the weights shown are the weights actually taken; for curves 1, 2, and 4 one sixth, one half, and twice the indicated weights were diluted to 200 ml. This procedure of weighing aliquots permitted preparation of all necessary solutions with convenience and high accuracy. Curves 1, 2, and 3 are straight lines with slopes greatly increasing as higher concentrations of color are used to set the zero point on the scale. Qualitatively it can be seen that increasing slopes represent increasing accuracies in determining concentrations, but the subject can be treated more accurately as follom: The error in determining concentrations, which is normally expressed as AC/C, can be expressed in terms of the curves shown as AG/G, where G is the number of grams of the permanganate solution corresponding to a given scale reading and AG is the minimum difference in G that we can detect a t that point. If we let S = the slope of the line in question, (dA./dG), and AA. the minimum difference in the absorbency of the sample that we can detect, it can be seen that: AG = A A J S or
For curve 1, distilled water was used to set the scale zero, so that the readings represent the true absorbancies of the samples; for curves 2, 3, and 4 successively increasing concentrations of permanganate were used to set the scale zero, so that the readings represent differences in absorbancy between the given samples and the zero point samples. All readings were taken with the sensitivity knob set 2 turns from the clockuise end, a t a wave length of 526 millimicrons, using 1-em. cells. As the horizontal axis indicates, the samples were prepared by weighing out appropriate amounts of a standard permanganate solution (1 N = 0.2 A’) on an analytical balance. All the samples were actually diluted in a single 200-ml. volumetric flask which also served as container for the weighing. The concentration ranges are expressed in terms of a uniform weight scale per
AG/G = AC/C = A d J S G Comparing the concentration error of curve 1 to curve 2 Error of 1 -= Error of 2
(1)
accuracy of 2 - AAal SZGZ accuracy of 1 AA,, SI GI
If we compare the relative accuracies a t a given point on the scale and assume that the reproducibility in reading the scale a t this point is the same regardless of the concentration of color taken to set the scale zero ( AAa, = AA,,), then: hccuracy of 2 Accuracy of 1
- S2 Gz S I GI
(3)
The relative accuracies depend on the scale reading taken for comparison. Arbitrarily choosing 0.40, we find that a t this point
160
V O L U M E 2 2 , N O . 1, J A N U A R Y 1 9 5 0
161
curve 2 yields 3.8 times the accuracy of 1 and curve 3 yields 5.5 times the accuracy of 1. Curve 4 is not a straight line, its slope falling off considerably a t the upper end of the range shown. I n order to evaluate the accuracy here the same procedure could be followed, except t h a t one would have to draw a tangent to get the slope a t the desired point. One can see that a t 0.40 curve 4 represents a lower accuracy than 3, for t he slope is less and G is less. The accuracy of 4 with respect to 3 becomes much less as n e pass to readings above 0.40. From the manner in which the slope of 4 is falling off it is evident that employing a still higher concentration range would result in a decreased, rather than increased, accuracy. It is evident that the differential method as described here has limitations imposed by: A. The maximum concentration of colored (or light-absolhing) substance which the available light will penetrate sufficiently to permit setting the scale zero. Without disturbing the light source on the instrument, this is limited by the maximum slit aperture (2.0 mm.). Because different slit apertures are iequired for normal operation a t different wave lengths, the increased light that a maximum aperture slit yields also varies with the wave length. B. Deviations of working curves from Beer's la^ in the direction shoivn by curve 4. These deviations may arise for several reasons, among which are (a)too high a concentration of color, ( h ) too great a band width of light, anti ( c ) stray light. Using the instrument as described, a and b are bound together hecause a higher concentration of color requires a TT-ider slit aperture and this in turn increases the band widt,h of light which emerges.
