Question

Consider an ionic compound, MX2 , composed of generic metal M and generic, gaseous halogen X .

Answer 1

Answer:

$\boxed{\text{-2791 kJ/mol}}$

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 $\boxed{\textbf{-2791 kJ/mol}}$.