Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Anonymous
Anonymous asked in Science & MathematicsChemistry · 1 month ago

A first-order reaction has a half life of 35.7 seconds. How long will it take for this reaction to be 84.4% complete?

2 Answers

Relevance
  • Ash
    Lv 7
    1 month ago
    Favorite Answer

    Half life formula can be written as

    N = N₀ (½)^(t/t½)

    N/N₀ = (½)^(t/t½)

    ln (N/N₀) = ln (½)^(t/t½)

    ln (N/N₀) = (t/t½) ln(½)

    (t/t½) = ln (N/N₀) / ln(½)

    t = t½ [ln (N/N₀) / ln(½)]   ...(1)

    Given t½ = 35.7 s

    Balance percentage of reaction = 100% - 84.4% = 15.6%

    [N/N₀] = 15.6 %

    [N/N₀] = 0.156

    plug in (1)

    t = 35.7 [ln (0.156) / ln(½)]t = 95.7 s

    It will take about 95.7 s for the reaction to be 84.4% complete

  • Dr W
    Lv 7
    1 month ago

    since it's first order

    .. ln[At] = -kt + ln[Ao]

    .. kt = ln[Ao] - ln[At]= ln([Ao] / [At]).. . . .recall = ln(a) - ln(b) = ln(a/b)

    .. t = ln([Ao] / [A]) / k

    and

    .. k = ln(2) / half life

    subbing

    .. t = (ln([Ao] / [At]) / ln(2)) * half life

    we want to know when [At] = 0.156 * [Ao] (that's 84.4% complete)

    so that

    .. t = (ln([Ao] / 0.156[Ao]) / ln(2)) * 35.7 sec

    .. t = (ln(1 / 0.156)) / ln(2)) * 35.7 sec

    .. t = (ln(1) - ln(0.156)) / ln(2)) * 35.7 sec.. .. . .recall ln(a/b) = ln(a) - ln(b)

    .. t = -ln(0.156) / ln(2) * 35.7 sec.. .. .. .. .. . . . recall ln(1) = 0

    and now we're ready to calc. 

    .. t = 95.7 sec

Still have questions? Get your answers by asking now.