Question

Question 1 Given the data below (taken from standard data tables), calculate the crystal lattice energy for sodium oxide: (You will be posting your Born-Haber cycle to the drop box within 20 minutes of submitting your assignment.) NOTE: Enter your answer in standard notation. If your calculated answer has a terminal zero (e.g. you get a value like -12 340) pretend that the zero is significant and just enter it as-is. (if you don't get a terminal zero in your answer, it isn't a problem for you and your sig figs will work out OK in standard notation) AH" (Na2017) - -424.6 kJ/mol E.A.1(0) - -133 kJ/mol E.A.2(0) - 247 kJ/mol B.D.E. (O2) = 495 kJ/mol I.E.1 (Na) = 495.5 kJ/mol I.E.2(Na) = 4562 kJ/mol 1.E.3(Na) = 6912 kJ/mol AHsubº (Na) = 105 kJ/mol

Answer 1

To calculate the crystal lattice energy for sodium oxide (Na2O), we can use the Born-Haber cycle, which relates various enthalpies of formation and dissociation to determine the lattice energy.

The Born-Haber cycle for sodium oxide (Na2O) can be represented as follows:

Na(s) + 1/2O2(g) → Na2O(s)

The cycle involves the following steps:

1. Formation of sodium oxide:
Na(s) + 1/2O2(g) → Na2O(s) ΔHfº

2. Dissociation of sodium metal:
Na(s) → Na(g) ΔHsubº

3. Ionization of sodium atoms:
Na(g) → Na+(g) + e- I.E.1

4. Second ionization of sodium:
Na+(g) → Na2+(g) + e- I.E.2

5. Third ionization of sodium:
Na2+(g) → Na3+(g) + e- I.E.3

6. Electron affinity of oxygen (first and second):
1/2O2(g) + e- → O-(g) E.A.1
O-(g) + e- → O2-(g) E.A.2

7. Formation of oxygen gas:
1/2O2(g) → O2(g) ΔHfº

Given enthalpy values (in kJ/mol):
ΔHfº (Na2O) = -424.6 kJ/mol
ΔHsubº (Na) = 105 kJ/mol
I.E.1 (Na) = 495.5 kJ/mol
I.E.2 (Na) = 4562 kJ/mol
I.E.3 (Na) = 6912 kJ/mol
E.A.1 (O) = -133 kJ/mol
E.A.2 (O) = -247 kJ/mol
ΔHfº (O2) = 495 kJ/mol

Step-by-step solution:

1. Calculate the lattice energy using the Born-Haber cycle:
Lattice energy = ΔHfº (Na2O) - ΔHsubº (Na) - I.E.1 (Na) - I.E.2 (Na) - I.E.3 (Na) - E.A.1 (O) - E.A.2 (O) - ΔHfº (O2)

Lattice energy = -424.6 kJ/mol - 105 kJ/mol - 495.5 kJ/mol - 4562 kJ/mol - 6912 kJ/mol - (-133 kJ/mol) - (-247 kJ/mol) - 495 kJ/mol

Now, perform the calculations to determine the crystal lattice energy for sodium oxide.