PROBLEM STATEMENT
The general form of the Arrhenius equation used to model the temperature dependence of the reaction rate
for chemical reactions is:
\begin{equation}
k = Ae^{-\frac{E}{RT_a}}
\end{equation} (equation 1)
where $k$ is the reaction rate ($s^{-1}$), A is the frequency factor ($s^{-1}$), E is the activation energy (J/mol), R is the ideal gas
constant [8.314 J/(mol K)], and $T_a$ is the absolute temperature (Kelvin, K). The constants A and E are empirically
derived (i.e. determine by fitting the model to data). A modified Arrhenius model:
\begin{equation}
k = AT_a^b e^{-\frac{E}{RT_a}}
\end{equation} (equation 2)
is often used with the $T_a^b$ factor added to improve the curve fit for some classes of chemical reactions. The exponent
b is a third empirical constant. The data file in project1_data.zip contains temperatures in the first column
and reaction rates in the second column for the following reaction:
O + H$_2$ ? OH + H
This reaction is generally included in all chemical reaction mechanisms used to model combustion of hydrocarbons.
Use the curve-fitting method of your choice to determine the values of A and E that achieve the best least-squares
fit of the unmodified Arrhenius model (equation 1) to the data. Next perform a second curve-fit to determine values
of A, b, and E in the modified Arrhenius model (equation 2) that achieve the best least-squares fit (note the values
of A and E will likely be significantly different in the second fit). Develop figures showing both of your curve fits
and report appropriate curve fit statistics to indicate the quality of each fit.
