Reactions in continuous mixtures

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Abstract
A continuous mixture is one which is so complex that it is no longer worthwhile to distinguish individual chemical species; instead, an index, such as the simulated boiling point, is chosen and ci, the concentration of the species Ai, is replaced by c(x)dx, the concentration of material with index in the interval (x, x + dx). It has been long known that the total concentration of a suitably distributed mixture, each of whose components disappears by a first‐order reaction with constant k(x), will appear to disappear according to a higher order of reaction. The generalization of this to a mixture that requires two indices for its description is worth considering for three reasons: First, there may well be materials that are so complex as to require this. Second, the second index may be considered to distribute reaction time. Third, this approach seems to answer the mathematical question of how to generalize from the continuum of first‐order reactions to one of parallel Nth‐order reactions.