Find Chemical Equilibrium for Networks of Reactions 

Chemical reaction systems that have equilibrium can typically be directly modeled as a polynomial system of equations. These problems are defined by conservation and reaction equations. The example below is from combustion chemistry and models the burning of fuel in a combustion chamber such as in a car engine. The goal is to find out what chemical components and compounds are in the combustion chamber at various stages. The system of reactions being studied is given by , , , , , , .

Introduce a variable for the quantity of each component. Here is treated as a component, since does not occur on its own.

Also introduce a variable for the quantity of each compound.

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If you assume a closed chemical system, quantities are conserved, which leads to conservation equations shown in their chemical and algebraic notation.

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Give the equations for equilibrium.

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Give parameter values.

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Solve the system over the reals, and select only non-negative solutions.

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Compute a higher-precision solution.

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