A Universal Integrated Rate Equation for Chemical Kinetics.

The overarching analytic integrated rate equation for the chemical kinetics of any reversible or irreversible reaction involving an arbitrary number of species and any integral orders is shown to be Π i=1 r [1 - f i -1 ξ( t)]γ i = e(-1) r   F0 t , where ξ( t) is the extent of reaction variable, the f i are roots of a polynomial of order r, the exponents are determined by γ i = Π k(≠ i) r ( f i - f k )-1 , and F0 is a factor involving the stoichiometric coefficients and rate constants ( k± ). All integrated rate equations of elementary reactions appearing in chemical kinetics are special cases of this universal solution. Not only does the solution provide insight into the analytical form of the exponents γ i and F0 that govern the time evolution of the system, but it also provides an elegant framework for the pedagogy and application of kinetics in physical chemistry.