Answer:
[tex]\boxed{\text{-2791 kJ/mol}}[/tex]
Explanation:
One way to calculate the lattice energy is to use Hess's Law .
The lattice energy U is the energy released when the gaseous ions combine to form a solid ionic crystal:
M²⁺(g) + 2X⁻(g) ⟶ MgX₂(s); U = ?
We must generate this reaction rom the equations given.
(1) M(s) + X₂ (g) ⟶ MX₂(s); ΔHf⁰ = -985 kJ·mol⁻¹
(2) M(s) ⟶ M(g); ΔHsub = 135 kJ·mol⁻¹
(3) M(g) ⟶M⁺(g) +e⁻ IE₁ = 731 kJ·mol⁻¹
(4) M⁺(g) ⟶ M²⁺(g) + e⁻ IE₂ = 1403 kJ·mol⁻¹
(5) X(g) + e⁻ ⟶ X⁻(g) EA = -335 kJ·mol⁻¹
(6) X₂(g) ⟶ 2X(g) BE = 207 kJ·mol⁻¹
Now, we put these equations together to get the lattice energy. Underlined species have been cancelled.
E/kJ
(7) M²⁺(g) + e⁻⟶ M⁺(g) -1403
(8) M⁺(g) + e⁻ ⟶ M(g) -731
(9) M(g) ⟶ M(s) -135
(10) M(s) + X₂(g) ⟶ MX₂(s) -985
(11) 2X(g) ⟶ X₂(g) -207
(12) 2X⁻(g) ⟶ 2X(g) + 2e⁻ +670
M²⁺(g) + 2X⁻(g) ⟶ MX₂(s) -2791
The lattice energy of MX₂ is [tex]\boxed{\textbf{-2791 kJ/mol}}[/tex].
