Begin your response to QUESTION I on this page.
1. The following equation represents the decomposition of \( \mathrm{N}_{2} \mathrm{O}_{5} \), for which the rate law is rate \( =k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \cdot \frac{2}{4} \)
\[
2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \rightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)
\]
A sample of pure \( \mathrm{N}_{2} \mathrm{O}_{5}(g) \) is placed in an evacuated container and allowed to decompose at a constant temperature of 300 K . The concentration of \( \mathrm{N}_{2} \mathrm{O}_{5}(g) \) in the container is measured over a period of time, and the measurements are recorded in the following table.
\begin{tabular}{|c|c|}
\hline Time \( (\mathrm{hr}) \) & {\( \left[\mathrm{N}_{2} \mathrm{O}_{5}\right](M) \)} \\
\hline 0 & 0.160 \\
\hline 1.67 & 0.0800 \\
\hline 3.33 & 0.0400 \\
\hline 5.00 & 0.0200 \\
\hline
\end{tabular}
(a) Determine the value of the rate constant, \( k \), for the reaction. Include units in your answer.