A new breakthrough model recently developed by Ding et al [1] is successfully applied for toxic industrial chemicals (TICs) on adsorptive and reactive industrial air purifying cartridges. The model is derived based on two assumptions: (a) for a constant feed adsorption process, the dimensionless chemical potential changes exponentially along the flow direction; (b) the speed of the concentration wave accelerates with time as it evolves through the bed. Our results show that the model is capable of accurately simulating the breakthrough curve over several orders of magnitude concentration, making it especially useful for describing and predicting breakthrough behavior of toxic chemicals with more favorable adsorption isotherms. All the parameters have well-defined physical significance. Thus, the model can be made predictive if the sensitivities of the model parameters are determined. Simulation results also show that the model can be applied to both adsorptive and reactive adsorbate / adsorbent systems.