Qualitative Analysis from Mass Spectra S. M. ROCK Consolidated Engineering Corp., Pasadena, Calif. Chemical analysis from mass spectrometric data may be either qualitative or quantitative. The latter has been extensively covered in the literature, but the methods used in the former have not been systematically presented. This paper presents several aids to qualitative analysis and outlines and illustrates various basic procedures: check of mass intervals to identify fragments and elements; use of peak-free regions to establish absence of fragments; comparison of peaks with those predicted from normal stable-isotope ratios; recognition of characteris-
I
tic half-mass and metastable-transition groups; and use of mass spectral compilations such as those available from A.P.I. Project 44. A table of isotope contributions of hydrocarbons through C I is given. Peaks are roughly classified by magnitude and charted against mass in a summary of the spectra of 279 compounds. One of the most valuable features of the mass spectrum of a mixture is that all materials present register; the method can be relied on for both positive and negative information, and unexpected components do not escape detection.
the molecule (3, 7 , 9, I ? ) , much useful information can be ohtained by checking mas8 intervals in the mass spectrum against possible fragments predicted from the structural formula. A series of peaks one unit apart, for instance, usually indicates successive removal of hydrogen atoms, and thus establishes the presence of that element in the unknown. Peaks 15 mash units apart strongly suggest a CH3+ ion. Among the many other intervals which may yield useful information are the following, which suggest the elementq or radicals coupled with them: 14 ( N or CH,), 16 ( 0 ) ; 17 ( O H ) ; 20 (CzHs or CHO); 32 (S), 35 (CI), 41 (CSHS); 43 (CaH,), and 19 (F). .I check of such intervals between peaks or groups of peaks in the spectrum of the unknowns is one of the first steps in qualitative work. If the unknoITn compound ionizes to its parent mass (the mass computed from its formula, using the mass number of the most abundapt isotope of each element present), the sizes of the one or two peaks a t masses successively higher than the parent can in almost every case be predicted from the known isotope ratios, on the assumption of random distribution of the heavier atoms. The same type of prediction can be made for many fragments, although it is then somewhat less certain, because of preferential ionization ( 2 ) or formation of peaks requiring rearrangement ( 9 ) . Even so, invwtigation of ratios of peaks 1, 2 , or 3 mass units above a majoi peak is usually helpful a t almost any point in the spectrum-for example, the appearance of one chlorine atom in either a parent or fragmented ion d l result in peaks 2 masses apart in the ratio of 3 to 1. Thus, 2-chloropropane, parent mass 78, s h o w a peak a t m/e 80 which is about ‘/B of the 78. The same ratio holds in the fragment CH3.C . CH C1 a t masses 63 and 65, the heavier peak being due, of course, to presence of heavy chlorine. Purely on the basis of the 80/78 ratio, it is thus possible to distinguish between this compound and its mas8 isomer, benzene. For benzene, the 79/78 would be about 6.4% (6 carbons) and 80/78 would be about 0.2% (see Table I).
S T H E literature on mass spectrometric analysis, numerous
articles have stressed accuracy of quantitative determinations and the speed with which they can be attained (6, 7 , 10, 12-16). Little has been published, however, regarding the extensive use of the instrument in qualitative analysis. In this field the mass spectrometer possesses a considerable advantage over many chemical methods, in that cvery substance present is autoniatically registered in the mass spectrum Thus, it is not necessary to make a distinctive test for each material to be determined, yet unexpected components do not escape detection. The thieshold of detection of various materials and the ease mith Ivhich they may be identified vary, depending 011 several factors, including the concentration of the unknoJrn and the identities, concentrations, and number of other materials present. The simplest cases are those in which each component of interest has several unicomponent peaks-Le., peaks t o uhich no other constituents ionize appreciably. A somewhat more difficult type of problem is the identification of an unknown, most of whose peaks also include contributions from other matclrials in thc mixture. Some of these problems involving overlapping spectra can be solved by minor calculations. Others-such as thosc involving comparison to a standard-may often be solved by inspection of relative peak heights, particularly when only an indication of presence or absence of impurity, without identification of it, is required. AS the complexity of the mixture incieases, either qualitative or quantitative information becomes more difficult to obtain. Finally, if there are more overlapping components than major peaks, or if various calibrating spectra are unavailable, the problem may become impossible to solve completely without recourse to other methods. This fact detracts in no .i7.ayfrom the value of the method in the large variety of problems which fall u-ithin its scope. In either the simple or more complex cases of qualitative mass spcctrometer analysis a ready knowledge of atomic weights, etructural formulas, and normal stable isotope abundance ratios is essential, together with a familiarity with the characteristics of as many mass spectra as possible.
