They call it chemical kinetics?

Calculus Level 3

\[\large k = A e^{-\frac{E_a}{RT}}\]

The Arrhenius equation above tell us how the rate constant \(k\) for a particular reaction depends on its activation energy \(E_a\) and temperature \(T\).

The figure above shows a typical plot of \(k\) versus \(T\). If the corresponding value of \(k\) for the point of inflection for the curve above is given by \(k' = A e^X\) for some constant \(X\) then find \(|X|\).

Assumptions and clarifications:

  1. The pre-exponential factor or \(A\) for the given reaction is essentially a constant.
  2. \(R=8.314 \text{ J/(K mol)}\) is the gas contant.

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