What is the lattice energy of NaH? Use the given information below:

Heat of formation for NaH = -56.442 kJ/mol
Head of sublimation for Na = 107.3 kJ/mol
Ionization energy for Na = 496.00 kJ/mol
Bond dissociation energy for H2 = 435.9kJ/mol
Electron affinity of H = -72.8

To calculate the lattice energy (LE) of NaH, we need to use Hess's law, which states that the total energy change in a chemical reaction is independent of the pathway between the initial and final states.

The lattice energy can be calculated using the Born-Haber cycle, which is an energy cycle that considers the enthalpy changes involved in forming an ionic compound from its constituent elements.

The Born-Haber cycle for the formation of NaH can be divided into several steps:

Step 1: Formation of Na(g) from Na(s)
This involves the sublimation of sodium (Na). The enthalpy change for this step is given as the heat of sublimation for Na, which is 107.3 kJ/mol.

Step 2: Ionization of Na(g)
In this step, sodium atoms lose an electron to form Na+ ions. The enthalpy change for this step is given as the ionization energy for Na, which is 496.00 kJ/mol.

Step 3: Formation of H(g) from H2(g)
Here, hydrogen (H2) molecules dissociate into individual hydrogen atoms. The bond dissociation energy for H2, which is 435.9 kJ/mol, represents the energy required to break the H-H bond.

Step 4: Electron affinity of H(g)
In this step, a hydrogen atom gains an electron to form an H- ion. The electron affinity of H, which is -72.8 kJ/mol, represents the energy change when a gas phase atom gains an electron.

Step 5: Formation of NaH(s)
This is the final step where Na+ and H- ions combine to form solid NaH. The enthalpy change for this step is the lattice energy (LE) of NaH.

Using Hess's law and the conservation of energy, the lattice energy can be calculated using the following equation:

LE = Heat of formation of NaH - [Heat of sublimation of Na + Ionization energy of Na + Bond dissociation energy of H2 - Electron affinity of H]

Substituting the given information into the equation:

LE = -56.442 kJ/mol - [107.3 kJ/mol + 496.00 kJ/mol + 435.9 kJ/mol - (-72.8 kJ/mol)]

Simplifying the equation:

LE = -56.442 kJ/mol - (107.3 kJ/mol + 496.00 kJ/mol + 435.9 kJ/mol + 72.8 kJ/mol)

LE = -56.442 kJ/mol - 1111.1 kJ/mol

LE ≈ -1167.542 kJ/mol

Therefore, the lattice energy of NaH is approximately -1167.542 kJ/mol.

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