23Detailed Lecture Notes on Group 13, Group 2, and Group 1 Elements

Group 13: The Triele (B, Al, Ga, In, Tl)

General Group Properties

The members of Group 13 include Boron ($B$), Aluminum ($Al$), Gallium ($Ga$), Indium ($In$), and Thallium ($Tl$). These elements exhibit a distinct transition from semi-metallic to metallic character as one moves down the group.

• Atomic and Physical Data:

  • Atomic Number ($Z$): $5$ ($B$), $13$ ($Al$), $31$ ($Ga$), $49$ ($In$), $81$ ($Tl$).

  • Electron Configuration:

    • $B$: $[He]\,2s^2\,2p^1$

    • $Al$: $[Ne]\,3s^2\,3p^1$

    • $Ga$: $[Ar]\,3d^{10}\,4s^2\,4p^1$

    • $In$: $[Kr]\,4d^{10}\,5s^2\,5p^1$

    • $Tl$: $[Xe]\,4f^{14}\,5d^{10}\,6s^2\,6p^1$

  • 1st Ionization Energy ($eV$): $8.3$ ($B$), $6.0$ ($Al$), $6.0$ ($Ga$), $5.8$ ($In$), $6.1$ ($Tl$).

  • Electronegativity (Pauling): $2.0$ ($B$), $1.5$ ($Al$), $1.8$ ($Ga$), $1.5$ ($In$), $1.4$ ($Tl$).

• Trends within Group 13:

  • Metallic Character: Increases down the group. Boron is a semi-metal (metalloid), while others are metals.

  • Basic Character of Oxides and Hydroxides: Increases down the group.

  • Salt Character of Chlorides: Increases down the group.

  • Stability of M(I) Compounds: Increases significantly toward the bottom of the group (Inert Pair Effect).

Boron (Group 14.1 - 14.4)

Occurrence and Synthesis

• Natural Occurrence: Boron is found as Borates, specifically:

  • Kernite: $Na_2B_4O_7 \cdot 4\,H_2O$

  • Borax: $Na_2B_4O_7 \cdot 10\,H_2O$

Structure and Allotropes

Elemental Boron is characterized by its complex structure based on the $B_{12}$ icosahedron (a Platonic solid with 12 corners, 20 triangular faces, and 30 edges).

• Modifications of Boron:

  • $\alpha$-rhombohedral: Consists of a nearly cubic densest packing of $B_{12}$ icosahedra.

  • $\beta$-rhombohedral: The thermodynamically most stable form. It contains 105 atoms per unit cell ($2 \times B_{28}$, $4 \times B_{12}$, and $1 \times B$). The $B_{28}$ units are interpenetrating icosahedra.

  • $\alpha$-tetragonal: Not a pure phase; requires foreign atoms like $C$, $N$, $Ti$, or $V$. Example composition: $B_{50}N_2$ or $B_{50}C_2$, containing $(B_{12})_4E_2$ units.

  • $\beta$-tetragonal: 190 atoms per unit cell ($4 \times B_{21}$, $8 \times B_{12}$, $1 \times B$). Note: $B_{21}$ is twinned $B_{12}$.

  • Cubic: 1708 atoms per unit cell.

• Bonding Characteristics:

  • 2-center-2-electron (2c-2e) Bond: $B-B$ distance is approximately $171\,\text{pm}$.

  • 3-center-2-electron (3c-2e) Bond: $B-B$ distance is approximately $202\,\text{pm}$. This is a multi-center bond required because Boron is electron-deficient ($2s^2\,2p^1$).

Phosphorus and Chemical Logic

Boron has fewer than 4 valence electrons and seeks to reach an octet via three paths:

1. Formation of $B-X\,\pi$-bonds (e.g., in monomeric $BX_3$).

2. Formation of Lewis Acid/Base adducts (e.g., $BH_3 \cdot NH_3$).

3. Formation of $B-X-B$ multi-center bonds.

Applications of Boron

• Nuclear Technology: $^{10}B$ is used in control rods of nuclear reactors due to its high neutron absorption cross-section.

• Elemental Boron: High-strength fibers.

• Compounds:

  • Detergents: Perborates are used as bleaching agents.

  • Organic Synthesis: Various reagents.

  • Materials: Fireproof Borosilicate glass (Pyrex), ceramic glazes, and wood preservatives.

  • Hard Materials: Boron carbide and Boron nitride.

Diborane ($B_2H_6$)

• Properties: A colorless, toxic gas. It exists almost exclusively as a dimer.

• Preparation: $4\,BCl_3 + 3\,LiAlH_4 \rightarrow 2\,B_2H_6 + 3\,LiCl + 3\,AlCl_3$

• Reactions:

  • Combustion: $B_2H_6 + 3\,O_2 \rightarrow B_2O_3 + 3\,H_2O$ (Highly exothermic flame).