As pointed out by Ayres ( I ) , there are some systems which deviate from Beer's law in such a way as to give accuracy greater than that represented by a straight-line function, even by normal colorimetry. This occurs when the plot of absorbency lis. concentration curves upward. Katurally, differential colorimetry could be used for such systems, but these systems are comparatively rare. The application of differential colorimetry to s:.stenis that deviate from Beer's l a w in the usual manner depends upon the extent of the deviations, but in general would be limited. COMPUTATIONS O F ACCURACY
It is desirable to be able to compute relative accuracies in a different, if less exact, manner than that already described. Make the following assumptions concerning the given system: 1. The plot of optical density scale reading against concentration is linear over each concentration range selected for comparison. 2. A given increment in concentration always gives the same increment in absorbency over the entire range of concentrations. This does not follow from assumption 1 because each higher concentration range is measured a t a wider slit aperture which yields a wider band width of light. If we set our instrument a t the wave length of maximum absorption for the given substance, and the substance has a sharp absorption peak, increasing the band width will give a somervhat lower absorption reading. Thus, although each concentration range may give a straightline plot, the slope of each higher range will be somewhat lesq than expected. If the color has a broad absorption peak, the effect is much less. The assumption made then is that the region of maximum absorption is broad enough to make assumption 2 valid over the band width range used. Data presented below for potassium dichromate and potassium permanganate tend to conform this reasoning. 3. The optical density scale is read a t the same point in coniparing relative accuracies. 4. The reproducibility in reading the optical density scale at any given point is independent of the concentration of the solution used to set the scale zero (independent of slit aperture). Data are given below to support assumption 4. From the above assumptions it follows that: Accuracy of differential method - A , for differential solution Accuracy of normal mcthod A , for normal solution
Table I. Optical Density Scale Reading
0.00 0.10 0.20 0.30 0.434 0.50 0.60 0.70 0.80 0.90 1.00 2.00
(4)
28
-x
AAs
for 0.2% Error in Tranamittancy 0.00087 0.00109 0.00138 0.00173 0,00236 0.00275 0.00346 0.00435
0.0055
0.0069 0.0087 0.087
Scale Zero Set with Reagent Blank m
10.9 6.9 5,s 5.4 5.5 5.8 6.2 6.9 7.7 8.7 44
1000
Scale Zero Set with Solution Having As Value o f : 4.0 0.434 1.0 2.0 0.22 2.00 0.87 0.44 0.27 2.04 0.99 0.52 1.15 0.33 2.2 0.63 1.33 0.75 0.40 2.4 1.6 0.53 2.7 0.97 1.8 1.1 0.61 2.9 2.2 1.3 0.75 3.3 0.93 2.6 1.6 3.8 3.0 2.0 1.1 4.5 1.4 5.2 3.6 2.4 6.1 4.3 1.7 2.9 36 29 22 15
determination, it c a n be obtained R ith bufficient accuracy to make this computation. ( I t is desired to know the concenti:ition as accurately a5 possible, nhereas it is usually pointless to know the relative accuracieb to better than one or two signiiicarit figures.) I t is convenient to compare relative accuracies a t scnalr readings of 0.434, as this is the optimum value utilizing the noimal procedure. I t is also convenient to rewrite Equation 4 in terms of the absorbency of the sample taken for the zero point in t h e differential procedure. For the scale reading of 0.434 we have:
A , for differential zero solution 0.434
+ 0.434
(3
OPTIMUM SCALE READIKG
Before proceeding further it is important to determine the optimum position in reading the optical dcnsity scale using the differential procedure. T o do this it is convenient to assume that assumptions 1, 2, and 4 hold. Under these conditions the concentration error, AC/C, can also be expressed as A A J A . over the entire range of concentrations. AAa varies with the scale reading, but the error in determining an increment in transmittancy remains constant under any given set of conditions. Inasmuch as loglo 1 / T , = A,, we can conipute AA8 from AT.. Assuming a constant error of 0.2% in dctermining transmittancy ( I ) , the values of AA, corresponding to given optical density scale readings are listed in the second column of Table I. I n the next column the errors in concentration resul ting from various scale readings in the normal proccdure are given, expressed in parts per thousand. I n the succeeding columns the assumption is made that thc same readings were made against differential zero solutions having A , values of 0.434, 1.0, 2.0, and 4.0, respectively. I n these cases, A , for the solution read equals A , for the zero solution plus the scale readings. As can be seen from Table I, A B , increases steadily with the scale reading, and is about 2.7 times as great at 0.434 as a t 0.000. From this fact alone we can see that if we compared a standard and unknown solution, each having A , values of 0.434 a t zero on the scale, vie ~ o u l dobtain 2.7 times as much accuracy as by reading the same unknown solution against a reagent blank. The concentration error in normal colorimetry reaches a minimum a t 0.434 not because the scale can be read best a t 0.434, but because up to this point on the scale A , increases more rapidly than AA8. As n-e go beyond 0.434, A& increases more rapidly than A If, however, we compare a solution to a differential zero solution having an A , value of 0.434 or greater, the error in determining concentration will rise steadily with the scale reading, and will be lowest at 0,000. The region of nearly constant error (I.
