Question

An example of pseudo first order reaction is

• A. Thermal decomposition of N\(_2\)O\(_5\)
• B. Inversion of cane sugar
• C. Decomposition of gaseous NH\(_3\) on hot Pt surface
• D. Radioactive decay of \(_{88}^{226}Ra\)
• E. Hydrogenation of ethene

Hint:

Hydrolysis reactions where water is the solvent are often pseudo first order.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
A pseudo first-order reaction is a chemical reaction that appears to be of the first order, but is actually a higher-order reaction. This occurs when one of the reactants is present in a large excess, causing its concentration to remain nearly constant throughout the reaction. The rate of the reaction then seems to depend only on the concentration of the other reactant(s).
Step 2: Detailed Explanation
Let's analyze the options:
(A) Thermal decomposition of N₂O₅: The reaction \(2\text{N}_2\text{O}_5 \rightarrow 4\text{NO}_2 + \text{O}_2\) is a classic example of a first-order reaction. The rate depends only on the concentration of N₂O₅.
(B) Inversion of cane sugar: This is the hydrolysis of sucrose (cane sugar) into glucose and fructose. The reaction is:
\[ \text{C}_{12}\text{H}_{22}\text{O}_{11} \text{ (Sucrose)} + \text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 \text{ (Glucose)} + \text{C}_6\text{H}_{12}\text{O}_6 \text{ (Fructose)} \] The rate law for this reaction should be Rate = \(k[\text{C}_{12}\text{H}_{22}\text{O}_{11}][\text{H}_2\text{O}]\). However, the reaction is typically carried out in an aqueous solution where water is the solvent and is present in a very large excess. Its concentration does not change significantly during the reaction. Therefore, the concentration of water is considered constant and is absorbed into the rate constant, giving a new rate constant \(k' = k[\text{H}_2\text{O}]\). The effective rate law becomes Rate = \(k'[\text{C}_{12}\text{H}_{22}\text{O}_{11}]\), which is first-order. This is a pseudo first-order reaction.
(C) Decomposition of gaseous NH₃ on hot Pt surface: This is an example of a zero-order reaction. The rate is independent of the reactant concentration because it is limited by the number of active sites on the platinum catalyst surface.
(D) Radioactive decay of ²²⁶Ra: All radioactive decay processes follow first-order kinetics.
(E) Hydrogenation of ethene: The catalytic hydrogenation of ethene (\(\text{C}_2\text{H}_4 + \text{H}_2 \rightarrow \text{C}_2\text{H}_6\)) is typically zero-order with respect to ethene and first-order with respect to hydrogen, but the overall kinetics can be complex. It is not a pseudo first-order reaction.
Step 3: Final Answer
Based on the analysis, the inversion of cane sugar is the correct example of a pseudo first-order reaction.