Consider the first-order reaction described by the equation At a certain tempera

Question

Consider the first-order reaction described by the equation At a certain temperature, the rate constant for this reaction is 5.22 x 10^-4 s^-1. Calculate the half-life of cyclopropane at this temperature. Given an initial cyclopropane concentration of 0.00290 M, calculate the concentration of cyclopropane that remains after 2.20 hours. Incorrect. The integrated rate equation for a first-order reaction is where [A] is the concentration at time t, [A] o is the initial concentration, and k is the rate constant.

Explanation / Answer

k = 5.22 x 10^-5 s-1

It is a first order reaction,

t1/2 = 0.693/k = 0.693/5.22 x 10^-4 = 1327.59 s

For a first order reaction,

ln[A] = ln[Ao] - kt

with,

[Ao] = 0.00290 M

t = 2.20 h = 2.20 x 60 x 60 = 7920 s

[A] = concentration after 2.2 hrs

we get,

ln[A] = ln(0.0029) - 5.22 x 10^-4 x 7920

[A] = 4.64 x 10^-5 M remaining

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