Knowledge Bank

An investigation of the reaction kinetics of some complex multicomponent systems by spectrophotometric means has prompted the development of methods that could be used for the analysis of spectral data from such systems that are undergoing reaction. The complexity of the mathematical computations requires the use of digital computing techniques for a reasonably quick and statistically meaningful analysis of the data. The complexity is such that the use of computer techniques is mandatory for dynamic systems consisting of more than three components, and even for two or three components, their use is very desirable. In order to make possible the analysis, a number of FORTRAN computer programs have been prepared for the IBM 7090 or CDC 1604--A computers. The application of conventional matrix methods, which require data representative of an equilibrium or instantaneous'' spectrum, to this problem yields erroneous concentration data for the individual components of a multicomponent system undergoing reaction. In order to analyze the spectrophotometric data obtained from a dynamic system by the techniques that have been developed, the absorbance of the multicomponent system is measured at each of a number of selected wavelengths as a function of time, and sufficient absorbance-time data is obtained to accurately define the behavior of the system, in addition to the conventional requirements for analysis of systems at equilibrium. Analytical curve-fitting and interpolation techniques are used to obtain a set of functions which describe the change in absorbance of the mixture with time at each of the wavelengths in the set of wavelengths selected. Sets of instantaneous'' spectra are then computed from these functions. Each computed ``instantaneous'' spectrum is then analyzed by conventional least-squares matrix methods. The instantaneous rate of reaction is also computed as a function of time from the computed concentration-time data for each component. Both iterative and non-iterative least-squares matrix methods have been investigated. A number of curve-fitting-interpolation methods have been studied for obtaining absorbance-time functions which will permit the accurate calculation of time-independent spectra from the time-dependent experimental results. These methods include: high-order polynomials; moving, point-groups of averaged or least-squared quadratic functions; variable-size, moving point-group Lagrangian interpolation, sums of exponential functions, and rational fraction polynomials. The optimum use of these various methods will be illustrated and discussed for three- to five-component reacting systems. The accuracy obtained is dependent upon the complex interaction of many extrinsic and intrinsic error parameters of the multicomponent system under study and the spectrophotometric technique employed. The program output of tabulated results and statistical data is extensive, generally under option, and includes: input data; experimental and computed absorbance-time data; computed concentration-time data, computed instantaneous reaction rate (slope) data for each component, card decks of the concentration-time data for each component, and the automatic preparation of both the absorbance-time and reaction rate curves for each component by CALCOMP plotter output.