# Suppose 100 moles of a chemical is spilled into a lake. After 15.0 days, the total amount of the...

## Question:

Suppose 100 moles of a chemical are spilled into a lake. After 15.0 days, the total amount of the chemical in the lake is 3.50 moles. Assuming that the reaction followed first-order kinetics and no chemical was lost due to advection or volatilization, then what is the rate constant for the degradation reaction? The units are 1/days.

## Kinetic order of degradation reactions

These are reactions that reduce the number of atoms in a molecule through a specific type of chemical transformation. A lot of chemical degradation reactions follow fixed-order kinetics.

The initial amount of chemical {eq}[A]_o {/eq} = 100

the final amount of chemical {eq}[A]_t {/eq}= 3.50

time = 15 days

rate constant K=?

The first-order integrated rate law is as follows

{eq}ln(\frac {[A]_t}{[A]_o}) = - K \times t {/eq}

lets put the values in the formula

{eq}ln(\frac {3.50 }{100})= - K \times 20 \:days {/eq}

{eq}-3.352 = -K \times 20 \:days {/eq}

{eq}K = \frac {3.352 }{ 20 \:days} {/eq}

{eq}K = 0.1676 /day {/eq}

Therefore the rate constat for the degradation is {eq}0.1676 /day {/eq}