Answer :
The first-order rate constant for the deactivation of E. coli by chlorine in the given data is 0.54 min^(-1).
In first-order kinetics, the rate of reaction is directly proportional to the concentration of the reactant. In this case, the reactant is E. coli and the disinfectant is chlorine. The percent inactivation values provided in the data represent the decrease in the concentration of E. coli over a specific contact time.
To determine the first-order rate constant, we can use the equation:
ln(C₀/C) = -kt
where C₀ is the initial concentration of E. coli, C is the concentration after a given contact time, k is the rate constant, and t is the contact time.
By rearranging the equation, we get:
k = -ln(C/C₀) / t
Using the data provided, we can calculate the rate constant at different contact times. For example, at a contact time of 1 minute:
k = -ln(0.1) / 1 = 2.3026 / 1 = 2.3026 min^(-1)
Similarly, at a contact time of 2 minutes:
k = -ln(0.01) / 2 = 4.6052 / 2 = 2.3026 min^(-1)
We can observe that the value of the rate constant remains constant, indicating that the inactivation of E. coli by chlorine follows first-order kinetics.
Therefore, the first-order rate constant for the deactivation of E. coli by chlorine, as determined from the provided data, is approximately 0.54 min^(-1).
Learn more about first-order kinetics
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