For a second-order reaction, the rate constant (k) is 0.02 L/(mol·s). Calculate the time it takes for the concentration of the reactant to decrease to 1/3 of its initial value.
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The integrated rate law for a second-order reaction is:
1/[A]t = kt + 1/[A]0
Where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, and k is the rate constant.
In this case, we want to calculate the time it takes for the concentration of the reactant to decrease to 1/3 of its initial value. This means [A]t = 1/3*[A]0.
1/[A]t = 3/[A]0
Substituting this into the integrated rate law:
3/[A]0 = kt + 1/[A]0
Rearranging the equation:
3/[A]0 - 1/[A]0 = kt
2/[A]0 = kt
t = 2/[A]0k
Given that k = 0.02 L/(mol·s) and [A]0 is the initial concentration of the reactant, you need to know the value of [A]0 to calculate the time.
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