-
OBSERVED CHARACTERISTICS OF MASS SPECTRA
The greatest aid to qualitative analysis is a large library of mass spectra. Most laboratories have collected the numerous spectra in which they are most interested; many have made punch card files for ready reference. Sow, an ever growing accumulation of spectral data is available through A.P.I. Project
USE O F FORMULA AND ISOTOPE RATIOS
The peaks to be expected in the mass spectrum can be more or less predicted from the structural formula. Prediction is limited; it is well known that many materials exhibit substantial peaks which rvould not be expected purely from fracture of bonds as represented in the conventional formula. The peak at mass 29 in isobutane is an example; others are the 57 peak in 3,3-diethylpentane, or the 33 peak in isobutyl alcohol. In spite of the occurrence of these anomalous peaks, requiring rearrangement of
44(1).
Study of the numerous available patterns yields many useful generalizations regarding various classes of materials. Some observations useful in qualitative analysis of organic mixtures are listed below. 1. General. iilmost no compounds shorn- peaks above the
261
ANALYTICAL CHEMISTRY
c c
.0
V O L U M E 2 3 , NO. 2, F E B R U A R Y 1 9 5 1
263
264
ANALYTICAL CHEMISTRY
V O L U M E 2 3 , NO. 2, F E B R U A R Y 1 9 5 1
265
tion in computing Table I. These factors are useful for many quantitative as well as qualitative determinations, even though the assumption of no preferential ionization may sometimes fail ( 8 ) . The ratio used for C13/C12was 1.04/98.96, and was obtained by averaging values from a number of repeated mass spectrometer runs of Cz through Ce paraffins, using only parent and heavier peaks for each compound. The common value, 0.00015/0.99985, was used for D / H ( 1 1 ) . Odd peaks are usually larger than even. Above C,, the parent peak is the largest peak in the parent C group in most hydrocarbon spectra. For example, for hexanes the 86 peak is the greatest in the group of peaks between CS+ and C6HI4+(masses from 72 through 86). For CS and heavier few peaks appear in the parent group except the parent itself and, in a few cases, the peak immediately preceding it. Thus compounds differing 2, 4, etc., units in mass are readily recognized-for example, cgcloparaffins or olefins in paraffins, or diolefins in materials of formula CnH2,, or CnH2,+? (see Figure 1 ) . Straight-chain hydrocarbons have parent peaks hut, as the carbon skeleton becomes more highly branched, the parent peak decreases. For example, peak 114 is inappreciable in 2,2,3,3tetramethylbutane, but of useful size in n-octane (see Example 1). Ca and CSolefin isomers have very similar spectra. Beginning with CS, greater differences among isomer patterns begin t o appear. 3. Oxygenated Materials. Saturated alcohols, ethers, and esters have parent peaks 2 units above those of the parafin of nearest parent mass--e.g., butanol is mass 74, n-pentane 72. Usually the spectra of oxygenated materials also contain peaks a t odd masses, such as 31 or 45, to which hydrocarbons do not appreciably contribute. They are thus readily detected in the presence of hydrocarbons. Aldehydes have the same molecular mass number or parent peak as hydrocarbons--e.g., propane and acetaldehyde both are of