sium dihydrogen phosphate fixing solution to illustrate its applicability as an ammonia fixing agent, while the other distillations employed a 1000p.p.m. boric acid fixing solution. The per cent relative standard deviation decreases as the concentratioll of am-
mania increases and indicates factory reproducibility.
LITERATURE CITED
( 1 ) Bolleter, W. T., Bushman, C. J., Tidwell, P. W., A N ~ LCHEM. . 33, 592 (1961). ( 2 ) Boltz, D. F., “Colorimetric Determination of Nonmetals)’’ -“Chemical Analysis,” V O l . 8, PP. 86-77 Interscience, New York, 1959. ( 3 ) Chapin, R. M., J . Am. Chem. SOC.56, 2211 (1934).
( 4 ) Kolthoff, I. M., Stenger, V. A,, IKD. ESG.CHEW,ANAL.ED.7, 79 (1935). ( 5 ) Kruse, J. M.1 Mel1on, M. G., CHEM.25, 1188 (1953). ( 6 ) Zitomer, F., Lambert, H. L., Zbzd., 34, 1738 (1962). RECEIVEDfor review March 20, 1964. Accepted April 30, 1964. Pittsburgh
Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 3, 1964.
Ultraviolet Spectrometric Determination of Mixtures of Arylsulfonic Acids J. M. ARENDS, HANS CERFONTAIN, 1. S. HERSCHBERG,’ A. J. PRINSEN, and A. C. M. WANDERS Laboratory for Organic Chemistry, University of Amsterdam, The Netherlands
b Mixtures of arylsulfonic acids in water or aqueous sulfuric acid can b e determined quantitatively by spectrophotometric analysis, based on observation of the ultraviolet absorption of the mixture and of its constituting sulfonic acids. The absorbances of the unknown mixture and of its constituents, measured a t a large number of wavelengths, are subjected to a least squares treatment by an electronic computer. This method seems of general applicability; it is illustrated for mixtures of benzenesulfonic acid and the three isomeric toluenesulfonic acids, for mixtures of benzenesulfonic acid and p- and m-tert-butylbenzenesulfonic acids, and for the system consisting of o-xylene-3- and o-xylene-4sulfonic acids with 0 - and p-toluenesulfonic acids. For all these mixtures very satisfactory analyses were obtained.
T
quantitative analysis of mixtures of arylsulfonic acids in sulfuric acid solution is not very attractive. The difficulties commonly encountered in such analyses have been discussed ( 3 ) . The excellent results obtained in the ultraviolet spectrophotometric determination of the three isomeric toluenesulfonic acids in excess aqueous sulfuric acid ( 3 ) encouraged us to study the applicability of this method to other mixtures of arylsulfonic acids. The principles of the multicomponent analysis have been adequately described (6, 9 ) . The analysis is based on a linear least squares resolution of the absorption spectrum of the mixture to be analyzed in terms of the spectra of the pure components. HE
1 Present address, Mining Research Establishment, Dutch State Jlines, Hoenshroek. The Netherlands.
1802
ANALYTICAL CHEMISTRY
To obtain a high precision in the analysis, it is necessary to determine the absorbances of the mixture and the components a t a number of wavelengths which is large relative to the number of components. The observed absorbances then define an overdetermined system to which, for the evaluation of the unknown concentrations, a least squares treatment by an electronic computer is applied. The applicability of the method depends on the differences in shape of the absorption spectra of the components. The infrared spectrophotometric multicomponent analysis of mixtures of four mononitrofluoroanthenes was recently reported (10). The particular constituents of the arylsulfonic acid test mixtures, as well as their composition, were chosen because of their expected relevance to sulfonation studies planned for the near future. EXPERIMENTAL
Materials. T h e preparation and purification of the three toluenesulfonic acids (11) and benzenesulfonic acid ( 2 ) have been described. The preparation of m- and p-tert-butylbenzenesulfonic acids and of o-xylene-3and o-xylene-4-sulfonic acids will be described in a separate paper (1). Apparatus. The optical measurements were made manually with a Zeiss PMQ I1 spectrophotometer. As a special device, this instrument was equipped with either a sliding or a rotating cell holder. These cell holders, both designed in our laboratory, can accommodate eight and 24 quartz absorption cells of 1-cm. path length, respectively. Procedure. Test mixtures were made bj- mixing appropriate amounts of standard solutions of the pure arylsulfonic acids. The concentrations of the standard solutions, and consequently those of the constituents in
the mixtures, were chosen so as to have maximum absorbances between 1.0 and 1.6 in the wavelength region employed. Absorbances of the test mixtures and of the reference solutions were measured at some 25 to 40 equidistant points in the wavelength region 240 to 300 mh, as nearly simultaneously as possible for any given wavelengthe.g., within 3 minutes for eight cells. CALCULATIONS
The X1 computer (8)was programmed to express the observed spectrum of the mixture as a linear combination of the simultaneously observed spectra of the reference solutions. The linear combination sought is best in the least squares sense; its coefficients represent the relative concentrations of the several components of the mixture when the known absolute concentrations of the references represent unity. Moreover, the calculations yield a mean square residual, 8 , which is a measure of the unexplained variance of the residuals-Le., that part of the absorbance of the mixture that cannot be accounted for as a linear combination of the reference absorbances. 8 is calculated as:
where n is the number of coefficients sought and r, are the residuals; the summation extends over all k wavelengths of observation. I n view of the assumption of a constant background absorbance, A A , n is one greater than the number of components analyzed. The mean square residual, 8, is of twofold interest. In the first place, it may serve to calculate l,the mean square estimated error per observation of absorbance. The relation between t* and 8 is:
Table I. Analysis of Mixtures of the Three Isomeric Toluenesulfonic Acids and Benzenesulfonic Acid in Water" Mixture 1 Mixture 2 Mixtwe 3
Taken
Toluenesulfonic acid concn., mmole/kg.
Found
0.136 0.016 0.546 2,480 3.178
0.131 0.019 P0.559 Benzenesulfonic acid c m c n . , mmole/kg. 2,495 Total sulfonic acid concn., mmole/kg. 3.204 A A x 103 2.8 o x 103 1.8 Wavelengths: 250 to 279 mp, 30 equidistant points. Estimated standard deviation acrording to Formula 5 0-
m-
where the P j represent the relative concentrations as estimated by the least squares method. The average value of 2, derived from a very large number of analyses, is 0.001 in absorbance. If this value, which is consonant with the read-out precision of' the instrument employed, is accepted as the true one, it follows from the theory of the distribution of estimated standard deviations that a n individual experiment will yield 0.00075 6
