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Equilibrium constants help! Enough work for 8 marks?

  1. Dec 12, 2011 #1
    Activation energy from a decomposition.

    1. The problem statement, all variables and given/known data

    . The rate constant for the decomposition of C2H6 is given in the table below. Calculate the activation energy.

    105 k/s Temperature/K
    2.5 823
    4.7 833
    8.2 843
    12.3 853
    23.1 863
    35.3 873
    57.6 883
    92.4 893
    141.5 903



    3. The attempt at a solution

    This is what i have so far......

    Ea = R x (("T1" x "T2") / ("T2" - "T1")) x ln("k2" / "k1")

    8.314 x (823 x 903) / (903 – 823) x In(141.5 / 823) = ???

    I havent a clue if this is even right, am i meant to plot a graph?

    Any help would be very much appreciated.
     
    Last edited: Dec 12, 2011
  2. jcsd
  3. Dec 13, 2011 #2
    I don't quite follow your table, but here's a general solution.

    For rate laws, the equation relating k to temperature is k = A * exp(-ΔE/RT).

    So you need to use your existing data and fit it to the equation by finding the constants A & ΔE (A is an arbitrary constant & ΔE is the activation energy).

    If you take the natural log of both sides, you will get

    ln k = ln A + (-ΔE/R)(1/T)

    That can be graphed:
    y-coordinate= ln k
    y-intercept= ln A
    x-coordinate = 1/T
    slope = -ΔE/R

    SO: If you graph ln k vs 1/T from your data, then multiply the slope by R, you will get your activation energy.
     
  4. Dec 13, 2011 #3
    Thank you so much, That did it :)
     
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