The reaction of cyclopropane to rearrange to propane has a rate constant of 5.65

Question

       The reaction of cyclopropane to rearrange to propane has a rate constant       of 5.65 s-1 at a certain temperature. How long does it take       for the concentration of cyclopropane to decrease to one-quarter of its       initial value?     

      Cyclopropane ? Propane, in which the coefficient for cyclopropane is one.     

      (Hint: the unit of the rate constant tells us that the reaction is 1st       order.)

***Please give a step-by-step explaination! I don't even know how to start this. The answer should be in seconds. Thanks!!!***     

Explanation / Answer

the reaction is 1st order so

let cyclopropane =A

r = K * [A] = -dA/dt

-dA/dt = K*[A]

integrating it we get

Kt = ln[A0] - ln[A]

[A0] = initial concentration of cyclopropane

Kt = ln([A0]/[A])

given [A0]/[A] = 4

t = ln4/K = 0.245 sec

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