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25 April, 12:56

How long will it take for a 750 mg sample of radium with a half life of 15 days to decay to exactly 68mg?

-48

-50

-52

-54

+4
Answers (1)
  1. 25 April, 15:13
    0
    52 da

    Step-by-step explanation:

    Whenever a question asks you, "How long to reach a certain concentration?" or something similar, you must use the appropriate integrated rate law expression.

    The integrated rate law for a first-order reaction is

    ln ([A₀]/[A]) = kt

    dа ta:

    [A]₀ = 750 mg

    [A] = 68 mg

    t_ ½ = 15 da

    Step 1. Calculate the value of the rate constant.

    t_½ = ln2/k Multiply each side by k

    kt_½ = ln2 Divide each side by t_½

    k = ln2/t_½

    = ln2/15

    = 0.0462 da⁻¹

    Step 2. Calculate the time

    ln (750/68) = 0.0462t

    ln11.0 = 0.0462t

    2.40 = 0.0462t Divide each side by 0.0462

    t = 52 da
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