The first order rate constant for the decomposition of a certain insecticide in water at 12C is 1.45yr^-1
A quantity of this insecticide washed into a lake leading to a concentration of 5.0x10^-7M. Assuming the temperature of the lake is constant, how long will it take for the concentration to drop to 3.0x10^-7M? Could you walk me through the steps to answer the questions.

Question

The first order rate constant for the decomposition of a certain insecticide in water at 12C is 1.45yr^-1
A quantity of this insecticide washed into a lake leading to a concentration of 5.0x10^-7M. Assuming the temperature of the lake is constant, how long will it take for the concentration to drop to 3.0x10^-7M? Could you walk me through the steps to answer the  questions.

aaronq · Answer

you can use the first order integrated rate law:

$ln[A]_t=-kt+ln[A]_o$

where  $[A]_o$ is the initial concentration
k is the decay (rate) constant
t is time 
$[A]_t$ is the concentration of the substance at time t