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Math Help - Integrated Rate Law

  1. #1
    Junior Member
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    Apr 2007
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    USA
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    Integrated Rate Law

    I found the order (first order) but I don't see how I can calculate the value of the rate constant without a rate! I only have time and M(right column). How do I calculate it? I know k= (A) and I haven't a clue on how to predict the concentration at 280 s. Will someone explain to me please?

    The data below show the concentration of versus time for the following reaction:

    Time M
    0 1.000
    25 0.822
    50 0.677
    75 0.557
    100 0.458
    125 0.377
    150 0 .310
    175 0.255
    200 0.210

    Determine the value of the rate constant: ???

    Predict the concentration of at 280: ?????
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  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276

    Exponential

    Your concentration should be undergoing an exponential decay, right: M(t)=M_0e^{-rt}? Take the natural log of both sides:
    \ln{M}=\ln(M_0e^{-rt})
    \ln{M}=\ln(M_0)-rt
    Thus the relationship between ln(M) and t is linear, with -r the slope of the line. You can take the logarithms of your M values, and then fit a line to that versus t with a standard least-squares linear regression and extract a value for r in the equation, and using the fact that \frac{dM}{dt}=-r\cdot{M}, obtain your rate constant.

    --Kevin C.
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