Question 12.4.1: Calculate a lattice energy from thermodynamic data. Calculat......
Calculate a lattice energy from thermodynamic data.
Calculate the lattice energy of KCl(s) using the following thermodynamic data (all data given is in kJ/mol). Do you expect this value to be larger or smaller than the lattice energy of NaCl(s)?
K(s) ΔH_{sublimation} = 89.6 kJ/mol Cl—Cl D_{Cl–Cl} = 242 kJ/mol
KCl(s) ΔH^{º}_{f} = -437 kJ/mol Cl(g) EA = -349 kJ/mol
K(g) IE = 419 kJ/mol
You are asked to calculate the lattice energy for a compound and to predict the relative magnitude of a similar compound’s lattice energy.
You are given the identity of the compound and thermodynamic data needed to calculate the lattice energy using a Born–Haber cycle.
The lattice energy of KCl is the enthalpy change for the reaction KCl(s) → K^{+}(g) + Cl^{-}(g). Use the data given to write five equations that will sum to give this net reaction, and then sum the respective enthalpy changes to calculate U(KCl(s)).
1. K(s) → K(g) ΔH_{sublimation} = 89.6 kJ
2. K(g) → K^{+}(g)+e^{-} ionization energy = 419 kJ
3. 1∕2 Cl_{2}(g) → Cl(g) 1∕2 bond energy = 121 kJ
4. Cl(g) + e^{-} → Cl^{-}(g) electron affinity = -349
5. KCl(s) → K(s) + 1∕2 Cl_{2}(g) -ΔH^{°}_{f} = -(-437 kJ) = 437 kJ
Sum 1–5: KCl(s) → K^{+}(g) + Cl^{-}(g) U = 89.6 + 419 + 121 – 349 + 437 = 718 kJ
The lattice energy of KCl is 718 kJ/mol.
This value is smaller than that for NaCl (786 kJ/mol), as expected because of the larger size of K^{+} compared with Na^{+}.