An accurate chlorine bulk decay model is needed to ensure that potable water meets the microbial and the chemical safeties at the treatment plant and throughout the distribution. Among the mathematical models available,the general second-order chlorine bulk decay model( GBDM) is the most fundamentally sound.Application of the GBDM,however,has been hindered by its numerous fictive parameters and lack of an analytical solution. This theoretical work removes the two obstacles. The GBDM is solved through transformation and integration. The analytical solution provides deep insights into the GBDM and facilitates the parameterization and sensitivity analysis. The background natural organic matter( NOM) is characterized with the probabilistic distribution of functional groups. It reveals that the mean of the function group distribution is correlated with the initial chlorine decay rate coefficient( κ_0). A simple formula is developed to determine κ_0 directly from the initial chlorine decay. The theoretical treatment reduces the fictive parameters to a minimum. For the common lognormal distribution,the GBDM needs only three parameters,well defined as initial chlorine demand X_0,median rate coefficient km,and heterogeneity index σ. For more complicated scenarios,composite distributions are constructed through superposition of individual distributions. A highlighted example is to predict chlorine decay in blends of different waters. With the theoretical and mathematical advancement here,the GBDM can be applied effectively to any reactive background matter in any reaction systems. An accurate chlorine bulk decay model is needed to ensure that potable water meets the microbial and the chemical safeties at the treatment plant and throughout the distribution. Among the mathematical models available, the general second-order chlorine bulk decay model (GBDM) is the most fundamentally sound. Application of the GBDM, however, has been hindered by its numerous fictive parameters and lack of an analytical solution. This theoretical work removes the two obstacles. The GBDM is solved through transformation and integration. The analytical solution provides deep insights into the GBDM and facilitates the parameterization and sensitivity analysis. The background natural organic matter (NOM) is characterized with the probabilistic distribution of functional groups. It reveals that the mean of the function group distribution is correlated with the initial chlorine decay rate coefficient (κ_0). A simple formula is developed to determine κ_0 directly from the initial chlorine decay The theoretical treatment reduces the fictive parameters to a minimum. For the common lognormal distribution, the GBDM needs only three parameters, well defined as initial chlorine demand X_0, median rate coefficient km, and heterogeneity index σ. For more complicated scenarios, composite distributions are constructed through superposition of individual distributions. A highlighted example is to predict chlorine decay in blends of different waters. With the theoretical and mathematical advancement here, the GBDM can be applied effectively to any reactive background matter in any reaction systems.