calculate the lattice energy of sodium oxide (Na2O) from the following data:

Ionization energy of Na(g): 495 kJ/mol

Electron affinity of O2 for 2e: 603 kJ/mol

Energy to vaporize Na(s): 109 kJ/mol

O2(g) bond energy: 499 kJ/mol

Energy change for the reaction 2Na(s)+ 1/2 O2(g)--> Na2O(s): -416 kJ/mol

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2Na(s) ==> 2Na(g) dHsub = 109*2 = ?

2Na(g) ==> 2Na^ + 2e IP = 495*2 = ?
O2(g) ==> 2O(g) B.E. = 499*1/2 = ?
O + 2e ==> O^2- EA = -603 = ?
2Na^+(g) + O^2-(g) ==> Na2O(s) Ecrystal
------------------------------------
2Na(s) + 1/2O2(g) ==> Na2O(s) = -416
Hf = 416
-416=dHsub + IP + BE + EA(-) + Ecrystal
Solve for Ecrystal.

To calculate the lattice energy of sodium oxide (Na2O), we can use the Born-Haber cycle. The lattice energy is the energy released when one mole of an ionic compound is formed from its constituent ions in the gas phase.

The Born-Haber cycle involves a series of steps that represent the formation of the ionic compound. Let's go through each step:

Step 1: Vaporization of sodium (Na)
This step involves vaporizing one mole of sodium (Na) in its solid state. The energy required to vaporize Na(s) is given as 109 kJ/mol.

Step 2: Ionization of sodium (Na)
In this step, one mole of sodium atoms is ionized by losing an electron to form Na+ ions. The ionization energy of Na(g) is given as 495 kJ/mol.

Step 3: Dissociation of oxygen (O2)
In this step, the O2(g) molecule is broken into two oxygen atoms. The bond energy of O2(g) is given as 499 kJ/mol.

Step 4: Electron affinity of oxygen (O)
Here, two moles of electrons are added to the oxygen atoms to form O2- ions. The electron affinity of O2 for 2e is given as 603 kJ/mol.

Step 5: Formation of sodium oxide (Na2O)
In this final step, one mole of sodium oxide (Na2O) is formed from Na+ and O2- ions. The energy change for the reaction 2Na(s) + 1/2O2(g) → Na2O(s) is given as -416 kJ/mol.

Using the Born-Haber cycle, the lattice energy of Na2O can be calculated as the sum of the energy changes for all the steps:

Lattice energy = (Step 1) + (Step 2) + (Step 3) + (Step 4) + (Step 5)

Lattice energy = 109 kJ/mol + 495 kJ/mol + 499 kJ/mol + 603 kJ/mol + (-416 kJ/mol)

Lattice energy = 1,290 kJ/mol

Therefore, the lattice energy of sodium oxide (Na2O) is 1,290 kJ/mol.

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