  • Hydrolysis: $B_2H_6 + 6\,H_2O \rightarrow 2\,B(OH)_3 + 6\,H_2$

  • Adduct Formation: It reacts with strong Lewis bases to form borohydrides: $2\,LiH + B_2H_6 \rightarrow 2\,LiBH_4$.

Oxygen Compounds of Boron

• Orthoboric Acid ($H_3BO_3$):

  • Prepared from Borax: $[Na(H_2O)_4]_2[B_4O_5(OH)_4] + H_2SO_4 \rightarrow 4\,H_3BO_3 + Na_2SO_4 + 5\,H_2O$.

  • Acts as a weak mono-acid by accepting an $OH^-$ ion rather than donating a proton: $H_3BO_3 + H_2O \rightleftharpoons H_3O^+ + B(OH)_4^-$.

  • $pKs = 9.2$. Adding polyvalent alcohols (like Mannitol) can drop the $pKs$ to $5.15$ due to complex formation.

  • Detection: Formation of volatile esters ($B(OMe)_3$) with methanol, which burn with a green flame.

  • Structure: Crystallizes in 2D layers held together by hydrogen bonds.

• Metaboric Acid/Borates: Consist of $BO_3$ groups linked into rings or chains.

• Boron Trioxide ($B_2O_3$): Dehydration product of boric acid.

• Borax Bead Test: A precursor in analytical chemistry where Borax is melted ($880\,^{\circ}\text{C}$) to form colored glasses with metal oxides.

Boron-Nitrogen and Halogen Compounds

• Halides ($BX_3$): Strong Lewis acids. Strength order: BF_3 < BCl_3 < BBr_3 < BI_3. The order is explained by the loss of $\pi$-bonding character when transitioning from a planar to a tetrahedral geometry upon adduct formation.

• Bornitride ($BN$):

  • $\alpha$-Bornitride (h-BN): Hexagonal structure like graphite; used as a lubricant ("white graphite").

  • $\beta$-Bornitride (c-BN): Cubic structure like diamond; the second hardest known material. Used for cutting steel as it does not release carbon into the metal unlike diamond.

  • $\gamma$-Bornitride (w-BN): Wurtzite-like; research suggests it may exhibit superior indentation strength under specific shear stress mechanisms.

• Borazine ($B_3N_3H_6$): Known as "Inorganic Benzene."

Aluminum and Heavy Group 13 Elements

Aluminum ($Al$)

• Extraction (Hall-Héroult Process): Fused salt electrolysis. Aluminum oxide ($Al_2O_3$, Tonerde) is dissolved in a melt of Kryolith ($Na_3AlF_6$) to lower the melting point from $2050\,^{\circ}\text{C}$ to approximately $900\,^{\circ}\text{C}$.

  • Cathode: $Al^{3+} + 3\,e^- \rightarrow Al$

  • Anode: $2\,O^{2-} \rightarrow O_2 + 4\,e^-$; the oxygen then reacts with the coal anode: $3\,O_2 + 3\,C \rightarrow 3\,CO_2$ (or $CO$).

• Production Economics (per 1 ton Al):

  • Primary Al: $5\,t$ Bauxite, $0.6\,t$ Electrode coal, $4\,kg$ Kryolith, and $15\,000\,kWh$ electrical energy.

  • Recycled Al: Only $800\,kWh$ ($6\%$ of primary energy).

• Alloys:

  • Duralumin: $2-5.5\%\,Cu$, $0.5-2\%\,Mg$, etc. Used for structural strength.

  • Hydronalium: $3-12\%\,Mg$, seawater-resistant.

• Aluminum Chloride ($AlCl_3$):

  • Ionic in the solid state (Coordination Number = 6).

  • Upon melting, it forms $Al_2Cl_6$ molecular dimers with bridge bonds.

  • Used as a Lewis acid catalyst in Friedel-Crafts reactions.

Gallium, Indium, and Thallium

• Ga & In: Similar chemistry to Al; prefer the $+III$ oxidation state. In shows a growing tendency for $+I$.

• Thallium ($Tl$): High stability of the $+I$ oxidation state. Highly toxic.

Metal Structures and Bonding

Physical Properties of Metals

Metals exhibit metallic luster, high electrical and thermal conductivity, and ductility.

Crystal Structures

1. Hexagonal Closest Packing (hcp): Layer sequence ABAB… (e.g., $Mg$).

2. Cubic Closest Packing (ccp / fcc): Layer sequence ABCABC… (e.g., $Al$, $Cu$). Space filling = $74\%$.

3. Body-Centered Cubic (bcc): Middle sphere touched by 8 neighbors. Space filling = $68\%$.

Bonding Models

• Electron Gas Model: Metal cations surrounded by a "sea" of delocalized valence electrons.

• Band Model:

  • Atomic orbitals overlap to form energy bands.

  • Valence Band (VB): Occupied band.

  • Conduction Band (LB): Empty or partially occupied band.