.4lthough it is not possible to obtain A, for the differential wblution with sufficient accuracy to make a direct concentration
Optimum Scale Reading
ANALYTICAL CHEMISTRY
162
\\hich occurs in the noinial cahe from about 0.3 to 0.7 does not o w u r n i t h the differential solutions, and the higher the scale reading employed, the more we tend to destroy the concentiation accuracy which can be gained by using the differential method. It will also be observed that the greater A , for the differential zeio qolution the greater is the proportion of potentially increased ~ W U I R Cwhich ~ is lost by going to higher scale readings. (This The relative errors within any point \\as not recognized in 2 given vertical column in Table I depend only upon assumption 1, thus making the considerations more general. .Irigorous mathematical tieatment of the complete error function in terms of transmittancies, which is highly recommended to the reader, has been made recently by Hiskey ( 6 ) . If .I, for the zero solution is less than 0.434 i t can be shown (proceeding as in Table I ) that the optimum scale reading will be liter volumetric flask and diluted to the mark with water a t 28" C. (temperature of the water from the still and within 1 " of room temperature). Observer 2 was given the known and unknown with the stipulation that the unknown be between 0.09 and 0.11 X, (This was the range that could be covered by the procedure to be described. ) Observer 2 obtained the data for the circles shown on Figure 2 by weighing out varying amounts of the 0.10000 ,V potassium dichromate and diluting all samples in the same 200-ml. flask with nater a t 28" C. These were read in a single 1-cm. absorp tion cell against a zero point concentration of 6.8306 grams of 0.10000 S potassium dichromate per 200 ml. contained in a companion cell. The zero point standard was also read against itself in the adjacent cell which provided the point near zero The slit was used a t 2.0 mm., and the sensitivity knob a t 1.5 turn$ from the clockwise end a t a wave length of 350 m@,which is in the region of maximum absorption. An initial curve was then drawn through these points, using a 10 X 15 inch graph paper. The scale of the graph was such as to permit reading the concentration to a precision of 1 to 2 parts per 10,000 (based on the total concentration). To obtain the additional points shown on the graph (done in batches as indicated by the different symbols), a zero standard was prepared by volume very nearly the same concentration as the original (6.84 ml. per 200 ml.). Samples were weighed and diluted as before, taking precautions only to ensure that all samples were a t the same temperature and within a few degrees of 28" C. These solutions \%ereall read in a single absorption cell against the zero point solution. The average deviation of each batch of points from the original line was determined and all of them in the group were shifted by this average amount. When all the points had been so shifted the best line was drawn through all of them.
