Question

The pesticide fenvalerate is a member of a class of compounds called pyrethrins. Fenvalerate is one of four compounds approved by NYC to combat mosquitos that spread West Nile virus. These compounds were originally isolated from plants (including chrysanthemums) that exhibited a tendency to repel insects. It degrades in the environment with first order kinetics and a rate constant of 3.9*10^-7 s^-1. An accidental discharge of 100 kg fenvalerate into a holding pond results in a fenvalerate concentration of 1.3*10^-5M. Calculate the concentration 1 month(2.6*10^6 s) after the spill.

Answer 1

Answer – We are given, rate constant of first order = 3.9*10^-7 s^-1 ,

Initial concentration fenvalerate, [A]o = 1.3*10^-5 M , [A]t = ?

Time, t = 1 month = 2.6*10⁶ s

We know first order reaction formula

ln [A]t/[A]o = - k *t

ln [A]t / 1.3*10^-5 M = -3.9*10^-7 s^-1*2.6*10⁶ s

ln [A]t / 1.3*10^-5 M =-1.014

so taking antiln from both side

[A]t / 1.3*10^-5 M = 0.363

So, [A]t = 1.3*10^-5 M * 0.363

              = 4.72*10^-6 M

So, the concentration 1month(2.6*10^6 s) after the spill is 4.72*10^-6 M