deletions | additions       diff --git a/2.tex b/2.tex  index d3342fd..b4c4cad 100644  --- a/2.tex  +++ b/2.tex 
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-\frac{d[A]}{dt}=k_{1}[A]-k_{-1}[B]  \end{equation}     \begin{equation} \frac{d[B]}{dt} = k_1[A]-k_{-1}[B]-k_2[B]+k_{-2}[C]  \end{equation} \begin{equation} \frac{d[C]}{dt} = k_2[B]-k_{-2}[C]  \end{equation} Note that, for the purposes of this work, the conversion of isomer C to A is ignored. This is a valid assumption if the rate of inter-conversion of \textit{ A } $\longleftrightarrow$ \textit{ C } is small.  Given the experimental data, a steady-state approximation for the system of rate equations is not valid for isomer \textit{B} because its concentration is rather close to those of \textit{A} and \textit{C} and changes appreciably. Thus, the differential equations in (2)-(4) must be solved explicitly. The exact solutions to these equations are:  \begin{equation}  A(t) &= =  A_0[\frac{k_{-1}k_{-2}}{mn}+\frac{k_1(m-k_2-k_{-2})}{m(m-n)}*\mathrm{e}^{-mt}+\frac{k_1(k_2+k_{-2}-n)}{n(m-n)}*\mathrm{e}^{-nt}] \\ \end{equation}  \begin{equation}  B(t) &= =  A_0[\frac{k_{1}k_{-2}}{mn}+\frac{k_1(k_{-2}-m)}{m(m-n)}*\mathrm{e}^{-mt}+\frac{k_1(n-k_{-2})}{n(m-n)}*\mathrm{e}^{-nt}] \\ \end{equation}  \begin{equation}  C(t) &= =  A_0[\frac{k_{1}k_{2}}{mn}+\frac{k_1k_{2}}{m(m-n)}*\mathrm{e}^{-mt}-\frac{k_1k_{2}}{n(m-n)}*\mathrm{e}^{-nt}] \end{equation}  Where,  \begin{equation}