The pesticide fenvalerate, C₂₅H₂₂ClO₃N, is a member of a class of compounds called pyrethrins. Fenvalerate is one of four compounds approved by New York City to combat the mosquitoes 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^-5 M. Calculate the concentration 1 month (2.6 = 106 s) after the spill.

Strategy

The problem states the decay is first order and we need to determine the concentration versus time dependence. Start by writing the integrated form of the first order rate law. Because [R]_o, k, and t are given, calculate [R]_t.