Use a Born Haber cycle to calculate the lattice energy (in kJ/mol) of Potassium Chloride (KCl) from the following data:
Ionization Energy of K(g) = 431kJ/mol
Electron affinity of Cl(g) = -346kJ/mol
Energy to sublime K(s) = 85kJ/mol
Bond energy of Cl2(g) = 236kJ/mol
Enthalpy for the reaction K(s) + 1/2Cl2(g) --> KCl(s) = -434kJ/mol
To calculate the lattice energy of Potassium Chloride (KCl) using a Born Haber cycle, we need to follow these steps:
1. Draw the Born Haber cycle: Start by drawing a diagram that represents the cycle. The cycle consists of a series of steps that involve the formation of KCl from its constituent elements.
2. Identify the given data: From the given data, we have:
Ionization Energy of K(g) = 431 kJ/mol
Electron affinity of Cl(g) = -346 kJ/mol
Energy to sublime K(s) = 85 kJ/mol
Bond energy of Cl2(g) = 236 kJ/mol
Enthalpy for the reaction K(s) + 1/2Cl2(g) → KCl(s) = -434 kJ/mol
3. Analyze the cycle: Break down the cycle into individual steps, and assign the corresponding energies to each step. The steps involved in the Born Haber cycle for KCl are as follows:
a) Formation of K(g) from K(s): This step involves the sublimation of solid potassium, and the energy required for this is given as 85 kJ/mol.
b) Formation of Cl(g) from Cl2(g): This step involves the bond dissociation of chlorine gas, and the energy required for this is the bond energy of Cl2, which is 236 kJ/mol.
c) Ionization of K(g): This step involves removing an electron from K(g), and the energy required for this is the ionization energy of potassium, which is 431 kJ/mol.
d) Electron affinity of Cl(g): This step involves adding an electron to Cl(g), and the energy change for this is the electron affinity of chlorine, which is -346 kJ/mol.
e) Formation of KCl(s) from K(g) and Cl(g): This step involves the formation of the ionic compound KCl from the gaseous ions. The change in enthalpy for this step is -434 kJ/mol.
4. Calculate the lattice energy: The lattice energy represents the energy released when gaseous ions come together to form an ionic solid.
Lattice energy = (Sum of ionization energy and electron affinity) - (Sum of energy to sublime and bond energy) + Enthalpy of formation
Lattice energy = (431 + (-346)) - (85 + 236) + (-434)
Lattice energy = 85 - 321 - 434
Lattice energy = -670 kJ/mol
Therefore, the lattice energy of potassium chloride (KCl) is -670 kJ/mol.