Match List I with List II

Choose the correct answer from the options given below:

A-III, B-IV, C-I, D-II

The correct answer is option 2. A-III, B-IV, C-I, D-II.

A. Decomposition of \(H_2O_2\) : III. First order reaction:

The decomposition of hydrogen peroxide (\(H_2O_2\)) can be described as a first-order reaction. In a first-order reaction, the rate of the reaction is directly proportional to the concentration of only one reactant.  For the decomposition of \(H_2O_2\), the reaction can be represented as:

\[2H_2O_2 \rightarrow 2H_2O + O_2\]

The rate of this reaction is expressed as:

\[rate = k[H_2O_2]\]

Where:

\(rate\) is the rate of the reaction,

\(k\) is the rate constant,

\([H_2O_2]\) is the concentration of hydrogen peroxide.

This equation shows that the rate of the reaction is directly proportional to the concentration of \(H_2O_2\), indicating a first-order reaction.

B. Decomposition of \(H_2\) in the presence of \(Hg\) and light : IV. Photosensitization:

The decomposition of hydrogen peroxide (\(H_2O_2\)) in the presence of mercury (\(Hg\)) and light is a photosensitization reaction. In this process, mercury acts as a photosensitizer, which absorbs light energy and transfers it to the hydrogen peroxide molecules, initiating their decomposition. The general reaction for the decomposition of hydrogen peroxide in the presence of mercury and light can be represented as follows:

\[H_2O_2 + Hg + \text{light} \rightarrow H_2O + O_2 + Hg^{2+}\]

In this reaction, the mercury (\(Hg\)) acts as a catalyst or sensitizer, absorbing light energy and transferring it to the hydrogen peroxide molecules. This process enhances the decomposition of \(H_2O_2\) into water (\(H_2O\)) and oxygen (\(O_2\)), while the mercury itself remains unchanged, making it an effective catalyst in this photosensitization reaction.

C. Hydrolysis of ester by alkali : I. Second order reaction:

The hydrolysis of an ester by alkali is a second-order reaction. The general equation for the hydrolysis of an ester in the presence of a base (\(OH^-\)) can be represented as follows:

\[ \text{R-COOR'} + OH^- \rightarrow R-COO^- + R'OH \]

This reaction involves the breaking of the ester bond (\(R-COOR'\)) and the formation of a carboxylate ion (\(R-COO^-\)) and an alcohol (\(R'OH\)).

The rate law for this reaction, assuming it follows second-order kinetics, can be expressed as:

\[ \text{Rate} = k [ester][OH^-] \]

Where:

\( \text{Rate} \) is the rate of the reaction,

\( k \) is the rate constant,

\( [ester] \) is the concentration of the ester, and

\( [OH^-] \) is the concentration of the hydroxide ion.

This equation indicates that the rate of the reaction is directly proportional to the concentration of both the ester and the hydroxide ion, making it a second-order reaction.

D. Hydrolysis of ester in excess of acid : II. Pseudo first order reaction:

The hydrolysis of an ester in excess acid can indeed be considered a pseudo-first-order reaction. In this scenario, the concentration of the acid is kept high, ensuring it remains in excess compared to the ester. The general equation for the acid-catalyzed hydrolysis of an ester can be represented as follows:

\[ \text{R-COOR'} + \text{H}_3\text{O}^+ \rightarrow \text{R-COOH} + \text{R'OH} \]

In this reaction, the acid (\(\text{H}_3\text{O}^+\)) catalyzes the hydrolysis of the ester, leading to the formation of a carboxylic acid (\(\text{R-COOH}\)) and an alcohol (\(\text{R'OH}\)). The rate law for this reaction, under conditions where the acid is in excess, can be simplified to a pseudo-first-order rate law, expressed as:

\[ \text{Rate} = k' [ester] \]

Where:

\( \text{Rate} \) is the rate of the reaction,

\( k' \) is the pseudo-first-order rate constant, and

\( [ester] \) is the concentration of the ester.

In this case, the concentration of the acid remains relatively constant, leading to a situation where the reaction rate depends only on the concentration of the ester. This simplification allows us to treat the reaction as pseudo-first order, even though it may involve multiple reactants.