Problem 168 - A Complete Resource Book in Chemistry for JEE Main

Question

Oxidizing power of chlorine in aqueous solution can be determined by the parameters indicated below: \(1 / 2 \mathrm{Cl}_{2}(\mathrm{~g}) \stackrel{1 / 2 \Delta \mathrm{H}_{\mathrm{Das}}}{\longrightarrow} \mathrm{Cl}(\mathrm{g}) \stackrel{\Delta_{\mathrm{eg}} \mathrm{H}^{-}}{\longrightarrow}\) \(\mathrm{Cl}^{-}(\mathrm{g}) \quad \stackrel{\Delta_{\mathrm{hyd}} \mathrm{H}}{\longrightarrow} \mathrm{Cl}^{-}(\mathrm{aq})\) The energy involved in the conversion of \(1 / 2 \mathrm{Cl}_{2}(\mathrm{~g})\) to \(\mathrm{Cl}^{-}(\mathrm{g})\) (Using the data, \(\Delta \mathrm{H}_{\mathrm{C}_{2}}=240 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{eg}} \mathrm{H}^{-\mathrm{Cl}}=\) \(-349 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{hyd}} \mathrm{H} \mathrm{Cl}=-381 \mathrm{~kJ} \mathrm{~mol}^{-1}\) ) will be (a) \(+152 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-610 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-850 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(+120 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The correct answer is (b) \\(-610 \, \text{kJ/mol}\\).

Step 1: Understand the Process

The process involves the conversion of chlorine gas to chloride ions. This occurs in three steps: (1) Chlorine gas needs to dissociate into chlorine atoms, (2) These chlorine atoms gain an electron to form chloride ions in gas form, and (3) The chloride ions then get hydrated to form chloride ions in aqueous solution.

Step 2: Dissociation of Cl2

For the dissociation of chlorine gas \ \( \frac{1}{2} \mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{Cl}(\mathrm{g}) \), the enthalpy change \( \Delta \mathrm{H}_{\mathrm{Das}} \) is given as half of \( \Delta \mathrm{H}_{\mathrm{C_2}} \), so \( \Delta \mathrm{H}_{\mathrm{Das}} = \frac{240}{2} = 120 \, \text{kJ/mol} \).

Step 3: Electron Capture by Chlorine Atom

The second step is the electron gain by a chlorine atom to form chloride ion in gas form \ \( \mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{Cl}^{-}(\mathrm{g}) \), with enthalpy change \( \Delta_{\mathrm{eg}} \mathrm{H}^- \) as given: \(-349 \, \text{kJ/mol} \).

Step 4: Hydration of Chloride Ion

For the hydration of chloride ion \ \( \mathrm{Cl}^{-}(\mathrm{g}) \rightarrow \mathrm{Cl}^{-}(\mathrm{aq}) \), the enthalpy change \( \Delta_{\mathrm{hyd}} \mathrm{H} \) is given: \(-381 \, \text{kJ/mol} \).

Step 5: Calculate Total Energy Change

The total enthalpy change for the entire process is the sum of enthalpy changes from each step: \\( \Delta H_{\text{total}} = 120 + (-349) + (-381) \). This evaluates to \( \Delta H_{\text{total}} = -610 \, \text{kJ/mol} \).

Step 6: Select Correct Answer

The total energy change we calculated matches option (b) which is \(-610 \, \text{kJ/mol} \). Hence, the correct answer is (b).

Key Concepts

Enthalpy Change

Enthalpy change is a measure of the total energy change in a system as it undergoes a chemical reaction. It's crucial for understanding various processes like phase transitions, chemical reactions, and even dissolution. Enthalpy is often expressed in kilojoules per mole (kJ/mol) and can be either positive or negative. A positive enthalpy change indicates an endothermic process where energy is absorbed. A negative indicates an exothermic process where energy is released.

In the context of the chlorine oxidation process, enthalpy change refers to the energy alterations as chlorine gas converts into hydrated chloride ions. The dissociation of chlorine, electron gain by chlorine, and hydration of the chloride ion each involve distinct enthalpy changes which together determine the overall energy change. Understanding this concept is critical for calculating energy changes in reactions, helping predict reaction behavior and stability.

Chlorine Dissociation

Chlorine dissociation is the first essential step in understanding the oxidizing power of chlorine. During this process, chlorine gas (\( \mathrm{Cl}_2 \)g) dissociates into individual chlorine atoms (\( \mathrm{Cl} \)g). This step is crucial as it's where the system absorbs energy to break the molecular bonds of chlorine. The given enthalpy change for this step is \( \Delta \mathrm{H}_{\mathrm{Das}} \), which is half of the total dissociation enthalpy (\( \Delta \mathrm{H}_{\mathrm{C}_2} \)).

• This step is endothermic, meaning that energy is required to break the chlorine molecule into atoms.
• The energy involved is calculated as \( 240/2 = 120 \, \text{kJ/mol} \).

Understanding this energy input is vital as it forms the foundation for subsequent reaction steps.

Electron Gain of Chlorine

The electron gain by a chlorine atom is a significant factor in the oxidation process. In this step, an electron is added to a chlorine atom to form a chloride ion (\( \mathrm{Cl}^- \)g). The enthalpy change for this step is \( \Delta_{\mathrm{eg}} \mathrm{H}^- \).

• This process is exothermic, as it involves the release of energy, making it favorable.
• The energy change is \(-349 \, \text{kJ/mol} \), indicating a strong release of energy.

Chlorine's high electron affinity allows it to gain an electron readily, augmenting its oxidizing ability. This step helps in understanding why chlorine is a robust oxidizing agent.

Hydration of Chloride Ion

Once chlorine has gained an electron, forming chloride ions in a gaseous state, the process of hydration takes place. Hydration is when water molecules surround a chloride ion to form an aqueous solution (\( \mathrm{Cl}^- \)\( \mathrm{(aq)} \)). The enthalpy change associated with this step is \( \Delta_{\mathrm{hyd}} \mathrm{H} \).

• This step is highly exothermic, suggesting that significant energy is released when the chloride ions become hydrated.
• The given energy change for this process is \(-381 \, \text{kJ/mol} \).

Hydration is a crucial step as it completes the transformation of chlorine into a useful ion in aqueous solutions, aiding in predicting how chlorine behaves as an oxidizer in water. Understanding this concept is important for chemistry applications where aqueous environments are involved.