1. Dipole Moment

$\mu = q \times d$

Units: Debye (D); 1 D = $3.336 \times 10^{-30}$ C·m. For a diatomic A–B: if μ = 0 → non-polar; if μ ≠ 0 → polar.

2. Born-Haber Cycle (Hess's Law)

$\Delta H_f = \Delta H_{sub} + \frac{1}{2}\Delta H_{diss} + IE + EA + U$

Rearranged for lattice energy:

$U = \Delta H_f - \Delta H_{sub} - \frac{1}{2}\Delta H_{diss} - IE - EA$

NaCl numerical values: U = −411 − 108 − 121 − 496 − (−349) = −787 kJ/mol

3. Bond Order (MOT)

$BO = \frac{N_b - N_a}{2}$

4. Steric Number → Hybridization

$SN = \sigma\text{-bonds} + \text{lone pairs on central atom}$

SN 2 → sp | SN 3 → $sp^{2}$ | SN 4 → $sp^{3}$ | SN 5 → $sp^{3}$d | SN 6 → sp^{3}$$d^{2}

5. Bond Properties Relationship

$BO \uparrow \Rightarrow \text{bond length} \downarrow \Rightarrow \text{bond energy} \uparrow$

Key numerical data:

• Bond angles: $H_{2}O$ = 104.5°, $NH_{3}$ = 107°, $CH_{4}$ = 109.5°, $BF_{3}$ = 120°, $CO_{2}$ = 180°
• Benzene C–C bond length = 1.40 Å (intermediate between 1.34 Å double and 1.54 Å single)