To calculate the standard enthalpy of formation (ΔH_f^(@)) for the chloride ion (Cl^-), we can use the provided reactions and their enthalpy changes.
### Step-by-Step Solution:
1. **Identify the Reactions and Their Enthalpy Changes**:
- Reaction 1:
\[
\frac{1}{2} H_2(g) + \frac{1}{2} Cl_2(g) \rightarrow HCl(g), \quad \Delta H = -92.4 \, \text{kJ}
\]
- Reaction 2:
\[
HCl(g) + n H_2O \rightarrow H^+(aq) + Cl^-(aq), \quad \Delta H = -74.8 \, \text{kJ}
\]
- Given:
\[
\Delta H_f^(@) H^+(aq) = 0.0 \, \text{kJ}
\]
2. **Set Up the Equation for Reaction 1**:
- The enthalpy change for Reaction 1 can be expressed as:
\[
\Delta H_{reaction 1} = \Delta H_f^(@) HCl - \Delta H_f^(@) \left(\frac{1}{2} H_2\right) - \Delta H_f^(@) \left(\frac{1}{2} Cl_2\right)
\]
- Since both \(H_2\) and \(Cl_2\) are in their most stable forms, their standard enthalpy of formation is 0:
\[
\Delta H_{reaction 1} = \Delta H_f^(@) HCl - 0 - 0 = \Delta H_f^(@) HCl
\]
- Therefore, we have:
\[
\Delta H_f^(@) HCl = -92.4 \, \text{kJ}
\]
3. **Set Up the Equation for Reaction 2**:
- The enthalpy change for Reaction 2 can be expressed as:
\[
\Delta H_{reaction 2} = \Delta H_f^(@) H^+ + \Delta H_f^(@) Cl^- - \Delta H_f^(@) HCl - n \Delta H_f^(@) H_2O
\]
- Given that \(\Delta H_f^(@) H^+ = 0.0 \, \text{kJ}\) and assuming that the enthalpy of water is negligible for this calculation (since it is in large excess), we can simplify this to:
\[
\Delta H_{reaction 2} = 0 + \Delta H_f^(@) Cl^- - \Delta H_f^(@) HCl
\]
- Therefore, we have:
\[
\Delta H_{reaction 2} = \Delta H_f^(@) Cl^- - (-92.4 \, \text{kJ})
\]
4. **Substituting the Known Values**:
- We know that \(\Delta H_{reaction 2} = -74.8 \, \text{kJ}\), so we can substitute this into the equation:
\[
-74.8 \, \text{kJ} = \Delta H_f^(@) Cl^- + 92.4 \, \text{kJ}
\]
5. **Solving for \(\Delta H_f^(@) Cl^-\)**:
- Rearranging the equation gives:
\[
\Delta H_f^(@) Cl^- = -74.8 \, \text{kJ} - 92.4 \, \text{kJ}
\]
- Calculating this gives:
\[
\Delta H_f^(@) Cl^- = -167.2 \, \text{kJ}
\]
### Final Answer:
\[
\Delta H_f^(@) Cl^- = -167.2 \, \text{kJ}
\]