how do you determine the activation energy from temperature and k?

The question is: determine the activation energy of this reaction.

t in celcius: 15.2, 20.3, 24.6, 27.0

k (in sec -1): .043,.067, .095, .150

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  • 1 decade ago
    Best Answer

    You're talking about the Arrhenius equation as the model, correct?

    k = A0 * Exp( Ea / RT )

    where

    k = reaction rate, sec ^ (-1)

    A0 = constant

    Ea = Activation Energy, J / mol

    R = ideal gas constant, 8.314 J / K mol

    T = temperature, in Kelvin

    * * * * * * * * * * * * * * * * * * * * * * * *

    If this is the equation, then let's proceed:

    k = A0 * Exp( Ea / RT )

    We can attack this in different ways. The best way is to graph it. But first, we need to put the Arrhenius equation in a form that best suits our needs...

    Take the natural log of both sides

    ln k = ln (A0 * Exp( Ea / RT ))

    = ln A0 + ln (Exp(Ea / RT))

    = ln A0 + (Ea / RT) * ln e

    = ln A0 + Ea / RT * 1

    = ln A0 + Ea / RT

    We can rewrite the equation as...

    ln k = (Ea / R) * (1/T) + ln A0

    If we let

    y = ln k

    b = ln A0

    m = Ea / R

    x = 1/T

    Then

    ln k = (Ea / R) * (1/T) + ln A0

    can be written as

    y = mx + b

    Where m is the slope.

    If you take your data:

    t in celcius: 15.2, 20.3, 24.6, 27.0

    k (in sec -1): .043,.067, .095, .150

    Convert the T into Kelvins, and then plot the data as

    1/T vs. ln k

    Draw a best fit line and determine the slope.

    Slope = m = Ea / R

    So Ea = R * m

    Ans. Activation energy, Ea = R * calculated slope.

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