Question

Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves $50$ percent of disinfection efficiency measured in terms of killing the indicator microorganisms (E-Coli) in 3 minutes. The minimum time required to achieve 99 percent disinfection efficiency would be

• A. 19.93 minutes
• B. 21.93 minutes
• C. 9.93 minutes
• D. 11.93 minutes

Answer 1

The correct option is A 19.93 minutes

Disinfection efficiency

$=\frac{N_o-N}{N_o}$

$=\frac{N_o-N_o{e}^{-kt}}{N_o}=(1-e^{-kt})$

$0.5=1-e^{-k\times 3}$

$\Rightarrow k=\frac{\ell n2}{3}$
Again, $0.99=1-e^{\frac{\ell n2}{3}\times t}$

$\Rightarrow 0.01=e^{\frac{\ell n2}{3}\times t}$

$-4.605=-\frac{\ell n2}{3}\times t$

$\Rightarrow t=19.93min$