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:

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

Total mass:

$m_{tot}=n_1\cdots M_1+n_2\cdots M_2+n_3\cdots M_3+n_4\cdots M_4$