Many sources of error TThich may be relatively unimportant in ordinary colorimetric n o r k must be considered in differential analysis because of the potentially increased accuracy. These include discrepancies in volumetric equipment and 45 absorption cells, and volumetric errors due to temperature 0 5 effects (the specific gravity of water varies about 2 parts in n < 10,000 per ' C., 7 ) . A very important consideration in w [L 35 taking advantage of the increased accuracy made possible w J by duplicate (or greater numbers of) determinations is that 6 0 we muFt concern ourselves with not only the unknown solurn tion but the differential zero solution as well. In other - 25 words, if we read three unknowns against a given zero point 0 z W standard, then the standard must be located with a precin I 492 29 sion equivalent to three individual determinations as well. 4' 15 2 494 24 The failure to do this in the previous work ( 2 ) probably 2 3 496 215 k constituted a serious source of error. a 4 498 158 0 Although it has been demonstrated that the most acnr. curate results obtainable by differential colorimetry occur 0 095 0 100 0 105 0.110 when the unknown is matched with the standard a t zero on NORMALITY OF K, C r p 0, the optical density scale, this requires that the concentration of the "unknown" be known accurately. Although Figure 3. Direct Analysis of Potassium Dichromate Solutions some situations may arise in M hich this is nearly the case, in most practical cases it is desirable to have a wider The unknown solution was allowed to stand together with the latitude in concentration. standard Solution Until both were a t lWJm temPGature. Three the n70rk that follows the authors have used the scale from standards were weighed corresponding to various regions on the 0.0 to about 0.5. I n each case the accuracy that should be obgraph, and three unknowns having weights in the vicinity of 7.8 tained by reading the curve at the lowest and highest point grams, so as to allow for a concentration variation of about 0.09 to 0.11 N . All standards and unknowns were diluted in the same plotted has been computed and the accuracy expressed in terms flask and read in the absorption cell against a zero point standard of a range. The computations have been made using * A , / A , prepared as above. (Several readings were taken on each sample where the have been computed from apertures, and the results were averaged.) The average deviation of the and the *"I8 values have been computed assuming a reproducibilthree standard from the graph was determined and the ity of *0.2% transmittancy in all cases. In the case of Figures unknown readings were all corrected by this value. "I
V O L U M E 2 2 , NO. 1, J A N U A R Y 1 9 5 0
165
Unknown weights were read from the graph using the caorrrcted scale readings and the concentration n-as computed from the relation:
Table VI.
Weight from graph X 0. 10000 = normality of unknown Actual weight of unknown .ictually, the relationship as stated is not entirel? correct. It would hold only if the specific gravity of the unknoRn and standard solutions were identical, because only then would it givrn weight of solution represent a given amount of solid potasd u m dichromate. A determination of the relative specific gravity of 0.09000 and 0.1100 -Irpotassium dichromate solutions utilizing a single 50-1111. specific gravity bottle showed a difference between these of about 0.7 part per thousand. For purposes of making the small corrertion involved we can assume a linear relationship between specific gravity and concentration. As a matter of fact, in the case taken, no correction was needed because the onre rent ration of the unknown was in the vicinity of the standard
Analysis of Potassium Dichromate Solution Normality of KzCrnOi Taken
Kormality of KlCrnOi Found 0.09892 0.09890 0.09889
0.09893
Av. 0.09890 * 0 . 1 part per thousand L'omputed error" * 0.5 t o *l.Z parts per thousand Error found -0.3 part per thousand a
Based on scale readings of 0.00 a n d 0.50 and t 0 . 2 5 4 transmittaIicy.
__-
'Fable VII.
