Problem 76 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are the examples of pseudo-unimolecular reactions? (1) acid catalyzed hydrolysis of an ester (2) inversion of cane sugar (3) decomposition of ozone (4) decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) Select the correct answers using the codes given below: (a) 1 and 2 (b) 1 and 3 (c) 2,3 and 4 (d) 1,2 and 4

Step-by-Step Solution

Answer

The correct answer is (a) 1 and 2.

Step 1: Understanding Pseudo-Unimolecular Reactions

A pseudo-unimolecular reaction is a reaction that involves two reactants but appears as if it involves only one reactant because the concentration of one reactant is in large excess and remains essentially constant throughout the reaction. The reaction follows first-order kinetics with respect to the limiting reactant.

Step 2: Analyzing Option 1: Acid Catalyzed Hydrolysis of an Ester

In the acid-catalyzed hydrolysis of an ester, the concentration of water is typically in large excess and doesn't change significantly during the reaction. Therefore, it behaves like a pseudo-unimolecular reaction with respect to the ester.

Step 3: Analyzing Option 2: Inversion of Cane Sugar

The inversion of cane sugar involves the hydrolysis of sucrose, usually in the presence of a catalyst like an acid. The water used in this reaction is in excess, so the reaction occurs under pseudo-unimolecular conditions similar to the ester hydrolysis.

Step 4: Analyzing Option 3: Decomposition of Ozone

Decomposition of ozone is a reaction that involves a single reactant and directly follows first-order kinetics, not pseudo-unimolecular, since there's no second reactant in excess.

Step 5: Analyzing Option 4: Decomposition of \( \mathrm{N}_{2} \mathrm{O}_{5} \)

The decomposition of \( \mathrm{N}_{2} \mathrm{O}_{5} \) also involves a single reactant decomposing into products, making it directly a first-order reaction rather than pseudo-unimolecular.

Step 6: Selecting the Correct Answer

Based on the analysis, options (1) and (2) are examples of pseudo-unimolecular reactions. Therefore, option (a), which includes these two, is the correct choice.

Key Concepts

First-Order Kinetics

First-order kinetics refers to reactions where the rate is directly proportional to the concentration of one reactant. This means that the rate of the reaction decreases exponentially as the reactant is consumed. It is mathematically represented as:

• \( \text{Rate} = k[A] \) where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant.

In a first-order reaction, if the concentration of the reactant is doubled, the rate of reaction also doubles. The rate constant, \( k \), has the unit of \( s^{-1} \). A typical example is the radioactive decay of elements. In the context of acid-catalyzed hydrolysis of an ester, first-order kinetics is observed. Despite involving more than one reactant, only the concentration of the ester affects the rate significantly when conditions are set for a pseudo-unimolecular reaction.

Acid-Catalyzed Hydrolysis

Acid-catalyzed hydrolysis is a chemical process where water and an acid (acting as a catalyst) interact with a compound to break it down. In the case of esters, the reaction converts them into carboxylic acids and alcohols. Here's a simplified chemical equation for this process:

• Ester + Water (+ Acid) → Carboxylic Acid + Alcohol

In most cases, water is present in large excess. This allows the reaction to appear as though it only involves the ester, thus giving rise to pseudo-unimolecular characteristics. The acid itself is not consumed but facilitates the breakdown of the ester by donating a proton (H⁺) to stabilize the transition state. As a result, the rate of reaction is determined solely by the concentration of the ester, making it follow first-order kinetics with respect to the ester.

Reaction Mechanisms

A reaction mechanism is a step-by-step description of how reactants are converted into products in a chemical reaction. It reveals the sequence of elementary steps or stages that lead to the final product formation. By understanding the mechanism, chemists can better grasp the behavior of the reaction, including its intermediates and transition states. For acid-catalyzed hydrolysis of esters, the mechanism involves:

• Protonation of the ester by the acid
• Nucleophilic attack by water
• Formation of a tetrahedral intermediate
• Deprotonation and breakdown to form the products

Each stage of this mechanism is crucial for the reaction's progression and ultimately affects the reaction rate. Understanding mechanisms is fundamental for predicting how changes in conditions might alter the reaction pathway.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates of chemical processes. It involves considering how different factors, like concentration, temperature, and catalysts, influence the speed of reactions. Key aspects include:

• Determining reaction order and rate laws
• Understanding energy profiles and activation energy
• Examining how catalysts affect reaction rates

Kinetics studies help chemists design reactions that are more efficient or are better controlled. For reactions like acid-catalyzed hydrolysis, kinetics provides insights into how pseudo-unimolecular reactions can be manipulated by adjusting the concentration of reactants. Through kinetic studies, predictions about reaction behaviors in different environments can be made, optimizing conditions for industrial or laboratory applications.