Comprehensive Study Notes on p-Block Elements: Group 13

Overview of p-Block and Group 13 Elements

• The p-block constitutes elements from groups 13 to 18 in the periodic table.

• These elements are characterized by the progressive addition of electrons to the p-orbitals: one electron ($ns^2 np^1$), two ($ns^2 np^2$), three ($ns^2 np^3$), four ($ns^2 np^4$), five ($ns^2 np^5$), and six ($ns^2 np^6$). The s-orbitals are already completely filled.

• The general electronic configuration for p-block atoms is $ns^2 np^{1-6}$.

• Together with the s-block, p-block elements are known as the representative elements.

• Group 13, often called the Boron family, consists of Boron ($B$), Aluminium ($Al$), Gallium ($Ga$), Indium ($In$), and Thallium ($Tl$).

• Except for Boron, which is classified as a non-metal, all other members of Group 13 are metals.

• Aluminium is the most abundant element in Group 13 and the third most abundant element in the earth's crust by weight (following oxygen and silicon).

• Boron occurs sparsely, while Gallium is twice as abundant as Boron. Indium and Thallium are much less common.

Electronic Configurations beyond Group 13

• The valence shell configuration for Group 13 elements is $ns^2 np^1$, indicating one electron in the outermost p-orbital and two in the s-orbital.

• Detailed configurations:

  • Boron ($B$, $Z=5$): $[He] 2s^2 2p^1$

  • Aluminium ($Al$, $Z=13$): $[Ne] 3s^2 3p^1$

  • Gallium ($Ga$, $Z=31$): $[Ar] 3d^{10} 4s^2 4p^1$

  • Indium ($In$, $Z=49$): $[Kr] 4d^{10} 5s^2 5p^1$

  • Thallium ($Tl$, $Z=81$): $[Xe] 5f^{14} 5d^{10} 6s^2 6p^1$

Atomic and Ionic Radii

• Group 13 elements have smaller atomic and ionic radii compared to Group 2 elements in the same period because moving from left to right increases nuclear charge while electrons are added to the same shell. Since same-shell electrons do not screen each other effectively, the effective nuclear charge increases, causing the size to decrease.

• Moving down the group, radii generally increase due to the addition of new electron shells.

• An anomaly exists between Aluminium and Gallium: the observed atomic radius of $Al$ ($143\,pm$) is slightly larger than that of $Ga$ ($135\,pm$).

• This anomaly is due to the presence of ten d-block elements ($Z=21$ to $30$) preceding Gallium. The d-orbitals have poor shielding power and shape, causing the effective nuclear charge in $Ga$ to be higher than in $Al$, which pull its electrons closer and reduces its size.

• Ionic radii ($M^{3+}$) increase consistently down the group:

  • $B^{3+}$: $27\,pm$

  • $Al^{3+}$: $53.5\,pm$

  • $Ga^{3+}$: $62.0\,pm$

  • $In^{3+}$: $80.0\,pm$

  • $Tl^{3+}$: $88.5\,pm$

Physical Constants and States

• Density increases down the group ($g\,cm^{-3}$):

  • $B$: $2.35$

  • $Al$: $2.70$

  • $Ga$: $5.90$

  • $In$: $7.31$

  • $Tl$: $11.85$

• Melting points do not follow a perfectly regular trend, but generally decrease:

  • $B$: $2453\,K$

  • $Al$: $933\,K$

  • $Ga$: $303\,K$

  • $In$: $430\,K$

  • $Tl$: $576\,K$

• Boiling points show a regular decrease moving down the group:

  • $B$: $3923\,K$

  • $Al$: $2740\,K$

  • $Ga$: $2676\,K$

  • $In$: $2353\,K$

  • $Tl$: $1730\,K$

Ionization Energies

• The first ionization energy ($IE_1$) for Group 13 is lower than for Group 2. This is because the $ns^2 np^1$ configuration involves removing an electron from a p-orbital, which is higher in energy and less strongly held by the nucleus than the s-orbital electron removed in Group 2.

• $IE_2$ and $IE_3$ are significantly higher because removing subsequent electrons requires breaking into a completely filled s-orbital ($ns^2$) or a more stable ion.

