deletions | additions       diff --git a/The_consecutive_two_step_reversible__.tex b/The_consecutive_two_step_reversible__.tex  index 482419b..5b29eec 100644  --- a/The_consecutive_two_step_reversible__.tex  +++ b/The_consecutive_two_step_reversible__.tex 
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\begin{equation}  \frac{d[A]}{dt} = \frac{k_1k{-1}k_{-2}}{k_1k_2+k_{-1}k_{-2}+k_1k_{-2}}+\frac{k_1k_2+k_1k_{-2}}{k_1k_2+k_{-1}k_{-2}+k_1k_{-2}}\mathrm{e}^{-k_1t}  \end{equation}  Thus, by inspection of Eqns (12) and (19), $x_1$ \approx $\approx$  $k_1$. Equation (4) may be similarly rearranged and integrated to solve assuming equilibrium conditions, where $x_3$ \approx $k_{-2}$. Unfortunately, equations (12)-(14) cannot be expressly used to determine exact values for $k_1$, $k_{-1}$, $k_2$, and $k_{-2}$ explicitly because those variables are coupled (recall the simplifying assumption that a three-component exponential fit to the experimental data converges to a two-component exponential fit when values of m and n are similar). It is, however, relatively straightforward to determine $K_1$ and $K_2$ by fitting the experimental data with a function of the form $y(t) = y_0+\alpha{}\mathrm{e}^{-\beta{}t}$ to obtain $y_0$ and $\beta$ for $A$, $B$, and $C$ at each temperature. It then follows that \begin{equation}  K_1=\frac{y_0(B)}{y_0(A)}  \end{equation}