Analysis of 0.09893 N Potassium Dichromate Solution Sormality Found 0,09890 0.09888 0.09896
Kave Length, mp 500 498 496 494 492
0.09901 0.09910
Av. 0.09897 * 0 . 7 part per thousand Computed error *O. 5 to t 1 . 0 p a r t per thousand Error found f O . 4 part per thousand
evei, gieat care must be taken in displacing and resetting the wave-length scale. This is due to the fact that we are in a region M here the absorption curve is steeper than a t the point of maximum absorption ( 8 ) . I n the above cas?, a magnifier was placed over the wave-length srale and two lines neie drawn on the glass rquidistant from the hair line to prevent errors due to parallax. The wave-length scale n a s displaced and reset >rvPral times in the roiiiw of the anah SIS i N A L 1 SIS OF POlASSIUM PERMAYGANATE SOLUTIONS
I 00
I
85
1
95
GRAMS OF 010544N KMn0,PER
IO 5 200 ML
Figure 4. Analysis of Potassium Permanganate Solutions
The rr-ults obtainrti aie given In Table \'I. The arcuracy 15 actually bettei than the computed range, mhich may indicate that the reproducibility in transmittancy is better than the assumed value. The extreme precision indicated by the average deviation probably has no special significance other than that it is better than that computed. The above procedure is believed to meet all the difficulties described in the previous section. As long as the standards are treated exactly as the unknowns, all these sources of errnr tend to c~nncelout. DIRECT ANALYSIS OF 0.1 N POTASSIUM DICHROMATE SOLUTIONS
To investigate the effect of working at higher concentrations ( ~ 1color, the possibility of analyzing 0.1 Ai solutions directly without further dilution was considered. This can be accomplished by working a t a wave length removed from the region of maximum absorption. Figure 3 sh0v.s a family of three-point curves at suitable wave lengths, all plotted against the same 0.09 LV zero point. Below 492 mp the plot was decidedly curved and consequently unsatistactory. The 0.09893 AT solution was checked on each curve. All solutions were a t room tempeiature and all were read in the same absorption cell. The results are given in Table VII. The computed accuracy range here n as obtained from the least and most accurate points shown on the graphs. The prerision is within the computed range, the accuracy slightly better. In working away from the region of maximum ahwi pt i o n , h ~ \
-
Two potassium permanganate snlritions were prepared and atandardized under as nearly identical conditions as possible by observer 3, utilizing Bureau of Standards sodium oxalate 20r and the procedure recommended by the bureau (IO). Because both samples were titrated under nearly identiral conditions, no blank correction was applied in either case. Colorimetric work was done by observer 2 i n a manner ainiilar to that already described. The work was done a t 526 mp, which is in the region of maximum absorption for potassium permanganate, slit width 0.25 mm., sensitivity knob setting 1.5 turns from clockwise end. Figure 4 and Table 1'111 summarize the results obtained. The specific gravity correction was made on the basis of a diiwt comparison of the known and rinknown snlrltions in the "30-ml." specific gravity bottle.
Table VIII.
Normality of Potassium Solutions Found (Colorimetrir I
Found (Oxalate)
0.09865 0.09888 0.09882 0.0988.5
0.09898 0,09888 0.09886 0,09897 0.09890 0.09886 0 09891
Av. 0.09880
0.8
=t
Permanganate
* 0.5 part per thousand
Value corrected for w e 0.09878 cific gravity Computed error *O. 4 to * 1 . 0 part per thousand Error found (taking oxalate value as correct) 7 1 . 3 parts per thousand Based on scale readings of 0.00 and 0.46 and precision of *O. 2'7' in transmittancy.
The results of the oxalate standardization on the permanganate from which Figure 4 was prepared showed an average deviation of +0.7 part per thousand. I n view of this, the reader might quwtion csxpressing the r e ~ i i l tshon-ri ~ to a precision of 0.1 part
166
ANALYTICAL CHEMISTRY
per thousand. This has been done only to compare the prrcisiori of the colorimetric and volumetric methods more closely. Actually, the average colorimetric value is very nearly within t h e experimental error involved in the oxalate standardizations DISCUSSION
Table TX. Ultraviolet Accuracy Increase in Values with New Lamp Wave Length, mw 225
A very inviting possible application of differential colorimetry would be in the determination of a base metal in an alloy, the content of which n-as known to be close to loo%, or in the analysis of a “pure” metal. Here a very short range graph could be prepared in the vicinity of zero on the optical density scale. It might also be possible to obtain an accuracy of 0.1% transmittancy over such a short range. All these factors would make for extreme accuracy. CONCLUSION
Differential colorimetry with the present Model DU Beckman spectrophotometer is capable of yielding results as accurate as most gravimetric and volumetric methods of analysis. The problem of finding colors that are stable and reproducible cnough to utilize needs investigation. ACKNOWLEDGMENT
The authors wish to thank Joan Stewart and Frank Bassani for preparing the graphs shown in this paper. 4DDENDA
Some time after the data in Table I11 were taken, the ultraviolet source employed burned out. The lamp, together with its reflector which showed signs of wear, was replaced and the ultraviolet data were rechecked a t a sensitivity equivalent to that previously employed. The results are given in Tahle I X .
