deletions | additions       diff --git a/Pseudo-First Order Reactions.tex b/Pseudo-First Order Reactions.tex  index 0cdb237..9a73e21 100644  --- a/Pseudo-First Order Reactions.tex  +++ b/Pseudo-First Order Reactions.tex 
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\begin{equation}  \Delta t \int_0^{\Delta t}k'(t)^2dt=\omega'^2\Delta t^2   \end{equation}  The inequality between the statistical length and divergence works in a pseudo-first order irreversible reaction. The difference between $\mathcal{J}(\Delta{t})$ and $\mathcal{L}(\Delta{t})^2$ not only measures the amount of static and dynamic disorder in a pseudo-first order decay, but also how psuedo-first order the reaction really is. A large difference between $\mathcal{J}(\Delta{t})$ and $\mathcal{L}(\Delta{t})^2$ may also suggest that there is not enough excess of one reactant to consider the reaction to be completely pseudo-first order. The only time a single pseudo-first order rate coefficient is sufficient to describe the population decaying over time is when $\omega'(\Delta{t})^2=(\omega\Delta{t})^2$. $\omega'^2\Delta{t}^2=(\omega\Delta{t})^2$.  This is also the only time where the reaction is truly pseudo-first order.