Mathematical modeling of physical processes in inorganic chemistry

This dissertation discusses the integration of ordinary differential equations in two different areas of chemistry and is therefore divided into two parts.; The first part deals with the rapid calculation of steady-state concentration profiles in contactors using the Purex Process. Most of the computer codes simulating the reprocessing of spent nuclear fuel generate the steady-state properties by calculating the transient behavior of the contactors. In this study, we simulate the steady-state concentration profiles directly without first generating the transient behavior. Two computer codes are developed, PUMA (Plutonium-Uranium-Matrix-Algorithm) and PUNE (Plutonium-Uranium-Non-Equilibrium). The first one simulates the steady-state concentration profiles under conditions of equilibrium mass transfer. The second one accounts for deviations from mass transfer equilibrium. Both of the codes reduce the computational times by about tenfold without loss of any accuracy over those required by codes that generate the steady-state profiles via transient state conditions.; The second part of this dissertation shows how to use the classical trajectory method to study the equilibrium and saddle-point geometries of MX{dollar}sb{lcub}rm n{rcub}{dollar} (n = 2-7) molecules. Two nuclear potential functions that have the property of invariance to the operations of the permutation group of nuclei in molecules of the general formula MX{dollar}sb{lcub}rm n{rcub}{dollar} are described. Such potential functions allow equivalent isomers to have equal energies so that various statistical mechanical properties can be simply determined. The first function contains two center interactions between pairs of peripheral atoms and its defined by V(r) = 1/2{dollar}Sigmasbalpha{dollar}k{dollar}Delta{dollar}r{dollar}sb{lcub}alphamu{rcub}sp2{dollar} + {dollar}Sigmasb{lcub}alpha