Problem 105 - A Complete Resource Book in Chemistry for JEE Main

Question

Calculate \(\Delta H_{f}^{\circ}\) for chloride ion from the following data: \(1 / 2 \mathrm{H}_{2}(\mathrm{~g})+1 / 2 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HCl}(\mathrm{g})\) \(\Delta \mathrm{H}_{\mathrm{f}}^{\mathrm{c}}=-92.4 \mathrm{~kJ}\) \(\mathrm{HCl}(\mathrm{g})+\mathrm{nH}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}\)(aq) \(\Delta \mathrm{H}_{\mathrm{Hyd}}=-74.8 \mathrm{~kJ}\) \(\Delta \mathrm{H}_{\mathrm{f}}^{*}\left[\mathrm{H}^{+}\right]=0.0 \mathrm{~kJ}\) (a) \(-189 \mathrm{~kJ}\) (b) \(-167 \mathrm{~kJ}\) (c) \(+167 \mathrm{~kJ}\) (d) \(-191 \mathrm{~kJ}\)

Step-by-Step Solution

Answer

The enthalpy of formation for Cl⁻(aq) is -167 kJ/mol.

Step 1: Understand the Reaction Components

We are given a formation reaction for HCl (g) and a hydration reaction that involves HCl (g) dissolving into H⁺ (aq) and Cl⁻ (aq). The goal is to find the enthalpy of formation (ΔH⁰ₑ) for Cl⁻ (aq).

Step 2: Analyze Given Data

1. For the reaction \[ \frac{1}{2} \text{H}_2(g) + \frac{1}{2} \text{Cl}_2(g) \longrightarrow \text{HCl}(g) \]ΔH⁰ₑ = -92.4 kJ.2. For the reaction \[ \text{HCl}(g) + n \text{H}_2 ext{O}(l) \longrightarrow \text{H}^+(aq) + \text{Cl}^-(aq) \]ΔH_{\text{Hyd}} = -74.8 kJ.

Step 3: Apply Hess's Law

Hess's law states that the total enthalpy change depends only on the initial and final states of the reaction, not the path. We use it to find ΔH⁰ₑ for Cl⁻(aq):\[ΔH_\text{total} = ΔH_{\text{f}}(\text{HCl}(g)) + ΔH_{\text{Hyd}} - ΔH_\text{f}([\text{H}^+](aq)) - ΔH_\text{f}([\text{Cl}^-](aq))\]Substituting the data:\[-92.4 + (-74.8) = 0.0 - ΔH_\text{f}([\text{Cl}^-](aq))\]This simplifies to:\[-167.2 = - ΔH_\text{f}([\text{Cl}^-](aq))\]

Step 4: Solve for ΔH⁰₁ for Cl⁻(aq)

From the equation in Step 3:\[ΔH_\text{f}([\text{Cl}^-](aq)) = 167.2 \text{ kJ/mol}\]The negative sign indicates that the actual enthalpy of formation is -167.2 kJ/mol.

Key Concepts

Hess's Law

Hess's Law is a principle in chemistry that shows us how we can determine the overall enthalpy change for a reaction. This law is based on the idea that energy is a state function. This means that the total enthalpy change is determined solely by the initial and final states of the system and is not influenced by the pathway of the reaction. With this in mind, we can take advantage of Hess's Law to compute enthalpy changes for complex chemical reactions using simpler reactions with known enthalpy changes.

In our problem, we want to find the enthalpy of formation of the chloride ion, \( \Delta H_f^{\circ}(\text{Cl}^-)\), from given reactions. By applying Hess's Law:

• We use the provided enthalpy values from the overall formation steps.
• The formation of HCl from hydrogen and chlorine is known and has a specific enthalpy change.
• The hydration reaction of HCl to H⁺ and Cl⁻ is also provided.

By using Hess's Law, we can solve for the unknown \( \Delta H_f^{\circ}(\text{Cl}^-)\), giving us insight into how energy changes during this ion formation.

Enthalpy Change

The term 'enthalpy change' refers to the heat absorbed or released during a chemical reaction at constant pressure. Enthalpy change is represented by the symbol \( \Delta H \). It's a crucial aspect to understand as it tells us whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat).

For standard enthalpy changes, such as the formation or reaction of substances, the conditions are usually set at 1 bar of pressure and a specified temperature (often 298 K). The symbol \( \Delta H^{\circ} \) is often used to denote these standard conditions.

In our exercise, two key enthalpy changes are provided:

• The formation of hydrogen chloride gas (HCl) from its elemental gases, which is exothermic (92.4 kJ).
• The hydration of HCl in water, turning it into ions, with an enthalpy change of 92.4 kJ.

By calculating the total enthalpy change of the reaction pathways, we can apply these values and derive the unknown enthalpy value through equations' balance.

Hydration Enthalpy

Hydration enthalpy is a type of enthalpy change related to the solvation of ions. Specifically, it's the enthalpy change when one mole of gaseous ions becomes hydrated or dissolved in water. This process plays a significant role in the dissolution of many salts and ionic compounds. It provides insight into the interactions between ions and water molecules.

In our specific chemical context, the hydration of HCl gas into its ionic form (H⁺ and Cl⁻ in water) involves breaking some bonds and forming new interactions between water molecules and ions. The given hydration enthalpy, \( \Delta H_{\text{Hyd}} = -74.8 \text{ kJ/mol} \), indicates that energy is released during this process.

Understanding hydration enthalpy helps to predict how energetically favorable a solvation process is. The data from our exercise reflects an exothermic process, further affecting our calculation of the overall enthalpy change needed to derive the enthalpy of formation for \( \text{Cl}^- \) ion.

By integrating these enthalpy values, students can establish a deeper understanding of energetic changes that occur when substances dissolve, and why ions, like chloride in this case, have negative enthalpy values indicating stability and spontaneity of the hydration process.