A particular reactant decomposes with a half life of 115 s when its initial concentration is .386 M. The same reactant decomposes with a half life of 245 s when its initial concentration is .181 M.What is the value and unit of the rate constant for this reaction?
Question
A particular reactant decomposes with a half life of 115 s when its initial concentration is .386 M. The same reactant decomposes with a half life of 245 s when its initial concentration is .181 M.What is the value and unit of the rate constant for this reaction?
Solution
The reaction described in the question is a second order reaction. The half-life of a second order reaction is given by the formula t1/2 = 1 / (k[A]), where t1/2 is the half-life, k is the rate constant, and [A] is the initial concentration of the reactant.
Given that the half-life is 115 s when the initial concentration is 0.386 M, we can substitute these values into the formula to find the rate constant:
115 s = 1 / (k * 0.386 M)
Solving for k gives k = 1 / (115 s * 0.386 M) = 0.0225 M^-1s^-1
Similarly, given that the half-life is 245 s when the initial concentration is 0.181 M, we can substitute these values into the formula to find the rate constant:
245 s = 1 / (k * 0.181 M)
Solving for k gives k = 1 / (245 s * 0.181 M) = 0.0225 M^-1s^-1
Therefore, the rate constant for this reaction is 0.0225 M^-1s^-1.
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