# Problem: Chlorine is commonly used to disinfect drinking water, and inactivation of pathogens by chlorine follows first-order kinetics. The following data are for E. coli inactivation:Determine the first-order inactivation constant, k. [ Hint: % inactivation = 100 x (1 – [A] t/[A]0).]

###### FREE Expert Solution

We’re being asked to determine the first-order inactivation constant, k.

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

where:

[N]t = concentration at time, t
k = decay constant
t = time
[N]0 = initial concentration

We're given the equation for percent inactivation:

$\overline{)\mathbf{%}\mathbf{inactivation}\mathbf{=}\mathbf{100}\mathbf{×}\left(1-\frac{{\left[A\right]}_{t}}{{\left[A\right]}_{0}}\right)}$

Solving [A]t/[A]0 at 1 min:

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###### Problem Details

Chlorine is commonly used to disinfect drinking water, and inactivation of pathogens by chlorine follows first-order kinetics. The following data are for E. coli inactivation:

Determine the first-order inactivation constant, k. [ Hint: % inactivation = 100 x (1 – [A] t/[A]0).]