mass 44. However, peak ratios differ considerably, so that they are readily recognized when a few essentially unicomponent peaks are available for PARENT PEAK CgPARAFFINS comparison. #2 c9 H20 Most of these observations may be verified and othew deduced if Figure 1 is closely U N E X P E C T E D MATERIAL s t u d i e d . T h i s c h a r t sumP R OBABLY H Y O R 0 G E N ATE 0 marizes 279 mass spectra and TERPENES indicates roughly the relative magnitudes of pattern coeffic i e n t s . T h e l e g e n d in the SOME C 7 0 V E R ISOTOPE NO .HIGHER MASSES TRACE C a w figure explains the symbols 7 used. Most of the spectra are n&SoToPL taken from the A.P.I. “Catalog io0 111 112 113 114 127 128 129 138 139 I40 141 142 of Mass Spectral Data” ( I ) , to which reference can be made for more refined coeffi# I cients. Twoexamples are cited below to illustrate how tho enumerated observations and others may be applied to yield valuCII able qualitative information on the mass spectra of unknown samples. NO HIGHER -C7OVER ,-1?9 C QYEB
parent peak, except those predictable from the heavy isotopes of elements present. Many spectra exhibit half-mass peaks (doubly charged ions) or metastable peaks (4, 6) whose distinctive mass, size, and shape are very useful in identification. Among the helpful half-mass peaks are the 22 peak in the carbon dioxide spectrum, 20 in argon, and the half-mass group between 19 and 21 in the propane and propene spectra. A well-knowm metastable peak is that a t m/e 31.9 in the n-butane spectrum. Some of the groups most distinctive in shape, and of large size, occur in the spectra of the aromatics-at 76 in benzene, 88 to 90 in toluene, and 58 to 59 in ethylbenzene (see Example 2). 2. Hydrocarbons. Paraffins do not ionize in substantial amounts to the parent peaks of lighter paraffins except for heavy isotope contributions-Le,, the 30, 44, 58, and 72 peaks in mass spectra of Ce and heavier hydrocarbons are due primarily to C2H6+, C3H,+, C4Hsf, and CbHllt ions, respectively, each containing one C13 or one D (17). This fact makes feasible the ready detection of light paraffins in those of higher molecular weights. Light olefins or cycloparaffins cannot so readily be detected among heavier compounds of the same type, except for those 14 units below the parent. For example, mass 56 in the pentene spectra (parent=70) is mostly isotope; 42, however, is not. The isotopic distribution in hydrocarbons has been computed here on the assumption of random distribution of heavy atoms and no preferential ionization. Table I shows the distribution of ions of each atomic constitution (or formula) a t successive masses, as percentages of the ions of principal mass, (mle),. Principle mass is defined as that computed from the ion formula using C = 12 and H = 1. Thus, the fragment CIH7has principal mass 43. Relative abundances of ions of formula CaH7 appearing a t masses 44 = ( m / e , 1 ) (containing one CIS or one D), and 45 = ( m / e 2) (containing 2 C13’s, 1 C13 and 1 D, or 2 D’s) are given in the table as 3.26 and 0.04%. The probability of appearance of either C13or D, or both, was taken into considera-
+
+
-
-
-
‘3 w
I
5 50
7
w a
n
MASS
9899
2 W
f
I:5 0 w
a
_.
--
nn
ll
-
ISOTOPE
ISOToePE
-1
cg
MASSES --L-c
n MASS
9 8 99100
Figure 2.
