How is this equation derived from the given equations on the equation list?
k'/k=Ea/R(1/T1-1/T2)
Activation energy equation
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Re: Activation energy equation
Do you mean this one?
I'm not sure about the one you asked but there's this one
I'm not sure about the one you asked but there's this one
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Re: Activation energy equation
For a reaction at a particular temperature, ln(k) = lnA -(Ea/R)(1/T), where Ea represents the activation energy of a reaction and A is correlated with collision frequency of reactants. Compared to the proportion of collisions with sufficient energy to overcome Ea, collision frequency changes little with respect to temperature, and so A is assumed to be relatively constant across temperature changes.
Constant values of A can be taken advantage of by rearranging the above equation to be lnA = ln(k) + (Ea/R)(1/T) at any temperature. Thus, for two temperatures T1 and T2, ln(k1) + (Ea/R)(1/T1) = lnA = ln(k2) + (Ea/R)(1/T2). This equation can then be arranged into the form
ln(k2/k1) = -(Ea/R)(1/T2 - 1/T1).
Constant values of A can be taken advantage of by rearranging the above equation to be lnA = ln(k) + (Ea/R)(1/T) at any temperature. Thus, for two temperatures T1 and T2, ln(k1) + (Ea/R)(1/T1) = lnA = ln(k2) + (Ea/R)(1/T2). This equation can then be arranged into the form
ln(k2/k1) = -(Ea/R)(1/T2 - 1/T1).
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