A metal forms an oxide with the general formula MO2 with a deltaHf=-580.7 kJ/mol. Using the Born-Harber Cycle and the following information, determine lattice energy for the compound.
Metal Information: deltaHsubl=302 kJ/mol, IE1=708.6 kJ/mol, IE2=1412 kJ/mol, IE3=2943 kJ/mol, IE4=3930. kJ/mol
Oxygen's information: EA1=-142 kJ/mol, EA2=844 kJ/mol, BE=498 kJ/mol
https://en.wikipedia.org/wiki/Born%E2%80%93Haber_cycle
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To determine the lattice energy for the compound using the Born-Haber Cycle, we need to consider the enthalpy changes in various steps involved in forming the compound from its constituent elements.
The Born-Haber Cycle consists of the following steps:
1. Formation of gaseous metal atoms: DeltaHsubl (enthalpy of sublimation)
2. Ionization of metal atoms: IE1 (first ionization energy), IE2 (second ionization energy), IE3 (third ionization energy), etc., if applicable.
3. Electron affinity of oxygen: EA1 (first electron affinity), EA2 (second electron affinity), etc., if applicable.
4. Bond dissociation energy of oxygen: BE (bond energy).
The lattice energy (LE) is the energy released when gaseous ions combine to form the ionic solid. It can be determined using the following equation:
LE = DeltaHformation - DeltaHsubl - IE(M) - Sum of EA(O) - BE(O)
where DeltaHformation is the enthalpy change for the formation of the compound.
In this case, the oxide has the general formula MO2 with a deltaHf (enthalpy change of formation) of -580.7 kJ/mol.
So, we can proceed step by step to calculate the lattice energy:
1. Formation of gaseous metal atoms:
DeltaHsubl = 302 kJ/mol (given)
2. Ionization of metal atoms:
The metal has ionization energies: IE1 = 708.6 kJ/mol, IE2 = 1412 kJ/mol, IE3 = 2943 kJ/mol, IE4 = 3930 kJ/mol (given)
The ionization energy required depends on the number of electrons that need to be removed from the metal atom to form the cation.
In this case, we need to determine the number of electrons removed, which corresponds to the charge on the metal cation in the oxide. Since the oxide has a general formula MO2, the metal ion has a charge of +4 (2 oxygen atoms each with a charge of -2).
To achieve a +4 charge, we need to remove 4 electrons:
Ionization energy required = IE1 + IE2 + IE3 + IE4
3. Electron affinity of oxygen:
Oxygen has electron affinities: EA1 = -142 kJ/mol, EA2 = 844 kJ/mol (given)
The compound MO2 consists of 2 oxygen atoms, so we need to consider the electron affinities for 2 oxygen atoms:
Total electron affinity = 2 * (EA1 + EA2)
4. Bond dissociation energy of oxygen:
BE = 498 kJ/mol (given)
Now, let's substitute the values into the equation for lattice energy:
LE = -580.7 kJ/mol - 302 kJ/mol - (IE1 + IE2 + IE3 + IE4) - 2 * (EA1 + EA2) - BE
By plugging in the given values, you can calculate the lattice energy for the compound MO2.