Ill 112 I13 114
127 128
138
156 151
Schematic Mass Spectra of Narrow Pine Oil Fractions
1. Almost pure CnHzr 2. Primarily CoHzo with unexpected impurity showing at masses 138 to 142
Example 1. Purity Check. The first example illustrates a purity check of two closely fractionated pine oil samples (8), for which calibrations were not a t the time available. S p e c t r a obtained are
ANALYTICAL CHEMISTRY
266 Table I.
Isotope Correction Factors for CI through C; Hydrocarbons
This table waa computed on the assumption of random distribution of heavy isotopes and no preferential ionization. The C13/Cl2 ratio used was obtained b y averaging ratios of (parent peak + l j / ( p a r e n t peak) for numerous repeat runs of C2-Co paraffins on the Consolidated Model 21-101 mass spectrometer. C13/C'* = 0.0104/0.9896 D!H = 0.00015/0.99985
Ion Formulaa
C CH CHz CHI CHk
(m/e)pb
12 13 14 I5 16
Percentage of Monoisotopic Peak a t ( m / e ) p Which Appears a t__ : (m/e)p 1 (m/ejp 2
+
1.0.5% 1.07 1.08 1.10 1.11
2.10% 2.12 2.13 2.15 2.16 2.18 2.19
CI CsH CaHz CaH: CrH4 CaHi CiHi CrH7 CsHs
n 1 . 6 X io-% 3 . 2 x 10-4 4 . 8 x 10-4 6 . 4 x 10-4 0.01 0.01 0.01 0.01 0 01 0.01 0 01
3.15% 3.17 3.18 3.20 3.21 3.23 3.24 3.26 3.27 48 49 50
a. b
+
Pertcentage of MonoiRotopic Peak at ( m l e ) p Which Appears at: Ion ForrnnlaQ ( 7 ~ / e ) ~ 5( r n / e ) , 1 (m/ej 2
4.20% 4.22 4.23 4.25 4.26 4.28 4.29 4.31 4.32 4.34 4.35
0 07
0 07 0 07 0 07 0.07 0 07 0 07 0 07 0 07 0.07 0.07
+
+
5. 26Y0 5.27 5.28 5.30 5.32 5.33 5.34 5.36 5.38 5.39 5.40 5.42 5.44
0.11 0.11 0.11 0.11 0.11 0.11 0.12 0.12 0.12 0.12 0.12 0.12 0.12
6.31% 6.32 6.34 6.35 6.37 6.38 6.40 6.41 6.43 6.44 6.46 6.47 6.49 6.50 6.52
0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.18 0 18 0.18 0.18 0. I S
Ion Formula
(~n/e)p
84 85 86 87 88 89 90 91 92 ox .,94 95 96 97 98 99 100
Percentage of Monoisotopic Peak a t ( m / e ) p Which Appears at: ( m / e ) p f 1 ( m / e ) p 4- 2 ( m / e ) p t 3 1.36% 7.37 7.39 7.40 7.42 7.43 7 . 4.5 7.46 7.48 7.49 7.51 7.52 7,54 7.55 7.57 7.58 7.g0
0.23 0.23 0.23 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.23 0.25 0.25 0.23
0.004
Chemical formula of monoisotopic ion. Principal m/e of ion (C = 12, H = 1).
Table 11. Mass Spectra of Cyclohexanone, Toluene, l,g-Dioxane, and Acetone
m/e 28
37
38 39 40 41 42 43
44 45 46 50
56 57 58 59 60
61
Consolidated Model 21-102 Mass range. 28, 37-99 Electron current. 9 pa. Tolu1,4Cycloene Dioxane hexanone 12.5 0.5
100
1.8 4.1 22.4 6.9 32.7 81.6 12.2
2.5 5.0 18.7 2.1 2.1 0.2 1.8
1.2 0.2
1.1
...
5.7 4.0
1.7 1.9 0.7 3.0 7.5 100 11.5 2.1
5.9 9.6 2.4 1.2
0.1
... ... 0.1
.. .. .. ..
i):3 2.1
... ...
0.2 0.2 0.7 1.9 10.9 2.4 3.0
... ... .... .. ...