Slit Aperture for Distilled
Water 0.50
A8 Corresponding t o 2.0-Mm. Slit
1.14 1.31 1.42
Accuracy Increase Using Formula 5 6
3.6 4.0 4.3
7 8 9
As anticipated, the accuracy increase values are greater than those given in Table 111, the most appreciable differences being a t wave lengths below 260 mp. Based on these results, differential colorimetry mould be feasible even at the shorter wave lengths. The data given should merely be taken as indicative of the performance to be expected from a new lamp, because these lamps probably vary in their light output. LITERATURE CITED
(1) &res, G. H., XSAL.CHEM.,21,652-7 (1949). (2) Bastian, R., Zbid., 21, 972-4 (1949). (3) Beckman National Technical Laboratories, BuZl. 91E,pp. 3, 10 1947. (4) Cary, H. H., and Beckman. .1.0..J . Optical SOC.A m . , 31, 682-9 (1941). (5) Hawes, R. C . , Katiorial Technical Laboratories, private communication. (6) Hiskey, C. F., Trans. S. IT. Acad. Sci., 11, 223-9 (1949). (7) Hodgman, C., “Handbook of Chemistry and Physics,” p. 1695, Cleveland, Chemical Rubber Publishing Co., 1947. (8) Kolthoff and Sandell, “Textbook of Quantitative Inorganic Anal3 sis.” p . 667, New York, Macmillan Co., 1943. (9) Mellon, M. G., Bx.4~.CHEY.,21,4 (1949). (10) Natl. Bur. of Standards, Provisional Certificate of A4nalysisof Standard Sample 40e, Sodium Oxalate. RECEIIEDMarch 5 , 1949.
Chromium and Manganese in Steel and Ferroalloys Simultaneous Spectrophotometric Determination JAMES J. LINGANE AND JUSTIN W. COLLAT Harvard ilniversity, Cambridge 38, Mass. The spectrophotometric method of Silverthorn and Curtis has been re-examined to determine whether the empirical calibration with standard steel samples is necessary. A study of the various optical and chemical factors demonstrates that Beer’s law is obeyed and the manganese and chromium contents can be computed from the densities observed at two appropriately chosen wave lengths. Corrections have been established for the effect of other elements commonly present in ferroalloys. Results obtained are equal in precision and accuracy to values derived from empirical calibrations.
S
ILVERTHORX and Curtis (6)described a spectrophotometric method for the simultaneous determination of chromium and manganese in steel, which inherently is of great practical utility, The method is based on a persulfate oxidation of the two elements to dichromate ion and permanganate ion, in the presence of phosphoric acid to decolorize the ferric iron. From measurements of the optical density of the solution a t two appropriate wave lengths the chromium and manganese contents can be computed. Under the particular conditions that they selected, Silverthorn and Curtis found that it was necessary to calibrate the method empirically with a series of standard steel samples. It is not clear from their description whether this apparent failure of
Beer’s law was due to the chemical aspects of their procedure or whether it was instrumental in nature and a reflection of the spectrophotometric technique which they employed. The purpose of the present investigation was a critical study of the various aspects of the Silverthorn and Curtis method. I t was found that under the proper chemical conditions, and nThen the absorption measurements are made with a spectrophotometer that operates with a relatively narrow spectral band width, Beer’s law is obeyed and it is not necessary to resort to empirical calibration. In the improved procedure periodate ion is used in addition to persulfate ion to ensure complete oxidation of the manganese and to eliminate the fading of the permanganate which occurs when persulfate is used alone. The influence of
