use the data given below to construct a Born-Haber cycle to determine the lattice energy of CaO

Ca(s)--->Ca(g) 193
Ca(g)--->Ca+(g) + e- 590
Ca+(g)--->Ca2+(g) +e- 1010
2O(g)---->02(g) -498
O(g) +e--->0-(g) -141
O-(g) + e---->O2-(g) 878
Ca(s) +1/2 O2(g)---> CaO (s) -635

http://chemistry.bd.psu.edu/jircitano/BH.html

To construct a Born-Haber cycle to determine the lattice energy of CaO, we need to consider the individual steps involved in the formation of CaO. Here's how we can build the Born-Haber cycle using the given data:

Step 1: Formation of Ca(g)
- This step represents the conversion of solid Ca(s) into gaseous Ca(g).
- Enthalpy change: ΔH = 193 kJ/mol (given)

Step 2: Ionization of Ca(g)
- Now, we need to ionize Ca(g) to form Ca+(g).
- Enthalpy change: ΔH = 590 kJ/mol (given)

Step 3: Second ionization of Ca+(g)
- Ca+(g) needs to lose one more electron to form Ca2+(g).
- Enthalpy change: ΔH = 1010 kJ/mol (given)

Step 4: Dissociation of O2(g)
- Oxygen gas (O2(g)) dissociates into individual oxygen atoms (O(g)).
- Enthalpy change: ΔH = -498 kJ/mol (given, negative because it is an exothermic process)

Step 5: Electron affinity of O(g)
- Oxygen atoms (O(g)) gain an electron to form negative ions (O-(g)).
- Enthalpy change: ΔH = -141 kJ/mol (given, negative because it is an exothermic process)

Step 6: Electron affinity of O-(g)
- O-(g) further gains an electron to form O2-(g).
- Enthalpy change: ΔH = 878 kJ/mol (given)

Step 7: Formation of CaO(s)
- Finally, we combine Ca(s) with 1/2 O2(g) to form CaO(s) - the desired compound.
- Enthalpy change: ΔH = -635 kJ/mol (given, negative because it is an exothermic process)

Now, we need to construct the Born-Haber cycle by arranging these steps in a loop, ensuring that the reactants and products match up:

Start:
Ca(s) → Ca(g) ΔH = 193 kJ/mol
ΔH = 193 kJ/mol

First side:
Ca(g) → Ca+(g) + e- ΔH = 590 kJ/mol
ΔH = 193 + 590 = 783 kJ/mol

Top:
Ca+(g) → Ca2+(g) + e- ΔH = 1010 kJ/mol
ΔH = 193 + 590 + 1010 = 1793 kJ/mol

Second side:
O2(g) → 2O(g) ΔH = -498 kJ/mol
ΔH = 193 + 590 + 1010 - 498 = 1485 kJ/mol

Bottom:
O(g) + e- → O-(g) ΔH = -141 kJ/mol
ΔH = 193 + 590 + 1010 - 498 - 141 = 1344 kJ/mol

Third side:
O-(g) + e- → O2-(g) ΔH = 878 kJ/mol
ΔH = 193 + 590 + 1010 - 498 - 141 + 878 = 2222 kJ/mol

Back to start:
Ca(g) + 1/2 O2(g) → CaO(s) ΔH = -635 kJ/mol
ΔH = 193 + 590 + 1010 - 498 - 141 + 878 - 635 = 1587 kJ/mol

The lattice energy (ΔH) for CaO is 1587 kJ/mol according to the Born-Haber cycle.

To construct a Born-Haber cycle to determine the lattice energy of CaO, we need to understand the steps involved in the formation of solid CaO from its constituent elements. A Born-Haber cycle is a series of steps that considers the enthalpy changes associated with each step of the formation process.

Here are the steps involved:

Step 1: Sublimation of solid calcium (Ca(s)) to form gaseous calcium (Ca(g)).
Given: ΔH = 193 kJ/mol (energy required to convert 1 mole of solid calcium to gaseous calcium)

Step 2: Ionization of gaseous calcium atoms (Ca(g)) to form gaseous calcium ions (Ca+(g)).
Given: ΔH = 590 kJ/mol (energy required to remove 1 electron from 1 mole of gaseous calcium atoms)

Step 3: Second ionization of gaseous calcium ions (Ca+(g)) to form doubly charged calcium ions (Ca2+(g)).
Given: ΔH = 1010 kJ/mol (energy required to remove a second electron from 1 mole of gaseous calcium ions)

Step 4: Formation of gaseous oxygen molecules (O2(g)) from gaseous oxygen atoms (O(g)).
Given: ΔH = -498 kJ/mol (energy released when 1 mole of gaseous oxygen atoms combine to form O2 molecules)

Step 5: Electron affinity of gaseous oxygen atoms (O(g)) to form gaseous oxide ions (O-(g)).
Given: ΔH = -141 kJ/mol (energy released when 1 mole of gaseous oxygen atoms gain an electron to form oxide ions)

Step 6: Electron affinity of gaseous oxide ions (O-(g)) to form gaseous oxide molecules (O2-(g)).
Given: ΔH = 878 kJ/mol (energy released when a gaseous oxide ion gains another electron to form an oxide molecule)

Step 7: Formation of solid calcium oxide (CaO(s)) from gaseous calcium oxide (CaO(g)) with the release of lattice energy.
Given: ΔH = -635 kJ/mol (heat released when 1 mole of solid calcium oxide is formed)

The lattice energy (ΔH_lattice) can be determined from the Born-Haber cycle by summing up all the enthalpy changes involved:

ΔH_lattice = ΔH_1 + ΔH_2 + ΔH_3 + ΔH_4 + ΔH_5 + ΔH_6 + ΔH_7

Substituting the given values into the equation, we get:

ΔH_lattice = 193 + 590 + 1010 + (-498) + (-141) + 878 + (-635)

Calculating the above expression, the lattice energy (ΔH_lattice) of CaO is approximately -103 kJ/mol.

Therefore, the lattice energy of CaO is approximately -103 kJ/mol.

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