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An experiment shows that a concentration of 0.1 g/m3 of free available chlorine yield a 99% kill of bacteria in 8 minutes. Calculate disinfection rate constant (1 /min)? Assume that Chick's Law and Watson's Law hold with n = 1.
1. 4.706 /min
2. 2.056 /min
3. 7.056 /min
4. 5.756 /min

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Correct Answer - Option 4 : 5.756 /min

Concept:

As per Watson and Chicks law

\({N_t} = {N_o}{e^{ - K{C^n}t}}\)

Where,

K = Rate constant which depends on the type of microorganism, the type of disinfectant and temperature

n = Constant for a particular microorganism and type of disinfectant

C = Disinfectant concentration (weight/volume)

Nt = Number of microorganism present at any time ‘t’

Calculation:

Given, t = 8 min, n = 1 and C = 0.1 g/m3

∵ We know that, \({N_t} = {N_o}{e^{ - K{C^n}t}}\)

Let 'x' be the number of micro organism present initially

99% kill of micro organism implies that at time 't' 1% of micro organism are still surviving

∴ Micro organism surviving at time 't' = (1/100) x

∴ \(\frac{1}{{100}}x = x.{e^{ - K \times 0.1 \times 8}}\)

⇒ \( - K \times 0.8 = \ln \left( {\frac{1}{{100}}} \right)\)

K = 5.76 /min

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