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The following data were obtained during the first order thermal decomposition of \( \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \) at a constant volume :
\[
2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_{2} \mathrm{O}_{4}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})
\]
\begin{tabular}{|r|r|c|}
\hline S. No. & Time \( / \mathrm{s} \) & Total pressure \( / \mathrm{atm} \) \\
\hline 1. & 0 & 0.5 \\
\hline 2. & 100 & 0.512 \\
\hline
\end{tabular}
Calculate the rate constant.
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