With a halogen X, a metal M forms ionic compounds MX, MX2 and MX3. The lattice energies of the compounds are -1340, -3840 and -7020 kJ/mol, respectively.
The ionization energies of the metal are 360 (for M+), 1236 (M2+) and 2990 (M3+) kJ/mol and the sublimation energy is 334 kJ/mol. Will MX and/or MX2 disproportionate?
I have no idea where to start, so any advice is highly appreciated.
To determine whether MX and/or MX2 will disproportionate, we need to compare the stability of the compounds based on their lattice energies and ionization energies.
1. Determine the formula of MX compounds:
- MX: Since the metal forms ionic compounds with the halogen X in a 1:1 ratio, the formula of the compound is MX.
- MX2: Similarly, the metal forms ionic compounds with the halogen X in a 1:2 ratio, so the formula of the compound is MX2.
2. Calculate the energy change for the disproportionation of MX:
The energy change for the disproportionation of MX can be calculated by comparing the lattice energies and ionization energies and considering the sublimation energy.
a) Calculate the energy required to form 1 mole of M+ ions:
The ionization energy for M+ is given as 360 kJ/mol.
b) Calculate the energy required to form 1 mole of M2+ ions:
The ionization energy for M2+ is given as 1236 kJ/mol.
c) Calculate the energy required to form 1 mole of M3+ ions:
The ionization energy for M3+ is given as 2990 kJ/mol.
d) Calculate the energy required to form MX crystal:
The lattice energy for MX compound is given as -1340 kJ/mol.
e) Calculate the energy required to form MX2 crystal:
The lattice energy for MX2 compound is given as -3840 kJ/mol.
f) Calculate the energy released during sublimation of M:
The sublimation energy for M is given as 334 kJ/mol.
g) Calculate the energy change for the disproportionation:
Energy change = [2*(energy required for M+)] - [(energy required for MX)] + [(energy required for MX2)] - [(energy released during M sublimation)]
3. Analyze the energy change:
- If the energy change is negative (less than zero), then MX will disproportionation.
- If the energy change is positive (greater than zero), then MX will not disproportionation.
By following these steps, you can calculate the energy change for the disproportionation of MX and MX2 and determine whether they will disproportionate.