... ...
paraffins, the absence of peaks between the expected C groups attesting absence of many AceTolu1,4possible c o n t a m i n a t i n g ene Dioxane tone m a t e r 1a1s-naphthenes and 4.2 0.1 aromatics, to mention only .. 8.6 0.1 two. 2.1 .. .. .. 13.1 .. Spectrum 2 was supposed .. 1.7 .. to be a comparably pure Cs. The substantial peak at 128 .. .. indicates a large amount of C, paraffin, a g a i n n o t h i g h l y branched. Small excesses over isotope a t 100 and 114 in.. dicate traces of C, and Cg. .. The major surprise, however, was the presence of substantial .. peaks from 138 to 142. There is no doubt of their presence. From other considerations (8) they are tentatively .. identified as h v d r o -a e n a t e d terpenes. ..* .. .. Thus, valuable information ... .. .. regarding presence or absence ... .. 39 48 of contaminants was obtained 47 from mere inspection of the record, without recourse t o specific calibrations. Example 2. Identification of Unknown Solvents. Example 2 shows the spectrum of a mixture of organic liquids. None of the components had been identified prior to running the mass spectrum. The presence of toluene x a s obvious a t first glance a t the spectrum, because of the distinctive metastable group around mass 90 and the half-maps peaks a t masses 43 through 46. These are shown in Figure 3, in which the lower spectrum was obtained from the mixture, the upper from pure calibrating toluene. The records are from a standard Consolidated Model 21-102 mass spectrometer, with three galvanometer traces
Electron accelerating voltage. 70 volts Ionization chamber temperature. 250' C.
MS.
Acetone 1.9 2.2 2.3 3.8 0.8 2.2 7.1 100
-
'
mle
62 63 64 65 66
Cyclohexanone 0.3 0.5 014 0.2
io 71
24.3 18.8 1.7
97
1. 7
69
2.3
0.2 ... ... ...
0.1 0.4 0:3
0.4 5.7
...
23.6 1.1 0.1 0.1
27.8 0.9
0.8
... 98 28.9 ... 99 2.0 Sensitivities 29 div. / P (n - C4 43 = 40 div./p)
schematically represented in Figure 2. Spectrum 1 is nearly pure CllH24 (mle = 156). The peak a t m / e 157 is due to presence of heavy isotope. S o straight-chain CllH2? . or CllHzo is present. The peak a t 138 is probably a minute impurity. Peak 128 is slightly greater than the peak ,predicted from isotope coefficients of Table I, so that a trace of CS1s present. The large parent peak ( m / e = 156) indicates straight-chain or nearly straight-chain Cll's rather than the highly branched compounds. The sample is thus shown to be practicnllp pure C11
..
262
V O L U M E 23, NO, 2, F E B R U A R Y 1 9 5 1
,
masked out, leaving only one showing to facilitate reproduction. The records on this instrument are taken a t a constant speed regardless of the peak size, so that the mass scale (abscissa) is the same for all records. Thus peaks in the toluene speotrum can be directly oompared to those of the mixture spectrum which are directly below them. The 58/43 ratio in the mixture spectrum suggested that acetone rather than normal or isohut,ane was the chief contributor to these peaks. The peaks a t masses 88 and 98 were assumed to he due to two separate materials, as the 10 unit mass difference could not be explained by any common radical. The spectra. had been run to mass 150, and no peaks found above mas8 98. Even so, it did not neoessarily f d 0 N that peaks 98 and 88 were the parent peaks of the substances romaining to be identified, for not all materials ionize to the parent mass. The initial assumption was made, honcver, that these u w e the molecular mass numbers. The 83 peak was associated with the peak rtt maas 08 bebause of the 16unit ma= difference usually rtssoeiated with C B + . Similarly, the peak a t mass 69 was most logicrtlly ascribed to the
Figure 3.
