Oxygen-limited autoxidation

Oxygen-limited autoxidation occurs when the availability of molecular oxygen restricts the observed reaction rate. Oxygen can be consumed faster than it is replenished through interphase mass transfer, even when the gas above a liquid contains plenty of oxygen. A slow oxidation trace therefore does not by itself establish efficient radical-trapping antioxidant action.

A primary study measured dissolved oxygen availability during liquid-phase hydrocarbon autoxidation, rather than relying only on transport predictions. Its reported oxygen-transfer coefficients differed between benzene and indan under the stated conditions, illustrating why a gas atmosphere alone does not specify the liquid's oxygen supply.^[ref]

An original well-mixed mass balance separates transfer from consumption. Let $C$ be dissolved oxygen concentration, $C^{\ast }$ its equilibrium value at the imposed gas composition, and $k_{L}a$ the volumetric transfer coefficient. If a simplified local rate law consumes oxygen at $kC$, thenWith constant coefficients, the steady state isFor $k\ll k_{L}a$, the liquid stays near $C^{\ast }$ and the rate responds strongly to chemical kinetics. For $k\gg k_{L}a$, the rate approaches the transfer ceiling $k_{L}a{C}^{\ast }$. This first-order consumption model illustrates the transport mechanism; it is not a universal elementary rate law for radical-chain oxidation.

For $k_{L}a=0.10{\mathrm{s}}^{-1}$ and $k=0.90{\mathrm{s}}^{-1}$, $C_{\mathrm{ss}}=0.10C^{\ast }$ and $r_{\mathrm{ss}}=0.090C^{\ast }{\mathrm{s}}^{-1}$. Doubling $k$ only raises the rate to about $0.0947C^{\ast }{\mathrm{s}}^{-1}$, a $5.3\%$ increase. A nearly flat response to a chemical perturbation can thus be a delivery limitation.

A discriminating experiment changes stirring or gas-liquid contact while matching temperature, substrate, initiator and optical settings, and records dissolved oxygen as well as the oxidation signal. Dependence on transfer conditions reveals a limitation that an optical trace alone can hide. In a closed vessel, finite total oxygen adds another constraint: the gas reservoir itself can become depleted, so $C^{\ast }$ cannot then be treated as constant.