Understanding Pseudo Unimolecular Reactions

A pseudo unimolecular reaction is a reaction that appears to be unimolecular (first order) but is actually bimolecular (second order) or trimolecular (third order). This typically happens when one of the reactants is present in a very large excess compared to the other reactant(s).

In such cases, the concentration of the reactant in excess remains essentially constant throughout the reaction. Therefore, the rate of the reaction depends only on the concentration of the reactant that is not in excess.

Molecularity vs. Order

• Molecularity: The number of reacting species (atoms, ions, or molecules) that collide simultaneously to bring about a chemical reaction. It is determined from the mechanism of an elementary reaction.
• Order of reaction: The sum of the powers of the concentration terms in the rate law expression. It is determined experimentally.

For a pseudo unimolecular reaction, the molecularity determined from the stoichiometric equation might be 2 or more, but the experimentally determined order of the reaction is 1.

Analyzing the Options

Let's examine the given options:

1. $\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}$
   This reaction is often cited as an example of a complex reaction with a chain mechanism. Its overall order is not straightforward and depends on conditions. It is not typically considered a simple bimolecular reaction that becomes pseudo unimolecular.
2. $\text{PbCO}_3 \rightarrow \text{PbO} + \text{CO}_2$
   This is a thermal decomposition reaction involving a single reactant molecule breaking down. The molecularity is 1, and the order is generally 1. It is a true unimolecular reaction, not a pseudo unimolecular one.
3. ${C_{12}}{H_{22}}{O_{11}} + {H_2}O\mathop \to \limits^{{H^ \oplus }} {C_6}{H_{12}}{O_6} + {C_6}{H_{12}}{O_6}$ (Hydrolysis of Sucrose)
   This reaction involves two reactants: sucrose ($\text{C}_{12}\text{H}_{22}\text{O}_{11}$) and water ($\text{H}_2\text{O}$). The molecularity of this elementary step would be 2.
   However, this reaction is typically carried out in an aqueous solution, where water is the solvent and is present in a very large excess. As the reaction proceeds, the concentration of water changes negligibly compared to the concentration of sucrose.
   The rate law for this reaction is experimentally found to be Rate $\propto$ $[\text{C}_{12}\text{H}_{22}\text{O}_{11}]$. The rate is effectively independent of the concentration of water.
   The rate equation can be written as: Rate $= k'[\text{C}_{12}\text{H}_{22}\text{O}_{11}]$, where $k' = k[\text{H}_2\text{O}]_\text{excess}$.
   This reaction is second order by molecularity but first order by kinetics (order 1). Therefore, it is a classic example of a pseudo unimolecular reaction (specifically, a pseudo first-order reaction).
4. None of the above
   Since option 3 is a valid example of a pseudo unimolecular reaction, this option is incorrect.

Based on the analysis, the hydrolysis of sucrose in the presence of acid is an example of a pseudo unimolecular reaction because water is in large excess, making the reaction rate dependent only on the concentration of sucrose.