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# The thermal decomposition of N$_2$O$_5$ to form NO$_2$ and O$_2$ is a first order reaction. The rate constant for the reaction is $5.1x10^{–4}s^{-1}$ at $318^{\circ} K$. Calculate the half-life of this reaction.

$\begin{array}{1 1} 1400\;s \\ 2800 \;s \\ 700\;s \\ 2100\;s \end{array}$

The half life $t_{1/2} = \large\frac{ ln\;2}{k}$$= \large\frac{0.693}{k}. \Rightarrow = \large\frac{0.693}{5.1x10^{–4}s^{-1}}$$ = 1400\;s$