The Born-Haber cycle for KCl is evaluated with the following data:
\(\Delta_f H^\ominus\) for KCl = -436.7 kJ \(mol^{-1}\); \(\Delta_{sub} H^\ominus\) for K = 89.2 kJ \(mol^{-1}\);
\(\Delta_{ionization} H^\ominus\) for K = 419.0 kJ \(mol^{-1}\); \(\Delta_{electron gain} H^\ominus\) for \(Cl_{(g)\) = -348.6 kJ \(mol^{-1}\);
\(\Delta_{bond} H^\ominus\) for \(Cl_2\) = 243.0 kJ \(mol^{-1}\).
The magnitude of lattice enthalpy of KCl in kJ \(mol^{-1}\) is _________. (Nearest integer)}
\(\Delta_f H^\ominus\) for KCl = -436.7 kJ \(mol^{-1}\); \(\Delta_{sub} H^\ominus\) for K = 89.2 kJ \(mol^{-1}\);
\(\Delta_{ionization} H^\ominus\) for K = 419.0 kJ \(mol^{-1}\); \(\Delta_{electron gain} H^\ominus\) for \(Cl_{(g)\) = -348.6 kJ \(mol^{-1}\);
\(\Delta_{bond} H^\ominus\) for \(Cl_2\) = 243.0 kJ \(mol^{-1}\).
The magnitude of lattice enthalpy of KCl in kJ \(mol^{-1}\) is _________. (Nearest integer)}
Show Hint
Correct Answer: 718
Solution and Explanation
Step 1: Understanding the Concept:
The Born-Haber cycle uses Hess's Law to relate various thermodynamic quantities involved in the formation of an ionic solid from its elements. The total enthalpy of formation is equal to the sum of the energies for individual steps.
Step 2: Key Formula or Approach:
\[ \Delta_f H^\ominus = \Delta_{sub} H^\ominus + \Delta_{IE} H^\ominus + \frac{1}{2} \Delta_{bond} H^\ominus + \Delta_{eg} H^\ominus + \Delta_{lattice} H^\ominus \]
Step 3: Detailed Explanation:
Substitute the given values into the formula:
- \(\Delta_f H^\ominus = -436.7\)
- \(\Delta_{sub} H^\ominus = 89.2\)
- \(\Delta_{ionization} H^\ominus = 419.0\)
- \(\Delta_{bond} H^\ominus / 2 = 243.0 / 2 = 121.5\)
- \(\Delta_{electron gain} H^\ominus = -348.6\)
\[ -436.7 = 89.2 + 419.0 + 121.5 + (-348.6) + \Delta_{lattice} H^\ominus \]
\[ -436.7 = 281.1 + \Delta_{lattice} H^\ominus \]
\[ \Delta_{lattice} H^\ominus = -436.7 - 281.1 = -717.8 \text{ kJ/mol} \]
The magnitude is \( |-717.8| = 717.8 \).
Rounding to the nearest integer, we get 718.
Step 4: Final Answer:
The magnitude of the lattice enthalpy is 718.
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