They call it chemical kinetics?

Calculus Level 3

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

The Arrhenius equation above tell us how the rate constant kk for a particular reaction depends on its activation energy EaE_a and temperature T:T:

The figure above shows a typical plot of kk versus TT. If the corresponding value of kk for the point of inflection for the curve above is given by k=AeXk' = A e^X for some constant X,X, then find X.|X|.

Assumptions and Clarifications:

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