Question

Chlorine is used as disinfectant in a municipal water treatment plant. It acheives 60% percent of disinfection efficiency measured in terms of killing the indicator microorganisms.(E-Coli) in 4 minutes. The minimum time required to acheive 99.9% disinfection efficiency would be____hrs

• A. 0.5

Answer 1

The correct option is A 0.5
Disinfection efficiency=$\frac{N_0-N}{N_0}$
=$\frac{N_0-N_0{e}^{-kt}}{N_0}$
=$1-e^{-kt}$
$0.6=1-e^{-k\times 4}$
$e^{-4k}=0.4$
$k=\frac{ln2.5}{4}$

Now for 99.9% efficiency,
$0.999=1-e^{-\frac{ln2.5}{4}\times t}$
$\frac{ln2.5}{4}t=6.908$
t=30.15 minutes
=0.502 hrs