Some remarks on the chemical Petri net and catalysis:

The feedback loop to the \\(\text{CO}_2\\) makes this system interesting. It means that once we obtain 1 equivalent of \\(\text{CO}_2\\), we no longer need to supply any since it is always regenerated with every reaction cycle.

\[ \text{CO}_2 + \text{NaOH} \longrightarrow \text{NaHCO}_3 \]
\[ \text{NaHCO}_3 + \text{HCl} \longrightarrow \text{H}_2 \text{O} + \text{NaCl} + \text{CO}_2 \]

So essentially, if one wanted to produce the products water \\(\text{H}_2\text{O}\\) and table salt \\(\text{NaCl}\\) from the reactants sodium hydroxide \\(\text{NaOH}\\) and hydrochloric acid \\(\text{HCl}\\) via this petri net, one could do so with only a single molecule of \\(\text{CO}_2\\), while only being limited by the amount of the reactants one has on hand. The reaction stops once one runs out of one.

One could thus simplify the above equations to:

\[ \text{HCl} + \text{NaOH} \xrightarrow{\text{'cat.'} \text{CO}_2} \text{NaCl} + \text{H}_2\text{O} \]

Where 'cat.' stands for 'catalyzed by'. I put it in quotations because in order for something to actually be catalysis it would have to increase the reaction rate by lowering the activation energy (this can happen by a number of mechanisms). With the above reaction (acid/base, thermodynamically favored), I very much doubt that in reality having the \\(\text{CO}_2\\) around would speed things up, but according to our Petri net model, it's required for the reaction to proceed.

The step we left out in the above simplified equation, i.e the middle step in:

$$ \text{CO}_2 + \text{NaOH} + \text{HCl}\longrightarrow \text{NaHCO}_3 \ + \text{HCl} \longrightarrow \text{CO}_2 \ + \text{H}_2 \text{O} + \text{NaCl} $$

would be referred to as the mechanism of catalysis by chemists. When one finds that adding a specific substance drastically increases the rate of a reaction, the search is on to find out how it does so. This often involves a lower energy intermediate that can only be formed in the presence of the catalyst.

As the book points out, the oven in the lemon pie example can be thought of as a 'catalyst' as well. Just to give a non-chemical example (although baking is in some sense also chemistry).