Chapter 3: Rate Laws

Activation Energy

The activation energy is a measure of how temperature sensitive the reactor is. Reactions with large activations energies are very temperature sensitive.

\[k = A e^{-E/RT}\]

Graph showing the relationship between the rate constant (k) and temperature (T). The curve starts at a low k value and gradually increases, showing an exponential rise in the rate constant as temperature increases.

\(\ln k = \ln A - \frac{E}{R} \left( \frac{1}{T} \right)\)

Graph of ln(k) versus 1/T showing two lines with different slopes. The line labeled 'Low E' represents activation energies less than 25 kcal/mole, and the line labeled 'High E' represents activation energies greater than 60 kcal/mole. The slopes indicate the relationship between activation energy and temperature.

One can also write the specific reaction rate as:

\(k = k_0 \exp \left[ \frac{E}{R} \left( \frac{1}{T_0} - \frac{1}{T} \right) \right]\)
Derive


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