Which of the following properties can be determined by using Born-Haber cycle ?

Options

A. Electronegativity
B. Hydration energy
C. Lattice energy of ionic crystals
D. Binding energy of electrons

Answer

To determine which properties can be calculated using the Born-Haber cycle, we need to understand the components involved in the cycle and what it represents. The Born-Haber cycle is a thermodynamic cycle that relates the lattice energy of an ionic compound to other thermodynamic quantities.

### Step-by-Step Solution:

1. **Understanding the Born-Haber Cycle**:
- The Born-Haber cycle is used to analyze the formation of ionic compounds from their constituent elements. It involves various steps, including sublimation, ionization, dissociation, electron gain, and lattice formation.

2. **Identify the Processes Involved**:
- The cycle includes:
- **Enthalpy of Sublimation**: Energy required to convert solid sodium to gaseous sodium.
- **Ionization Energy**: Energy required to remove an electron from gaseous sodium to form Na⁺.
- **Bond Dissociation Energy**: Energy required to break Cl₂ into two Cl atoms (halved for one mole).
- **Electron Gain Enthalpy**: Energy released when a Cl atom gains an electron to form Cl⁻.
- **Lattice Energy**: Energy released when gaseous ions combine to form the solid ionic compound (NaCl).

3. **Write the Relationship**:
- The enthalpy of formation (ΔH_f) for NaCl can be expressed as:
\[ \Delta H_f = \Delta H_{\text{sublimation}} + \Delta H_{\text{ionization}} + \frac{1}{2} \Delta H_{\text{dissociation}} + \Delta H_{\text{electron gain}} + \Delta H_{\text{lattice}} \]

4. **Determine Which Properties Can Be Calculated**:
- From the above relationship, we can derive:
- **Lattice Energy**: This is the main focus of the Born-Haber cycle.
- **Enthalpy of Formation**: Can also be calculated.
- **Ionization Energy**: Can be derived from the cycle.
- **Dissociation Energy**: Can be calculated as well.
- **Electron Gain Enthalpy**: Can also be determined.

5. **Conclusion**:
- Among the options given:
- **Option A (Electron Activity)**: Not directly determined by the Born-Haber cycle.
- **Option B (Hydration Energy)**: Not determined by the Born-Haber cycle.
- **Option C (Lattice Energy of Ionic Crystal)**: Yes, this can be determined.
- **Option D (Binding Energy of Electrons)**: Not directly determined.

Thus, the correct answer is **Option C: Lattice Energy of Ionic Crystal**.