Consider an ionic compound, MX,, composed of generic metal M and generic gaseous halogen X. • The enthalpy of formation of MX, is AH; = -605 kJ/mol. • The enthalpy of sublimation of M is A Hsub = 129 kJ/mol. • The first, second, and third ionization energies of M are IE, = 691 kJ/mol, IE2 = 1581 kJ/mol, and IE3 = 2627 kJ/mol. • The electron affinity of X is AHEA = -361 kJ/mol. (Refer to the hint). • The bond energy of X, is BE = 163 kJ/mol. Determine the lattice energy of MX,. kJ/mol AH attice
Consider an ionic compound, MX,, composed of generic metal M and generic gaseous halogen X. • The enthalpy of formation of MX, is AH; = -605 kJ/mol. • The enthalpy of sublimation of M is A Hsub = 129 kJ/mol. • The first, second, and third ionization energies of M are IE, = 691 kJ/mol, IE2 = 1581 kJ/mol, and IE3 = 2627 kJ/mol. • The electron affinity of X is AHEA = -361 kJ/mol. (Refer to the hint). • The bond energy of X, is BE = 163 kJ/mol. Determine the lattice energy of MX,. kJ/mol AH attice
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![### Determining the Lattice Energy of MX₃
Consider an ionic compound, MX₃, composed of a generic metal M and a generic gaseous halogen X. The given thermodynamic data includes:
- **Enthalpy of formation of MX₃ (\( \Delta H_f \))**: \(-605 \, \text{kJ/mol}\).
- **Enthalpy of sublimation of M (\( \Delta H_{\text{sub}} \))**: \(129 \, \text{kJ/mol}\).
- **Ionization energies of M**:
- First ionization energy (\( \text{IE}_1 \)): \(691 \, \text{kJ/mol}\).
- Second ionization energy (\( \text{IE}_2 \)): \(1581 \, \text{kJ/mol}\).
- Third ionization energy (\( \text{IE}_3 \)): \(2627 \, \text{kJ/mol}\).
- **Electron affinity of X (\( \Delta H_{\text{EA}} \))**: \(-361 \, \text{kJ/mol}\).
- **Bond energy of X₂ (BE)**: \(163 \, \text{kJ/mol}\).
To determine the lattice energy (\( \Delta H_{\text{lattice}} \)) of MX₃, combine these values according to Hess's Law and the Born-Haber cycle.
\[ \Delta H_{\text{lattice}} = \text{[calculated value]} \, \text{kJ/mol} \]
### Calculation Steps
1. **Atomization of metal and nonmetal**: Convert solid M to gaseous M and dissociate X₂ to X:
- Sublimation of M.
- Half the bond energy for the dissociation of X₂.
2. **Ionization Energies**: Add up the energies required to remove electrons from M to form M³⁺.
3. **Electron Affinity**: Consider the energy change when X gains electrons.
4. **Combine**: Use these values to calculate the lattice energy through the energy conservation equation of the Born-Haber cycle.
\[ \Delta H_{\text{lattice}} = - \Delta H_f + \Delta H_{\text{sub}} + \text{IE}_1 + \text{IE}_2 + \text{IE}_3 + \Delta H_{\text{EA}} + \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b7ec4e2-929f-4e5a-b9e2-d730b007ea8c%2Ff8452ba1-ed9e-4674-bf34-bc11325d5d80%2F65kgxd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Lattice Energy of MX₃
Consider an ionic compound, MX₃, composed of a generic metal M and a generic gaseous halogen X. The given thermodynamic data includes:
- **Enthalpy of formation of MX₃ (\( \Delta H_f \))**: \(-605 \, \text{kJ/mol}\).
- **Enthalpy of sublimation of M (\( \Delta H_{\text{sub}} \))**: \(129 \, \text{kJ/mol}\).
- **Ionization energies of M**:
- First ionization energy (\( \text{IE}_1 \)): \(691 \, \text{kJ/mol}\).
- Second ionization energy (\( \text{IE}_2 \)): \(1581 \, \text{kJ/mol}\).
- Third ionization energy (\( \text{IE}_3 \)): \(2627 \, \text{kJ/mol}\).
- **Electron affinity of X (\( \Delta H_{\text{EA}} \))**: \(-361 \, \text{kJ/mol}\).
- **Bond energy of X₂ (BE)**: \(163 \, \text{kJ/mol}\).
To determine the lattice energy (\( \Delta H_{\text{lattice}} \)) of MX₃, combine these values according to Hess's Law and the Born-Haber cycle.
\[ \Delta H_{\text{lattice}} = \text{[calculated value]} \, \text{kJ/mol} \]
### Calculation Steps
1. **Atomization of metal and nonmetal**: Convert solid M to gaseous M and dissociate X₂ to X:
- Sublimation of M.
- Half the bond energy for the dissociation of X₂.
2. **Ionization Energies**: Add up the energies required to remove electrons from M to form M³⁺.
3. **Electron Affinity**: Consider the energy change when X gains electrons.
4. **Combine**: Use these values to calculate the lattice energy through the energy conservation equation of the Born-Haber cycle.
\[ \Delta H_{\text{lattice}} = - \Delta H_f + \Delta H_{\text{sub}} + \text{IE}_1 + \text{IE}_2 + \text{IE}_3 + \Delta H_{\text{EA}} + \
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