Disinfection is the essential final barrier in water treatment designed to destroy pathogenic micro-organisms and prevent waterborne disease transmission. The inactivation rate of pathogens follows Chick's Law of disinfection kinetics, which states that the rate of microorganism destruction is directly proportional to the concentration of active organisms remaining at any time $t$: $$\frac{dN}{dt} = -k \cdot N$$ Integrating this relationship over time yields the concentration reduction expression: $$\ln\left(\frac{N_t}{N_0}\right) = -k \cdot t \quad \implies \quad N_t = N_0 \cdot e^{-k \cdot t}$$ Where $N_0$ is the initial pathogen count, $N_t$ is the pathogen concentration at time $t$, and $k$ is the reaction rate constant. Expanding this to account for chemical disinfectant concentration $C$ leads to the empirical Watson-Chick Model : $$k = k' \cdot C^n \quad \implies \quad C^n \cdot t = \text{Constant}$$ Where $n$ represents the coefficient of dilution. The v...