Diels-Alder Reaction Experimental Design
The Diels-Alder Reaction is an organic chemical reaction. A conjugated diene and a substituted alkene react and form a substituted cyclohexene system.
More information about the reaction can be found in ...
Model Formulation
The reactionkinetics can be modelled by the following differential equation system:
The reaction velocity constant consists of two parts. One part reflects the non-catalytic and the other the catalytic reaction. The velocity law follows the Arrhenius relation
Total mass:
Temperature in Kelvin:
The ODE system is summarized to:
Optimum Experimental Design Problem
The aim is to compute an optimal experimental design which minimizes the uncertainties of the parameters . So, we have to solve the following optimum experimental design problem:
Name | Symbol | Initial value () |
Molar number 1 | ||
Molar number 2 | ||
Molar number 3 | ||
Solvent |
Name | Symbol | Value |
Molar Mass | 0.1362 | |
Molar Mass | 0.09806 | |
Molar Mass | 0.23426 | |
Molar Mass | 0.236 | |
Universal gas constant | 8.314 | |
Reference temperature | 293 | |
St.dev of measurement error | 1 |
Name | Symbol | Value |
Steric factor | ||
Steric factor | ||
Activation energie | ||
Activation energie | ||
Catalyst deactivation coefficient |
with
Name | Symbol | Interval |
Initial molar number 1 | [0.4,9.0] | |
Initial molar number 2 | [0.4,9.0] | |
Initial molar number 4 | [0.4,9.0] | |
Concentration of the catalyst | [0.0,6.0] | |
Initial molar number 1 | [20.0,100.0] |
Measurement grid
Constraints
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): {\begin{array}{rcl}0.1&\leq &n_{{a1}}\ \cdot \ M_{1}\ +\ n_{{a2}}\ \cdot \ M_{2}\ +\ n_{{a4}}\ \cdot \ M_{4}&\leq 10\\0.1&\leq &{\frac {n_{{a1}}\ \cdot \ M_{1}\ +\ n_{{a2}}\ \cdot \ M_{2}}{n_{{a1}}\ \cdot \ M_{1}\ +\ n_{{a2}}\ \cdot \ M_{2}\ +\ n_{{a4}}\ \cdot \ M_{4}}}&\leq 0.7\end{array}}
References
R. T. Morrison and R.N. Boyd. Organic Chemistry. Allyn and Bacon, Inc., 4th edition, 1983 \\ Dissertation Stefan Körkel