Kinetics of Observable with Power-law Mixing Rule in the First-order Reaction Process

Abstract

A theoretical analysis was given for the kinetics of an observable in general first-order reaction process (R→P) . It was assumed that reaction degree x≡ [P] / ( [R] + [P] ) obeyed a first-order reaction rate equation and that the observable o of sample during reaction was related with reaction degree through the mixing rule of a power-law type o^ν= (1-x) o^ν_R+xo^ν_P where o_R and o_P represent the values of observable, being proper to the reactant and the product respectively (o_R<o_P) . It was demonstrated for ν<1 that an observable-time curve could possess an inflection point at o^*= (1-ν) ^1/ν o_P with the maximum growth rate do/dt= (1-ν) ^1/ν-1o_PK₁. These results coincide in the ν→0 limit with those obtained for a logarithmic (ln o) mixing rule.