In an industrial gas‐liquid reactor both mass transfer and kinetics have, in principle, a role to play. This paper describes studies on the oxidation of cyclohexane in two‐phase, gas‐liquid reactors. Regimes of absorption have been clarified by measurements of dissolved oxygen concentrations. The behavior is found to be complex, arising from the fact that the reaction is autocatalytic, and zero order in oxygen over almost the entire absorption range. As reaction velocity increases, due to the autocatalytic kinetics, enhanced physical mass transfer rates arise. Bubble swarms have properties that prevent the simple application of mass transfer and enhancement from flat‐surface systems. A theory is developed here that accounts qualitatively for the enhancement found in bubble swarms in the present case. The theory is also shown to predict quantitatively the appropriate physical mass transfer coefficients.