Concept:The Born-Haber cycle uses Hess's law to map out the entire energy profile of an ionic solid. We must sum all steps to equal the total heat of formation.
Formula:$$ \Delta H_f = \Delta H_{\text{sub}} + IE + \frac{1}{2}\Delta H_{\text{diss}} + EA + LE $$
Solution:- Because KBr contains only one Br atom, we only need half a mole of \( Br_2 \) gas. Thus, dissociation energy = \( 192.5 / 2 = 96.25 \text{ kJ/mol} \).
- Set up the equation:
\( -405.8 = 98 \text{ (sub)} + 414 \text{ (IE)} + 96.25 \text{ (diss)} + (-334.7) \text{ (EA)} + LE \)
- Sum the indirect step energies: \( 98 + 414 + 96.25 - 334.7 = 273.55 \text{ kJ/mol} \).
- Solve for Lattice Energy (LE):
\( LE = -405.8 - 273.55 = -679.35 \text{ kJ/mol} \).
- The closest matched option is exactly \( -679.3 \).
Why other options are incorrect:Option A (-669.5) results from mathematical errors. Positive values (B and D) imply the formation of the lattice absorbs energy, which violates the fundamental stability laws of ionic compounds.
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