Consider an ionic compound, MX2, composed of generic metal M and generic, gaseous halogen X.
The enthalpy of formation of MX2 is ΔHf° = –799 kJ/mol.
The enthalpy of sublimation of M is ΔHsub = 157 kJ/mol.
The first and second ionization energies of M are IE1 = 785 kJ/mol and IE2 = 1451 kJ/mol. The electron affinity of X is ΔHEA = –349 kJ/mol.
The bond energy of X2 is BE = 157 kJ/mol.
What's the Question? If it's Crystal Lattace Energy, you need to review Born-Haber Cycle.
It is to Determine the lattice energy of MX2.
To determine the stability of the ionic compound MX2, we can use the Born-Haber cycle, which involves the enthalpy changes associated with various steps involved in the formation of the compound from its elemental components.
The Born-Haber cycle consists of the following steps:
1. Formation of gaseous metal cations:
M(s) → M(g) ΔHsub
This step represents the enthalpy change required to convert the solid metal M into gaseous metal cations. In this case, the enthalpy of sublimation (ΔHsub) is given as 157 kJ/mol.
2. Ionization of metal cations:
M(g) → M+(g) + e- IE1
This step represents the first ionization energy (IE1) required to remove an electron from a metal cation in the gas phase. The first ionization energy (IE1) is given as 785 kJ/mol.
3. Ionization of metal cations:
M+(g) → M2+ (g) + e- IE2
This step represents the second ionization energy (IE2) required to remove a second electron from a metal cation in the gas phase. The second ionization energy (IE2) is given as 1451 kJ/mol.
4. Formation of gaseous halide anions:
X2(g) → 2X-(g) ΔHEA
This step represents the enthalpy change accompanying the addition of electrons to form gaseous halide anions. The electron affinity (ΔHEA) of the halogen X is given as -349 kJ/mol.
5. Formation of MX2:
M2+(g) + 2X-(g) → MX2(s) ΔHf°
This step represents the enthalpy change associated with the formation of the ionic compound MX2. The enthalpy of formation (ΔHf°) is given as -799 kJ/mol.
The sum of the enthalpy changes in the cycle should be zero. Therefore, we can set up the equation:
ΔHsub + IE1 + IE2 + ΔHEA - ΔHf° = 0
Substituting the given values:
157 + 785 + 1451 - 349 - 799 = 245 kJ/mol
Since the sum is not equal to zero, the compound MX2 is not stable.
To determine the lattice energy (ΔHlattice) of the ionic compound MX2, we can use the following equation:
ΔHlattice = ΔHf° + ΔHsub - (IE1 + IE2) - ΔHEA - BE/2
Let's substitute the given values into the equation:
ΔHlattice = -799 kJ/mol + 157 kJ/mol - (785 kJ/mol + 1451 kJ/mol) - (-349 kJ/mol) - 157 kJ/mol/2
Now, let's simplify the equation:
ΔHlattice = -799 kJ/mol + 157 kJ/mol - 1236 kJ/mol - (-349 kJ/mol) - 78.5 kJ/mol
ΔHlattice = -799 kJ/mol + 157 kJ/mol + 349 kJ/mol - 78.5 kJ/mol - 1236 kJ/mol
ΔHlattice = -1607.5 kJ/mol
Therefore, the lattice energy of the ionic compound MX2 is -1607.5 kJ/mol.