Question

A wastewater is to be disinfected using ultraviolet (UV) light. Batch experiments find that the bacterial concentration decays under UV light with first-order kinetics, with a half of the initial bacteria killed after 6.2 minutes of illumination. You need to design a reactor than can kill 99% of bacteria in a stream having a flow rate of 140, 000 gal/d. Assume that regardless of the reactor type it will be possible to have UV illumination conditions identical to those of the batch experiment. a. Based on the batch experiments, what is the first-order rate constant k for bacterial inactivation

Answer 1

k = 0.1118 per min

Step-by-step explanation:

Assume;

Initial number of bacteria = N0

Number of bacteria IN 'T' time = Nt

So,

`Nt=N0e^(-kt)\\\\in\ 6.2 min\\\\\\frac{N0}{2}= N0e^(-k(6.2))\\\\ln(1)/(2) = -k[6.2]`

k = 0.1118 per min