The enthalpy of formation of MX is ΔHf° = –493 kJ/mol. The enthalpy of sublimation of M is ΔHsub = 143 kJ/mol. The ionization energy of M is IE = 437 kJ/mol. The electron affinity of X is ΔHEA = –317 kJ/mol. (Refer to the hint). The bond energy of X2 is BE = 193 kJ/mol.
Determine the lattice energy of MX??
Hformation = sub + IE + EA + 1/2*BE + Ecryst
Solve for Ecrystal, then lattice energy is - of Ecrystal.
To determine the lattice energy of MX, we need to use the Born-Haber cycle. The Born-Haber cycle is a series of steps that allow us to calculate the lattice energy of an ionic compound using various thermodynamic data.
Here are the steps to calculate the lattice energy:
Step 1: Write the balanced chemical equation for the formation of MX from its constituent elements.
M(s) + X2(g) → MX(s)
Step 2: Calculate the enthalpy change for each step of the Born-Haber cycle.
a. ΔHf° (enthalpy of formation of MX) = –493 kJ/mol
This is given in the problem statement.
b. ΔHsub (enthalpy of sublimation of M) = 143 kJ/mol
This is given in the problem statement.
c. IE (ionization energy of M) = 437 kJ/mol
This is given in the problem statement.
d. ΔHEA (electron affinity of X) = –317 kJ/mol
This is given in the problem statement.
e. BE (bond energy of X2) = 193 kJ/mol
This is given in the problem statement.
Step 3: Use the given thermodynamic data to calculate the lattice energy.
The lattice energy (ΔHlattice) is the difference between the energy required to break the ionic compound into its gaseous ions (IE + ΔHEA) and the energy released when the ions combine to form the solid ionic compound (ΔHf°).
ΔHlattice = (IE + ΔHEA) – ΔHf°
Substituting the given values:
ΔHlattice = (437 kJ/mol + (-317 kJ/mol)) – (-493 kJ/mol)
= 437 kJ/mol + 317 kJ/mol + 493 kJ/mol
= 1247 kJ/mol
Therefore, the lattice energy of MX is 1247 kJ/mol.