A Method for the Deductive and Unique Determination of the Values of Three Parameters Involved in Fractional Functions Applicable to Relaxation Kinetics

Abstract

A novel method is proposed to determine deductively and uniquely the values of three param-eters, a, b, and c in a fractional function of the form,
y=a+bx/(c+x)
where x and y are experimentally obtainable variables. This type of equation is frequently encountered in chemistry and biochemistry involving relaxation kinetics.
The method of least squares with the Taylor expansion is employed for direct curve fitting of observed data to the fractional function. Approximate values of the parameters, which are always necessary prior to commencing the above procedure, can be obtained by the method of rearrangement after canceling the denominator of fractional functions. This procedure is very simple, but very effective for estimating provisional values of the parameters. Deductive and unique determination of the parameters involved in the fractional function shown above can be accomplished for the first time by the combination of these two procedures.
This method is extended to include the analysis of relaxation kinetic data such as those of temperature-jump method where the determination of equilibrium concentrations of react-ants in addition to the three parameters is also necessary.