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Jonathan Nichols edited Intro1.tex
over 9 years ago
Commit id: a433b17255735decdc49a6910fe5deb2f8a95827
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k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)
\end{equation}
The same can be derived for $n^{th}$ order reactions, where $A+nA\rightarrow B$. The integrated rate law of these reactions is
\begin{equation}
\frac{1}{[A_t]^{n-1}}=\frac{1}{[A_0]^{n-1}}+(n-1)\omega t
\end{equation}
From the integrated rate law, we obtain the survival function
\begin{equation}
S(t)=\frac{[A_t]}{[A_0]}\sqrt[n-1]{\frac{1}{1+(n-1)\omega t[A_0]^{n-1}}}