remaining peaks were identified by their relative aizes, as those of dioxane. Spectra of a11 four solvents are shown in Table 11. Negligible residuals remained after quantitative determination of the four components, Showing that the constituents had been correctly identified. SUMMARY
The fact that all matorials prosent in concentrations above their threshold of detection automatically indicate their presence on tho mass spectrum is particulsrly umful in establishing the prcsence or absence of compounds, whether or not they were previous1y anticipated. Of the many deviccs and techniques used by the mass spectroscopist to extract qualitative information from the mass spcetrum, the following have heon discusmd and some of them illustrated: Check o probably pi
Mass Spectra of Toluene (upper) and Liquid Mixture (lower)
Record obtained on Consolidated Model 21-102 mass speotrorneter. with traces 1 3 and 30 masked off. IIdf-m&espeaks at 44 to 46 and metastable at 00 immediately identify toltede mixture. Msjor Deaks oontributed by three other components of mixture &re &bo marked.
mass 98 material because it represmtcd loss of the fragment CIHs+ ($9). Similarly, tho large peak a t 55 was probably due to the mass 98 snhst.ance. The ratio of peaks 99/98 shows that not more than 6 carbons u ~ r cpresent, 80 that C7 olefins and eycloparaffina were eliminated. The small 100/98.ratio (0.5% r~ determined on more sensitive traces not shown here) eliminated chlorine and sulfur as possihilities and suggested the presence of oxygen. Comparison with spectra of Cs oxygenated m a terials identified this material as cyclohexanone. The mass 88 material NFBSnow known to contribute to peak 31, hnranrr nnnn nf tho n t h m enn+itiion+c innimorl tn "".._. ~".."l."l".. "l."... "" ""tho+. ~ m a r s to 3" appreciable extent. When acetone, toluene, and cyclohexanone contributions were subtracted from the mixture spectrum, the
""~~-"".."..~". ".."
."~-
Ohserv&m of peak-free regions to establish absence of materials contributing to those portions of the record. Comparison of relative siaes of major peaks and those immediately fohwing with thoso enpeoted from heavy isotopes, to ssoertain probable presence or absence of elements with stable isotopes. ' Recognition of chilraaoteristic pcak shapes and distinctive peak groupings on the reoord to identify constituents-e.g,, metastable and half-mass peaks. Use of general knowledge of mass spectral characteristics of
~-".."..~ ".
r i a r i m i s e l g ~ ~ o nf e.. ..nmnnlsnAe mo+o*i.le _ " " . . . I I " " . . " " tn "" irlantifv tirnei "~11"" nf ...l"-I1w."
".l""l"
present. The observations cited o m be supplemented by study of Figure 1. This table also facilitates the preliminary sween-
ANALYTICAL CHEMISTRY
268
ing check of the peaks to be identified against a number of mass spectra. ACKNOW LEDG.M E Y T
The constructive suggestions offered by H. W. Washburn and A. P. Gifford were most helpful and are much appreciated. LITERATURE CITED
(1) Smerican Petroleum Institute Research Project 44, Natl. Bur.
Standards, “Catalog of Mass Spectral Data.” Sets of spectra may be obtained from: D. V. Stroop, American Petroleum Institute, 50 West 50th St., New York 20, N. Y. (2) Beeck, O., Otvos, J. W., Stevenson, D. P., and Wagner, C. D., J . Chem. Phus., 16, No. 3, 255 (1948). (3) Bloom, E. G., Mohler, F. L., Lengel, J. H., and Wise, E. C., J . Research Natl. Bur. Standards. 40, 437 (1948). (4) Ibid., 41, 129 (1948). (5) Bloom, E. G., Mohler, F. L., Wise, E. C., and Wells, E. J., Ibid., 43, 65 (1949).
(6) Brown, R. A., Taylor, R. C., Melpolder, F. W., and Young, W. S., ANAL.CHEM.,20, 5 (1948). (7) Gifford, A. P., Rock, S. M., and Comaford. D. J.. Ibid., 21, 1026 (1949).
