Estimate the time required to reduce the ammonia

Question

1. When HOCl (Cl₂) is added to water, it will react with ammonia to form chloramine:

NH₃ + HOCl → NH₂Cl + H₂O

A solution containing 0.5 mg/L of ammonia is dosed with 4.0 mg/L of Cl₂ in a batch contact vessel. If the rate constant for the reaction is k = 5 x 106 L/mol-s, estimate the time required to reduce the ammonia concentration by 50%.

2. When ultraviolet light is used for disinfection, the rate of die-off of bacteria may be expressed as r_N = - k' I N, where I is the light intensity. Unfortunately, intensity decreases exponentially with penetration depth, i.e., I = I₀e^?ax. The average intensity over a depth, x, may be expressed as I = (I₀/ax) [1 - e^?ax]. A disinfection system is designed for a 99.9% kill rate when the water depth is 2 inches. During operation, however, the water depth is 2.5 inches. What is the resulting percent kill? The absorption (extinction) coefficient ("a") has been measured as 0.05 cm^?1.