  • Band Gap (Forbidden Zone): Energy difference between VB and LB.

  • Classification:

    • Metals: Bands overlap; electrons move freely.

    • Insulators: Wide band gap.

    • Semiconductors: Narrow band gap allowing thermal excitation.

Group 2: Alkaline Earth Metals (Be, Mg, Ca, Sr, Ba, Ra)

Group Properties

• Atomic Number ($Z$): $4$ ($Be$), $12$ ($Mg$), $20$ ($Ca$), $38$ ($Sr$), $56$ ($Ba$).

• Electron Configuration: Ends in $ns^2$.

• Hydration Enthalpy ($M^{2+}$, $kJ/mol$): $-2494$ ($Be$), $-1921$ ($Mg$), $-1577$ ($Ca$), $-1443$ ($Sr$), $-1305$ ($Ba$).

• Flame Colors: Ca (Brick red), Sr (Carmine red), Ba (Green).

Occurrence

• Beryllium: Beryl ($Be_3Al_2[Si_6O_{18}]$).

• Magnesium: Dolomite ($CaMg(CO_3)_2$), Magnesite ($MgCO_3$).

• Calcium: Calcite/Marble/Aragonite ($CaCO_3$), Gypsum ($CaSO_4 \cdot 2\,H_2O$), Fluorite ($CaF_2$).

• Strontium: Coelestin ($SrSO_4$), Strontianit ($SrCO_3$).

• Barium: Schwerspat ($BaSO_4$), Witherit ($BaCO_3$).

Biominerals and Functions

Preparation and Chemistry

• Be: Reduction of $BeF_2$ with $Mg$ at $1300\,^{\circ}\text{C}$.

• Mg: Primarily through fused salt electrolysis of $MgCl_2$.

• Ca: Electrolysis or aluminothermic reduction of $CaO$ at $1200^\circ\text{C}$.

• Water Hardness: Defined by the concentration of $Ca^{2+}$ and $Mg^{2+}$ ions ($mmol/L$).

Group 1: Alkali Metals (Li, Na, K, Rb, Cs, Fr)

Group Properties

• Electron Configuration: $ns^1$. They are highly reactive and powerful reducing agents.

• Atomic Number ($Z$): $3$ ($Li$), $11$ ($Na$), $19$ ($K$), $37$ ($Rb$), $55$ ($Cs$).

• Hydration Enthalpy ($M^+$, $kJ/mol$): $-519$ ($Li$), $-406$ ($Na$), $-322$ ($K$), $-293$ ($Rb$), $-264$ ($Cs$).

• Flame Colors (Slide 80):

  • $Li$: Purple-red

  • $Na$: Yellow

  • $K$: Light violet

  • $Rb$: Red-violet

  • $Cs$: Blue-violet

Chemistry and Compounds

• Occurrence: Li in Amblygonit; Na in Rock salt ($NaCl$); K in Sylvin ($KCl$).

• Extraction: Li and Na via fused salt electrolysis. K, Rb, and Cs via reduction (e.g., Cs from $Cs_2Cr_2O_7$ with $Zr$ at $500\,^{\circ}\text{C}$).

• Oxygen Compounds:

  • Oxides ($M_2O$): Formed primarily by $Li$.

  • Peroxides ($M_2O_2$): Formed by $Na$.

  • Hyperoxides/Superoxides ($MO_2$): Formed by $K$, $Rb$, and $Cs$.

• Specific Uses:

  • $6Li$: Base for Hydrogen bombs ($6Li_2H$).

  • $Na$: Coolant in nuclear reactors; vapor lamps.

  • $Cs$: Photocells.

Questions & Discussion

Review of Group 2 (Slide 2)

• Mg Reactions: $Mg + O_2 \rightarrow MgO$; $Mg + N_2 \rightarrow Mg_3N_2 \xrightarrow{H_2O} NH_3 + Mg(OH)_2$.

• Ca Reactions: $Ca + C \rightarrow CaC_2 \xrightarrow{N_2} CaCN_2$ (Calcium Cyanamide). $CaCN_2 + H_2O \rightarrow CaCO_3 + NH_3$. This demonstrates the industrial Nitrogen fixation process via Cyanamide.

• Ba Reactions: $Ba + O_2 \xrightarrow{\Delta} BaO_2$ (Barium peroxide).

Fireworks Chemical Constituents (Slide 68)

Industrial list of compounds used in pyrotechnics:

• Oxidizers: $KNO_3$, $KClO_3$, $KClO_4$, $NH_4ClO_4$, $Ba(NO_3)_2$, $Sr(NO_3)_2$.

• Fuels/Binders: Dextrin, Glucose, Sorbitol, Lactose, Shellac, PVC, Wood flour.

• Colorants/Effect Additives: Copper(II) oxide ($CuO$), Antimony trisulfide ($Sb_2S_3$), Magnesium powder ($Mg$), Aluminum powder ($Al$).