(8) Haagen-Smit, A. J., Redemann, C. T., and Miroo, N. T., J . Am. Chem. Soc., 69, 2014 (1947). (9) Honig, R. E., private communication. (10) Langer, Alois, and Fox, R. E., ANAL.CHEM., 21, 9 (1949). (11) Seaborg, G. T., and Perlman, I., Rev. Modern Phys., 20, 585 (1948). (12) Shepherd, M., ANAL.CHEM., 19, 635 (1947). (13) Starr, C. E., Jr., and Lane, Trent, Ibid., 21, 572 (1949). (14) Taylor, R. C., Brown, R. A,, Young, W. S.,and Headington, C. E., Ibid., 20, 396 (1948). (15) Thomas, B. W., and Seyfried, W. D., Ibid., 21, 9 (1949). (16) Washburn, H. W., Wiley, H. F., Rock, S. M., and Berry, C. E., IND.ENG.CHEM., ANAL.ED.,17, 74 (1945). (17) Wiley, H. F., and Berry, C. E., “Mass Spectrometry” in “Mod-
ern Instrumental Analysis,” D. F. Boltz, ed., Ann Arbor, Mich., Edwards Brothers, 1949. RECEIVED March 7, 1950. Presented in part before the Divisionof Analytical and Micro Chemistry at t h e 112th Meeting of the . ~ X E R I C A N CHEMICAL S O C I E T Y , New York, N. Y .
Effect of Finite Slit Width on Infrared Absorption Measurements A. R. PHILPOTTS, WILLIAM THAIN, AND P. G. SMITH The Distillers Co., Ltd., Great Burgh, Epsom, Surrey, England Extinction coefficients in the infrared vary with the resolving powelci.e., they depend on the optical arrangement of a spectrometer and on the slit width used. This work attempts to find practically and (within the limits of the assumptions made) theoretically the extent of this variation. Plots of absorption against concentration for solutions of three hydrocarbons were made at different slit settings, using a Perkin-Elmer Model 12B spectrometer. The variations in slope and the deviations from linearity were found to fit (formally at least) the theoretical explanation given. The magnitude of the effect shows that spectroscopists must be very careful when using extinction coefficients determined under optical conditions not identical with those of the analysis. A method of correlating data taken at different slit settings on the same spectrometer in the same state of optical adjustment is given. It is hoped that the correction of extinction coefficients to “infinite resolving power” suggested will enable extinction coefficient measurements to be used on all spectrometers.
E
STIMATIOXS by absorption spectrophotometry are greatly simplified when deviations from the Beer-Lambert law are smaller than experimental error, especially when multicomponent mixtures can be analyzed by the method of solving linear simultaneous equations. The dependence of extinction coefficients on instrumental conditions (a great difficulty of infrared spectroscopy) is also bound up with the applicability of the law. Much work has therefore been devoted t o the investigation of deviations. Failures of the law due t o the inherent properties-e.g., intermolecular forces, etc.-of the sample in question are t o some extent unavoidable, but it should be possible t o correct for or a t least calculate the magnitude of instrumental limitations. These chiefly concern scattered radiation in the monochromator and the effect of finite slit width. Methods of dealing with the first have been reported (4). While attention (6, 10) has recently been drawn t o the second, and the general principles (3,7) have been laid down, there has been no discussion of the magnitude of the errors caused when conventional infrared spectrometers are used.
The case of the area of absorption bands has been considered (8, 11). While this manuscript was in the course of preparation, applications to ultraviolet problems were published b y Eberhardt ( 8 ) . Whether single- or double-beam spectroscopy is employed, the observed density is always the logarithm of the ratio of incident t o transmitted intensity, each intensity being integrated over the pass band of the monochromator. The error is introduced by assuming that the density obtained in this way is identical with the true density at the central wave length. The magnitude of the error at the maximum of an absorption band depends on the relation of the pass band width t o the true shape of the band. It is very difficult t o obtain the shape of a band at infinite resolving power and the pass band of a monochromator depends on such indefinite quantities as image aberration and line-up, as well.as the (possibly) calculable geometric slit width, diffraction effect, and image curvature. The best method of procedure seems t o be: Calculation of errors in terms of an idealized absorption band and spectrometer response
,
