The decomposition of a certain insecticide in water at 12 degree C follows first

Question

The decomposition of a certain insecticide in water at 12 degree C follows first-order Kinetics with a rate constant of 1.45 yr^-1. A quantity of this insecticide is washed into a lake on June 1. leading to a concentration of 5.0 times 10^-7 g/cm^3. Assume that the temperature of the lake is constant (so that there are no effects of temperature variation on the rate). What is the concentration of the insecticide on June 1 of the following year? How long will it take for the insecticide concentration to decrease to 3.0 times 10^7 g/cm^3?

Explanation / Answer

for 1st order kinetics Ct= Co*e(-kt)

K= rate constant = 1.45/yr , t= time =1 year

Co= 5*10-7 g/cc ( initial concentration of insecticide)

Ct= 5*10-7*exp(-1.45*1)=1.24*10-7 g/cc

2,

C= 3*10-7, Co= 5*10-7, K= 0.145/yr

3*10-7= 5*10-7*exp(-0.145t)

exp(-0.145t)= 0.6

taking ln

1.45 t= 0.5108

t= 0.5108/1.45 = 0.35 yrs

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