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17 November, 01:16

The half-life of an anticancer drug is 170 days at 25 oC. Degradation follows the first-order kinetics. When the drug is stored at 5 oC, the degradation rate decreases to one third (1/3) of the rate at 25 oC. What is the shelf life of the drug at 5 oC?

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  1. 17 November, 01:18
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    1694 days

    Explanation:

    In first-order kinetics, the rate is proportional to the amount.

    dA/dt = kA

    For first-order kinetics, the rate k can be found using the half-life:

    t₁,₂ = (ln 2) / k

    In other words, the half-life is inversely proportional with the rate.

    At the lower temperature, the rate is reduced to a third, so the half-life increases by a factor of 3. Meaning that the new half-life is 170 * 3 = 510 days.

    The "shelf life" is the time it takes to reduce the initial amount to 10%. We can solve for this using the half-life equation.

    A = A₀ (½) ^ (t / t₁,₂)

    A₀/10 = A₀ (½) ^ (t / 510)

    1/10 = (½) ^ (t / 510)

    ln (1/10) = (t / 510) ln (½)

    ln (10) = (t / 510) ln (2)

    ln (10) / ln (2) = t / 510

    t = 510 ln (10) / ln (2)

    t ≈ 1694
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