The aqueous homogeneous reactor has assumed some importance in recent years as a potential medical isotopes production system. The kinetic behavior of such systems depends on the rate of generation of the radiolytic gas bubbles and the associated reactivity void coefficient. In this work we describe a method based on perturbation theory, and a simple description of bubble production, for deriving a value of the void coefficient of reactivity. It is shown that, in the small void fraction limit, the void coefficient is dependent only on the system properties and does not depend on power level or the bubble properties. Values are given for the void coefficient for a range of parameters assuming that the voids are distributed in three different ways, i.e., uniformly, proportional to power, and equal to the distribution due to buoyancy. The results are in reasonable agreement with values obtained by others, using more detailed methods, based on the reactors SILENE and MIPR.