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Homework Help: Half life (very very simple question)

  1. Mar 21, 2007 #1
    1. The problem statement, all variables and given/known data
    A certain first-order reaction has a rate constant of 6.70×10−3 . How long will it take for the reactant concentration to drop to 1/8 of its initial value?

    2. Relevant equations

    half life =0.693/k

    3. The attempt at a solution

    half life = 0.693/(6.70×10−3) = 103.43


    but after that I'm confused how many half lives does 1/8 refer to?
    I tried doing it by half life =4 but the answer came wrong.
    any help would be appreaciated.
     
  2. jcsd
  3. Mar 22, 2007 #2
    Since this is a first order reaction, the function at hand is exponential, meaning the half life is constant. This means that after 1 half life, 1/2 of the reactants is left, after 2 half lives, 1/4 is left and so on. Can you do it now?
     
  4. Mar 22, 2007 #3
    so its 3 half lives .. right ?
     
  5. Mar 22, 2007 #4
    Yes it is.
     
  6. Mar 22, 2007 #5
    Yup;

    half of a half of a half = 1/2 x 1/2 x 1/2 = 1/8

    Best of health.

    Steve
     
  7. Mar 22, 2007 #6
    Thanks a lot Werg!
     
  8. Mar 22, 2007 #7
    Thanks a lot Smith !
     
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