finished results

main.tex

@@ -94,7 +94,7 @@ has simply been esterified differently than ASA.\\
   \label{fig:methyl-salicylate}
 \end{figure}
 
-Due to the similarity between the two molecules, ASA can be reacted to synthesize methyl salicylate~\cite{Hartel2009}. 
+Due to the similarity between the two molecules, ASA can be reacted to synthesize methyl salicylate~\cite{Hartel2009,nilered2017aspirin}. 
 The purpose of this experiment was to convert acetylsalicylic acid obtained from 
 commercial aspirin tablets into methyl salicylate through acid-catalyzed esterification 
 in methanol under reflux conditions.
@@ -173,6 +173,33 @@ The transformation encompasses two concurrent equilibrium-driven processes:
 
 To drive the reaction toward the methyl salicylate product, a substantial stoichiometric excess of methanol was employed, utilizing Le Chatelier's principle to overcome the reversible nature of the esterification.
 
+\subsection{Kinetic and Thermodynamic Analysis}
+
+The transformation efficiency of the tandem hydrolysis--esterification is determined by the interplay between reaction rate and equilibrium position.
+
+\subsubsection{Thermal Activation and Collision Theory}
+The reflux duration is required to provide the activation energy ($E_{a}$) necessary for the nucleophilic attack on the sterically hindered aryl ester. According to the Arrhenius relationship, the rate constant $k$ increases exponentially with temperature:
+\begin{equation}
+    k = Ae^{-E_{a}/RT}
+\end{equation}
+Operating at the boiling point of the solvent increases the frequency of effective collisions and facilitates the formation of the required carbocation intermediates. 
+
+Furthermore, by employing a vast molar excess of methanol, the system effectively follows pseudo-first-order kinetics. Under these conditions, the concentration of the alcohol remains negligible in its variation, and the rate depends solely on the concentration of the limiting aspirin precursor:
+\begin{equation}
+    -\frac{d[\text{ASA}]}{dt} = k'[\text{ASA}] \implies [\text{ASA}]_{t} = [\text{ASA}]_{0}e^{-k't}
+\end{equation}
+
+\subsubsection{Equilibrium Shifts and Chemical Potential}
+As a reversible process, the yield is limited by the equilibrium constant ($K$). Because the esterification step is endothermic ($\Delta H^\circ > 0$), the application of heat shifts the equilibrium toward the products. This temperature dependence is quantified by the Van't Hoff equation:
+\begin{equation}
+    \frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^{2}}
+\end{equation}
+
+The high reactant-to-substrate ratio further ensures that the reaction quotient ($Q$) remains lower than $K$ throughout the process. This maintains a negative Gibbs free energy ($\Delta G$), driving the reaction toward the formation of methyl salicylate:
+\begin{equation}
+    \Delta G = \Delta G^\circ + RT \ln Q
+\end{equation}
+The combination of thermal input and stoichiometric bias effectively overcomes the reversible nature of the Fischer esterification.
 \subsection{Work-up and Purification}
 
 Following reflux, the reaction was quenched in ice-cold distilled water. Methyl salicylate ($\rho \approx 1.17$ g/mL) was isolated as the organic phase via liquid--liquid extraction. Residual acidic species (\ce{H2SO4}, \ce{CH3COOH}) were neutralized using saturated \ce{NaHCO3}:
@@ -183,113 +210,9 @@ Following reflux, the reaction was quenched in ice-cold distilled water. Methyl
 
 The organic extract was dried over anhydrous \ce{MgSO4} and filtered to yield the pure essential oil.
 
