Group 13 Core Facts:

• Outer configuration: $ns^{2}$ $np^{1}$; three valence electrons; +3 dominant oxidation state
• Boron is anomalous: only nonmetal in Group 13; electron-deficient covalent compounds
• $B_{2}H_{6}$ has 2 bridging H (3c-2e bonds) and 4 terminal H (2c-2e bonds); no B-B bond exists
• Borax = $Na_{2}B_{4}O_{7}$·$10H_{2}O$; contains 2 $BO_{3}$ (trigonal) + 2 $BO_{4}$ (tetrahedral) units
• H_{3}$$BO_{3} is a monobasic Lewis acid; accepts $OH^{-}$ from water; forms layered H-bonded solid
• $AlCl_{3}$ forms dimer $Al_{2}Cl_{6}$; Lewis acid; Friedel-Crafts catalyst
• Inert pair effect increases down group; Tl most commonly +1

Group 14 Core Facts:

• $ns^{2}$ $np^{2}$ configuration; tetravalency typical
• Diamond: $sp^{3}$, 3D network, hardest natural substance, insulator
• Graphite: $sp^{2}$, layered, delocalized π electrons, conductor and lubricant
• $C_{60}$: 12 pentagonal + 20 hexagonal rings; spherical; $sp^{2}$ carbon
• CO: neutral ligand; binds Hb 200× more than $O_{2}$; 2Mg + C$O_{2}$ → 2MgO + C
• Silicates: $SiO_{4}^{4-}$ tetrahedra units; zeolites: molecular sieves + ion exchange

Group 15 Core Facts:

• N≡N triple bond = 945 kJ/mol; strongest homonuclear diatomic bond
• Haber: $N_{2}$ + $3H_{2}$ ⇌ 2N$H_{3}$; Fe catalyst; 450°C; 200 atm
• Ostwald Step 1: Pt-Rh at 500°C; Step 2: no catalyst; Step 3: NO recycled
• Nitrogen oxides: $N_{2}$O (+1), NO (+2) neutral; N_{2}$$O_{3} (+3), N$O_{2}$ (+4), N_{2}$$O_{5} (+5) acidic
• Only NO and N$O_{2}$ are paramagnetic (odd-electron molecules)
• N_{2}$$O_{3} = HN$O_{2}$ anhydride; N_{2}$$O_{5} = HN$O_{3}$ anhydride
• Phosphorus allotropes: White ($P_{4}$, reactive, toxic) < Red (polymeric) < Black (most stable)
• $PCl_{5}$: $sp^{3}$d, trigonal bipyramidal; equatorial bonds shorter (~202 pm) than axial (~214 pm)
• $NCl_{5}$ cannot exist — N has no d-orbitals for $sp^{3}$d hybridization
• P oxoacid basicity = number of P-OH bonds (not total H atoms)
• $H_{3}$P$O_{2}$: 1 P-OH → monobasic; $H_{3}$P$O_{3}$: 2 P-OH → dibasic; H_{3}$$PO_{4}: 3 P-OH → tribasic