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10 January, 20:30

A biochemist studying breakdown of the insecticide DDT finds that it decomposes by a first-order reaction with a half-life of 12.0 yr. How long does it take DDT in a soil sample to decompose from 655 ppbm to 10.0 ppbm (parts per billion by mass) ?

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  1. 10 January, 20:52
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    Given that,

    Half life = 12years

    How long does it take to decompose form 655ppbm to 10ppbm.

    Rate of decay is given as

    Q=Qo• exp (-λt)

    at t=0 Qo=655

    Then, Q=10

    λ is decay rate and it is

    λ = In2 / t½

    λ = In2/12

    λ=0.05776

    Therefore,

    Q=Qo• exp (-λt)

    10=655exp (-0.05776t)

    10/655=exp (-0.05776t)

    0.01527=exp (-0.05776t)

    Take In of both sides

    In (0.01527) = -0.05776t

    -4.182=-0.05776t

    Then, t=-4.182/-0.05776

    t=72.4years

    Then the time to decay to 10ppbm is 72 years and 3 months

    Or 72 years approximately
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