-\subsection{Outline}
-
-The document layout should follow the style of the journal concerned. Where
-appropriate, sections and subsections should be added in the normal way.
-
-\subsection{References}
-
-References should be given in the normal way in \LaTeX{}. If you are using
-\textsf{biblatex} (as recommended) then you can use the full range of citation
-commands it provides. If you choose to use classical Bib\TeX{}, the
-\textsf{natbib} package will be loaded and you can use it's commands.
-
-\subsection{Floats}
-
-New float types are set up in the preamble. The means graphics are included as
-follows (Scheme~\ref{sch:example}). As illustrated, the float is ``here'' if
-possible.
-\begin{scheme}
-  \centering
-  Your scheme graphic would go here: PDF graphics are recommended.
-  %\includegraphics{graphic}
-  \caption{An example scheme}
-  \label{sch:example}
-\end{scheme}
-
-
-
-The use of the different floating environments is not required, but it is
-intended to make document preparation easier for authors. In general, you
-should place your graphics where they make logical sense; the production
-process will move them if needed.
-
-\subsection{Math}
-
-If packages such as \textsf{amsmath} are required, they should be loaded in the
-preamble. However, the basic \LaTeX\ math(s) input should work correctly
-without this. Some inline material $1 + 1 = 2$ followed by some display. \[ A =
-\pi r^2 \]
-
-It is possible to label equations in the usual way (Eq.~\ref{eqn:example}).
-\begin{equation}
-  \frac{\mathrm{d}}{\mathrm{d}x} \, r^2 = 2r \label{eqn:example}
-\end{equation}
-This can also be used to have equations containing graphical content. To align
-the equation number with the middle of the graphic, rather than the bottom, a
-minipage may be used.
-\begin{equation}
-  \begin{minipage}[c]{0.80\linewidth}
-    \centering
-    As illustrated here, the width of \\
-    the minipage needs to allow some  \\
-    space for the number to fit in to.
-    %\includegraphics{graphic}
-  \end{minipage}
-  \label{eqn:graphic}
-\end{equation}
 
 \section{Experimental}
 
-The usual experimental details should appear here. This could include a table,
-which can be referenced as Table~\ref{tbl:example}. Notice that the caption is
-positioned at the top of the table.
-\begin{table}
-  \caption{An example table}
-  \label{tbl:example}
-  \centering
-  \begin{tabular}{ll}
-    \hline
-    Header one  & Header two  \\
-    \hline
-    Entry one   & Entry two   \\
-    Entry three & Entry four  \\
-    Entry five  & Entry five  \\
-    Entry seven & Entry eight \\
-    \hline
-  \end{tabular}
-\end{table}
-
-Adding notes to tables can be complicated. Perhaps the easiest method is to
-generate these using the basic \texttt{\textbackslash textsuperscript} and
-\texttt{\textbackslash emph} macros, as illustrated (Table~\ref{tbl:notes}).
-\begin{table}
-  \caption{A table with notes}
-  \label{tbl:notes}
-  \centering
-  \begin{tabular}{ll}
-    \hline
-    Header one                            & Header two \\
-    \hline
-    Entry one\textsuperscript{\emph{a}}   & Entry two  \\
-    Entry three\textsuperscript{\emph{b}} & Entry four \\
-    \hline
-  \end{tabular}
-
-  \textsuperscript{\emph{a}} Some text;
-  \textsuperscript{\emph{b}} Some more text.
-\end{table}
-
-The example file also loads the optional \textsf{chemformula} and
-\textsf{mhchem} packages, so that formulas are easy to input:
-\texttt{\textbackslash ce\{H2SO4\}} gives \ce{H2SO4}. The two have similar
-syntax but authors may prefer one or the other.
-
-The use of new commands should be limited to simple things which will not
-interfere with the production process. For example, \texttt{\textbackslash
-mycommand} has been defined in this example, to give italic, mono-spaced text:
-\mycommand{some text}.
 
 \section*{Acknowledgements}
 

references.bib

@@ -54,4 +54,15 @@
   year = {2009},
   month = Apr,
   pages = {475}
+}
+
+@online{nilered2017aspirin,
+  author       = {NileRed},
+  title        = {Turning aspirin pills into mint flavor},
+  year         = {2017},
+  month        = jul,
+  day          = {17},
+  organization = {YouTube},
+  url          = {https://www.youtube.com/watch?v=3NN9IUvrKi4},
+  note         = {YouTube video, 10.7M subscribers, 2,057,102 views, accessed 2026-05-12}
 }