In analyzing a reaction mixture of very many components, treating the mixture as a continuum can produce results of generality. In many practical situations (e.g., hydrodesulfurization), it is highly desirable to predict the overall behavior of the mixture at large times (high conversions) with minimum information on the mixture property. For irreversible first-order reactions in a plug-flow reactor, it was previously shown that the continuum approximation cannot be valid at arbitrarily large times. This work is an investigation of the validity of the approximation for mixtures with complex kinetics. It is found that the approximation can be conditionally or universally valid, depending on kinetics, reactor type, pore diffusion, and mixture properties. The validity conditions for a variety of situations, nontrivial as they may seem, take a power-law form. Backmixing and pore diffusion widen the range of validity. The underlying physics and some dichotomies/subtleties are discussed. The results are applied to catalytic hydroprocessing in petroleum refining. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 1894-1906, 2010