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\section{Second-order decay, $A+A\to\textrm{products}$}  Taking our definitions of the integrated rate law, survival function, and time dependent rate coefficient, we are able to apply them toto  second order irreversible decay. The integrated second-order rate law gives the survival function %\begin{equation}  % C_A(t) = \frac{C_A(0)}{1+\omega tC_A(0)}  %\end{equation}