Sample question 14:7 : The decomposition of a certain insecticide in water at 12

Question

Sample question 14:7   : The decomposition of a certain insecticide in water at 12 °C follows first-order kinetics with a rate constant of 1.45yr^-1 . A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10^-7 g/cm^3 . Assume that the average temperature of the lake is 12 C.

Using Equation 14.15, calculate t1/2 for the decomposition of the insecticide described in Sample Exercise 14.7. (b) How long does it take for the concentration of the insecticide to reach one-quarter of the initial value?

Explanation / Answer

First order rate equation is k = 2.303/t log(initial/final)

   so t1/2 = 0.693/k

t1/2 = 0.693/1.45

t1/2 = 0.478 years.

................................................................

b) as we Know First order rate equation is k = 2.303/t log(initial/final)

      K = 1.45yr^-1 ,   , initial = 5.0*10^-7g/cm^3 , final = 1/4( 5.0*10^-7g/cm^3 )

      substituting above values in the first order rate equation

     1.45 = 2.303/t log[5.0*10^-7/1/4( 5.0*10^-7g/cm^3 )]

     1.45 = 2.303/t log(4)

      t = 0.9562 years

            or

    t = 0.96 years.

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