Overall Rate Analysis of the Gaseous Reduction of Stable Oxides Incorporating Chemical Kinetics, Mass Transfer, and Chemical Equilibrium

A unified mathematical relationship for the overall rate of gaseous reduction of a stable oxide that produces a volatile suboxide has been derived including the effects of a product gas in the bulk stream, chemical kinetics, mass transfer, and chemical equilibrium. The important effect of the small equilibrium constant is quantified. How the reaction conditions affect the overall rate at different asymptotic conditions is also elucidated. By using the obtained results, the conflicting previous claims on the rate-controlling mechanism for the hydrogen reduction of silica has been critically examined and reconciled. The small equilibrium constant of this reaction causes it to be rate controlled by mass transfer under typical conditions and its rate to be slow. How the presence of even a small amount of water vapor in the bulk gas greatly enhances the effects of the small equilibrium constant is elucidated from the mathematical derivation. In addition, the small equilibrium constant also causes the apparent activation energy of silica reduction by wet hydrogen to approach the Δ H ° of reaction and that by dry hydrogen to approach     Δ H °. Because of the large positive Δ H ° value associated with reactions with a large positive Δ G ° value, such a reaction has been mistaken to be rate controlled by chemical kinetics.