
\section{Introduction}

In this project the combustion of a hydrogen-oxygen mixture is studied.
If a high precision in the time resolution of this reaction is wanted,
regarding all intermediate products, it is not sufficient just to regard
the simplified process 
\begin{align}
\ce{2H2 + O2 -> 2H2O}
\end{align}

Instead a lot of intemediate states like \ce{H}, \ce{O}, \ce{OH}, \ce{HO2}, \ce{H2O2} and their equilibrium reactions need to be considered.

From this a set of first order differential equations can be derived.
These can be integrated using suitable algorithms.

This work provides a toolset that is capable of reading in and interpreting the equilibrium reaction coefficients in a somewhat human-readable format (see FORMAT TODO), to derive the rate equations, to solve the differential equation in an adjusted way and to write the time evolution of the involved initial, intemediate and final substances.

I also used this project as an opportunity to update my compiler and
to dive in to the world of C++11 \cite{ISOCPP}.
Therefore I am using some features that are only implemented by newer C++ compilers \cite{CPP11Compiler}.
The makefile requires the GCC compiler in version 4.7 or higher.
(Tested with version 4.8.)

This text was written using the facilities of the documentation systen Doxygen.
Thus it consists of two parts:
- Chapter 1 contains the lab report for this project
- Chapter 2 \& 3 contain the documentation of the written code as produced by Doxygen.

\section{Chemical formalism}

Arrhenius formalism

In this programm the modified Arrhenius equation is used:
\begin{align}
k = A T^n \exp - \frac{E}{RT} \text .
\end{align}
This differs from the original Arrhenius equation
\begin{align}
k = A \exp - \frac{E}{RT} \text .
\end{align}
in the additional temperature difference that can occur in some processes.

\cite{clayden2012organic}

Troe Formula \cite{troe1983theory} \cite{gilbert1983theory}

For reasons of simplicity
\begin{align}
k = \frac{k_0 k_\infty}{k_0 + k_\infty}
\end{align}


\section{Data basis}

As a data basis the data for the involved reactions should be used.

The list of reactions stated in the task sheet for this project turned out to be incomplete in terms of giving all required coefficients. Thus it was looked for the original source of the data. The trace was:
- The picture in the task sheet was copied from a picture in a talk \cite{H2Presi}.
- This talk took the picture from a table in the dissertation \cite{chiavazzo2009invariant}.
- \cite{chiavazzo2009invariant} simply copied the table from \cite{i2007arXiv07122386C}.
- \cite{i2007arXiv07122386C} took the data from \cite{li2004updated}, but omitted some important data.

In most of the papers it was not clearly displayed where the data was taken from. This is a story of copying data without copying all the data or explicitely stating, where the data comes from.

So finally the data from table I in \cite{li2004updated} (which is fortunately also mentioned in the task sheet) was used.

The change of (Gibbs-)energy was not denoted in \cite{li2004updated} for the reactions (though I later found out that it could be calculated from the data in table II.) Thus the data from the older paper \cite{mueller1999flow} was used, where the energy change is state explicitely per-reaction.