Correction for Interfering Absorption in Spectrophotometric Analyses Application to Determination of C6,Ci, and C, Aromatic Hydrocarbons and to Determination of Naphthalene by Ultraviolet Absorption D. D. TUNNICLIFF, R . S. R,IS.\.IUSSEW, A N D M . L. MORSE’ Shell Development Company, E m e r y d l e , Ca1;f. tion as well as the concentFations of the desired components. However, in practice, the calculation of the constants is omitted. The specific applications described are for the determination of benzene and toluene; ethylbenzene, o-wlene, m-xylene, and p xllene; and naphthalene. The degree of correction for different types mf interfering absorption is shown bj the results of the analysis of a number of synthetic samples containing interference.
hn algebraic method for the correction of spectrophotometric data for the effect of interfering absorption is based on the assumption that the optical density of the interference can be represented by an analytical function of wate length, and that this function does not represent the optical densitj of any of the components being determined. The optical density is measured at a sufficient number of wave lengths to determine the constants of the func-
THE
application of spectrophotometric analpis is often seriously limited by the presence of unknown substances which absorb a t one or more of the wave lengths used in the analysis. This intcreference can often be removed by chemical treatment (6). However, in cases where the interfering material resists chemical treatment, the interference may cause such large errors in the analysis that the results are, valueless unless suitable corrections are applied. This condition is frequently encountered in the determination of aromatics by ultraviolet absorption. It is very difficult to ascertain Pefinitely the nature of these interfering compounds or even to determine the exact shape of their absorption curves. Possible compounds include olefins, compounds containing sulfur, and peroxides. Although many compounds in the first two categories can be removed hv chemical treatment, others are very resistant. Experience has shown that the interfering absorption in the spectral region used for the analyses is usually a smooth function of the wave length; the absorption decreases, with various degrees of steepness, as wave lengths increase. Occasionally the absorption curve of the interference has a maximum or a minimum in the spectral region used for the analysis. Absorption curves of types believed to be typical-actual absorption curves of various pure compounds-are shown in Figures 1, 2, and 3. The compounds chosen for this purpose are not necessarily those that niay be present in actual samples but were selected because their absorption curves simulate the absorption curves of the actual interfering substances. Two methods, which arc simpler than the algebraic method, are frequently useful. Figure 4, curve 1, s h o w the absorption curve of an interfsring substance; curve 2 shows the absorption curve of a sample of benzene containing this substance. A very simple method which gives an approximate correction for the interference is based on a measurement of the optical density of the sample a t a benizene peak and a t the base of the peak--e.g., a t 2545 and 2530 -4. The benzene content is then calculated from this difference (d, in Figure 4) and from calibration data obtained at the same wave lengths with pure benzene. This method assumes that thcinterference does not, differ significantly between 2545 and 2530 =I.-Le., Ad1 is not significant. This assumption is valid only if the interfering optical density is changing very slowly 1
Figure 1. Absorption of Interfering Materials Added to Synthetk Samples Listed in Table I
~ i t the h wave length or the absorption peak is very steep on one side, so that two wave lengths can be chosen xhich lie very close together. Although the earrection in this example is not very accurate, this method is ofken useful in favorable circumstances. A more accurate method (1, 3, 4,7 ) consists of measuring the optical density on both sides of the absorption peak and calculating the correction to be applied a t the peak by linear interpolation. This method is commonly referred to as the base-line method. Referring to the example in Figure 4, the benzene concentration would then be calculated from the difference, d?. In this case it is assumed that the absorption is changing linearly through this short spectral inderval-i.e., ad2 is not significant. This method usually gives good results for very sharp absorption peaks where the wave-length positions on opposite sides of the peak are close together, as is the case with benzene.
I’rrsent addreas. 2732 Benvenue Are., Brrkeley, Cali!.
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ANALYTICAL CHEMISTRY ALGEiBRAIC CORRECTIOS ,METHOD
The algebraic correction method described in this paper is an extension of the base-line method. Instead of the assumption that the interference is lincw OVPI ii small spectral interval, it is assumed that the optical density of the interference can be represented by some general analytic expression as a function of the wave length. A suitable function with adjustable parameters is chosen from a general knowledge of the absorption curves of the interfering materials found in the samples. The optical density of the sample is measured a t a sufficientnumber of wave lengths to fix the numerical values of the parameters and the concentrations of each of the components being determined. In practice the function must be expressed as a series with variable coeffirients as the parameters:
where D,nt(A) is the optical density of the interference as a function of the wave length, A. The function chosen to represent the optical density of the interference must satisfy two conditions: (1) It must accurately represent the optical density of the interference through the required spectral interval. (2) I t must be impossible for the function to represent even approximately, a t the wave lengths used in the analysis, the optical densities of any one component or any combination of the components to be determined. The particular functions which have been found to be useful are the power series and a sum of descending exponentials. The general method followed in the use of these functions is illustrated below with the power series. The application of both types of functions to specific analyses is described in later sections. In the case of the power series the optical density of the interference is represented by an equation of the following form: Dint(X)
= UD
+ u ~ ( X - Xo)az(X+- Xo)' + . . . . . + ap(A - Xo)p
(2) The choice of AD, the origin of the wave-length scale, is purely arbitrary; its purpose is solely to reduce the size of the numbers in the subsequent calculations. The total optical density a t wave length i of a sample containing interfering absorption in addition t o n components to be determined is then given by the expression:
0,= uo
+ UI(L- Xo) + az(L - AD)' + . . . . + - A o ) ~+ E ~ I C +I E ~ z+c .~. . + EIncn ~p(Xt
(3)
1.0
08
$0.0
z
x
J
a
0 go4
02
2500
I
I
2600
I
I
2700 WAVE
Figure 2.
I LENGTZEY
2900
ly
3000
Absorption of Interfering Materials Added to Synthetic Samples Listed in Table 111
V O L U M i 2 1 , NO. 8, A U G U S T 1 9 4 9
897
8. Substitute these optical densities in Equations 4 and solve for the concentrations of each of the n components. The values of the a’s can be calculated also, if desired, but they are seldom of interest. A similar procedure is followed when the interference is expressed in terms of a sum of descending exponentials. These exponentials will have the general form: D,,t(A)
= a0 allO-h(h
+
- Ao)
+
The value of the k in each term is chosen in accordance with the naFigure 3. Absorption of N a p h t h a l e n e w i t h ture of the interference Interfering Materials Added to S y n t h e t i c rxpected in the samples. Samples Listed in T a b l e V Figure 4. Absorption Curves 4 value of k is chosen 1. Interference in one term so that this 2. Benzene plus interference where el = concentration of component j and E
