Question

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): For the hydrogen halogen photochemical reaction, the quantum yield for the formation of \(\mathrm{HBr}\), is lower than that of \(\mathrm{HCl}\). (R): \(\mathrm{Br}+\mathrm{H}_{2} \rightarrow \mathrm{HBr}+\mathrm{H}\) has higher activation energy than \(\mathrm{Cl}+\mathrm{H}_{2} \rightarrow \mathrm{HCl}+\mathrm{H}\)

Short answer

Option (a) is correct: Both A and R are true, and R is the correct explanation of A.

Step-by-step solution

Understanding the Assertion

The assertion (A) states that the quantum yield for the formation of HBr in a photochemical reaction is lower than that for the formation of HCl. Quantum yield refers to the efficiency of a photochemical reaction, and a lower quantum yield implies that the reaction occurs with less efficiency, producing fewer product molecules per photon of light absorbed.

Analyzing the Reason

The reason (R) explains that the reaction involving bromine (Br + H2 → HBr + H) has a higher activation energy compared to the reaction involving chlorine (Cl + H2 → HCl + H). Higher activation energy typically means the reaction proceeds more slowly or with less probability under the same conditions.

Connecting Assertion and Reason

Higher activation energy in the reaction forming HBr compared to forming HCl suggests that the formation of HBr is less efficient or has a lower quantum yield, as implied in the assertion. Thus, the reason given directly explains the assertion, making the reason a valid explanation for the assertion.

Assessment of the Statements

Both the assertion (A) and the reason (R) are correct. Moreover, the reason (R) correctly explains the assertion (A), as the higher activation energy for the bromine reaction accounts for its lower quantum yield compared to the chlorine reaction.

Key concepts

Quantum Yield

A photochemical reaction's **quantum yield** is an essential concept in understanding how efficiently a chemical reaction happens when light is absorbed by the reacting molecules. Simply put, quantum yield measures the number of molecules produced or reacted for each photon absorbed. The formula for quantum yield \( \Phi \) is given by:\[\Phi = \frac{\text{Number of molecules reacted or produced}}{\text{Number of photons absorbed}}\]When a reaction has a high quantum yield, it means that a large number of molecules are converted into products for each photon that the system absorbs. Conversely, a lower quantum yield indicates that fewer molecules undergo the reaction, showing lower efficiency. In the context of hydrogen halogen reactions, comparing the quantum yield of the formation of HCl and HBr shows how these reactions differ in efficiency. The assertion states that HCl formation has a higher quantum yield than HBr, implying that the reaction producing HCl is more efficient.The distinction between **HCl** and **HBr** yields can result from other influencing factors like:

• The energy needed to break existing bonds in reactant molecules.
• The effectiveness of forming new bonds between hydrogen and halogen atoms.

Hydrogen Halogen Reactions

Hydrogen halogen reactions are a type of photochemical process where hydrogen reacts with a halogen element such as chlorine (Cl) or bromine (Br) under the influence of light. These reactions are initiated when molecules absorb light photons, supplying the necessary energy to break bonds and form new ones. There are key differences in the photochemical reactions involving bromine and chlorine. The reaction steps for these processes generally involve:

• **Initiation**: Light absorption creates reactive atoms (e.g., \( \text{Br}_2 \rightarrow 2\text{Br}^\cdot \) or \( \text{Cl}_2 \rightarrow 2\text{Cl}^\cdot \)).
• **Propagation**: Reactive halogen atoms collide with hydrogen molecules (\(\text{H}_2\)) to form hydrogen halides, such as HCl or HBr, releasing additional energy.
• **Termination**: The reactive species are eventually neutralized, ceasing the reaction chain.

For instance, in the formation of HBr, bromine radicals react with hydrogen molecules to propagate the reaction, but this process can vary in efficiency compared to chlorine radicals which form HCl. Differences in the reactions' quantum yields are often linked to the reaction mechanisms and efficiencies at each step.

Activation Energy

**Activation energy** is the minimum energy required for a chemical reaction to proceed. It acts as an energetic barrier that reactants must overcome to transform into products. In photochemical reactions, light provides the energy needed to surpass this barrier. The activation energy for a given reaction involves several key aspects:

• It affects the reaction rate—higher activation energy means that reactants need more energy to react, slowing down the process.
• Reactions with lower activation energy happen more readily under the same conditions.

In the context of hydrogen halogen reactions, the assertion highlights the difference in activation energy between reactions forming HCl and HBr. The reasoning given for a lower quantum yield in the HBr formation stems from the fact that it has a higher activation energy compared to HCl formation. This implies that more energy is needed for each step of the bromine-related reaction. As a result, fewer successful molecular collisions happen compared to the chlorine reaction, which requires less energy to proceed. This difference in activation energy leads to the contrasting efficiencies or quantum yields observed in these photochemical reactions.