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Homework Help: Half-life decomposition, find final concentration

  1. Sep 22, 2012 #1
    1. The problem statement, all variables and given/known data

    In a first order decomposition in which the rate constant is 0.03 sec-1, how much of the compound (in mol/L) is left after 39 sec, if there was 2.00 mol/L at the start?

    I'm using a few equations and trying to plug it in but I don't know whether they are appropriate or not.

    The answer is .621 but I'm not sure how to get there

    2. Relevant equations

    Ln(A(initial) /A(final) = -kt

    A(final) = -KT + A(initial)

    3. The attempt at a solution

    I've tried plugging into these equations but haven't gotten the right answer yet. Are these the correct equations to use?
  2. jcsd
  3. Sep 23, 2012 #2


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    Staff: Mentor

    They can't be both right at the same time - one is for the zeroth order reactions.

    Which one is for first order reactions?

    What is k?

    Show details of what you did.
  4. Sep 23, 2012 #3
    I used the formula ln[A] = -kt + ln[A]o

    Ao = unknown
    Ao = 2 M
    K = .03 sec^-1
    t=39 seconds

    Ln A = (-.03)(39 seconds) + Ln2
    LnA = -.4767 which I can't take the natural log of. I think I'm doing something wrong in the equation but I'm really not sure what :|
  5. Sep 23, 2012 #4


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    Staff: Mentor


    So it is an unknown with a known value? But let's assume it was just a typo.

    That's were your thinking got derailed. Why do you want to take a logarithm of logarithm and not an antilogarithm?
  6. Sep 23, 2012 #5
    Yea to be honest logarithms have always been confusing to me. I found out how to get the answer but I used e^(-.4767)

    Why would I use the Ln on the 2mol/l and then switch to e, even though the formula has LnA? I don't really get the concept of logs yet :|
  7. Sep 23, 2012 #6


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    Staff: Mentor

    Your problem is with math, not with the chemistry.

    From the logarithm definitions, if b=ln(A), A=eb. You have calculated ln(A), so the value you are looking for is eln(A).
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