Diels-Alder Reaction Experimental Design

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Model Formulation

Differential equation system:

$\begin{array}{rcl} \dot{n_1}(t) &=& -k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}}, \\ & & \\ \dot{n_2}(t) &=& -k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}}, \\ & & \\ \dot{n_2}(t) &=& \ \ k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}} \end{array}$

Reaction velocity constant:

$k = k_1 \ \cdot \ exp(- \frac{E_1}{R} \cdot (\frac{1}{T} \ - \ \frac{1}{T_{ref}}) ) + k_{cat} \cdot \ c_{cat} \cdot \ exp(-\lambda \ cdot \ t)$