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Jonathan Nichols edited Mixed Second Order Reactions.tex
over 9 years ago
Commit id: 13992c4e1a21d8068d947badc4309a8da021b828
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However, $\frac{dx}{dt}=\omega([A_0]-x)([B_0]-x)$
Filling in $\frac{dx}{dt}$ in the integral and evaluating, we get that k(t)=$\omega$t, which goes on to provide the same results that are seen in first order, except that the statistical length and the divergence are no longer dimensionless since the second order rate constant has units of $\frac{1}{[concentration][time]}$. The inequality this result leads to has already been seen in first order kinetics as
\begin{equation}
$\omega^2(\Delta{t})^2-(\omega\Delta t)^2\geq0$ \omega^2(\Delta{t})^2-(\omega\Delta t)^2\geq0
\end{equation}