• Trends in $IE_1$ ($kJ\,mol^{-1}$):

  • $B$ (highest): $801$

  • $Al$: $577$

  • $Ga$: $579$ (unexpectedly higher than $Al$)

  • $In$: $558$

  • $Tl$: $589$ (higher than $In$)

• The slight increase in $IE$ for $Ga$ compared to $Al$ is due to the poor shielding of the nucleus by the 10 d-electrons, holding the outer electron more strongly.

• Similarly, the increase from $In$ to $Tl$ is due to the poor shielding effect of the 14 f-electrons in Thallium's inner configuration.

Oxidation States and the Inert Pair Effect

• Boron consistently shows the $+3$ oxidation state.

• Other elements show both $+3$ and $+1$ oxidation states. The stability of the $+1$ state increases as one moves down the group, reaching a maximum at Thallium ($Tl$), where $+1$ is more stable than $+3$.

• Gallium appears to show a $+2$ state in compounds like $GaCl_2$, but these are actually $Ga^+ [GaCl_4]^-$ dimers containing $Ga$ in $+1$ and $+3$ states.

• Inert Pair Effect: This describes the reluctance of the outermost s-electron pair ($ns^2$) to participate in chemical bonding due to poor shielding by d and f electrons. After the removal of the p-electron, the s-electrons behave like a stable noble gas configuration. This is why lower oxidation states ($+1$) are stable for heavier elements like Thallium.

• Consequently, thallous compounds like $TlOH$ and $TlClO_4$ are more stable than thallic ($+3$) equivalents.

Electropositive Character and Covalent Tendency

• Group 13 elements are less electropositive (metallic) than Group 2 elements due to higher ionization energies.

• Electropositive character increases down the group as ionization energy decreases; Boron is a non-metal, while others are metals.

• Boron shows a strong tendency to form covalent compounds due to the exceedingly small size of the trivalent $B^{3+}$ ion, which exerts a high polarizing effect on anions.

• Aluminium compounds exhibit mixed character: anhydrous $AlCl_3$ is covalent, while hydrated $[Al(H_2O)_6]^{3+}$ is ionic.

Hydrides of Group 13

• Boranes: Boron forms several hydrides with formulas $B_n H_{n+4}$ and $B_n H_{n+6}$. Examples include:

  • Diborane: $B_2H_6$

  • Tetraborane-10: $B_4H_{10}$

  • Pentaborane-9: $B_5H_9$

  • Pentaborane-11: $B_5H_{11}$

  • Hexaborane-10: $B_6H_{10}$

• These hydrides contain multicentre bonds. Aluminium forms polymeric hydrides $(AlH_3)_n$ that decompose above $200^\circ\text{C}$. Indium and Thallium hydrides are highly unstable.

• Complex Hydrides: These include $Li[AlH_4]$ (Lithium Aluminium Hydride) and $Na[BH_4]$ (Sodium Borohydride). Their formation is enabled by vacant p-orbitals in the Group 13 element that accept an electron pair from a hydride ion ($H^-$).

• Properties of Complex Hydrides:

  • $Li[BH_4]$ has some covalent character and reacts violently with water ($Li[BH_4] + 2H_2O \rightarrow LiBO_2 + 4H_2$, releasing hydrogen).

  • $Na[BH_4]$ is more stable and reacts slowly with water.

  • $Li[AlH_4]$ and $Na[AlH_4]$ are powerful reducing agents, used to reduce aldehydes and ketones to alcohols and nitriles to amines.

  • Reaction for Preparation: $4LiH + AlCl_3 \xrightarrow{\text{Ether}} Li[AlH_4] + 3LiCl$

Oxides and Hydroxides

• Elements form oxides ($M_2O_3$) and hydroxides ($M(OH)_3$).

• Acidity and Basicity Trends:

  • $B_2O_3$ and $B(OH)_3$: Acidic (though weakly). $B(OH)_3$ is orthoboric acid.

  • $Al_2O_3$ and $Al(OH)_3$: Amphoteric (dissolves in both acids and bases).

  • $Ga_2O_3$ and $Ga(OH)_3$: Amphoteric.

  • $In_2O_3$ and $In(OH)_3$: Basic.

  • $Tl_2O_3$, $Tl_2O$, and $TlOH$: Basic. $Tl_2O$ is more stable than $Tl_2O_3$.

• Cleavage of the M-O bond becomes easier down the group as ionization energy decreases, leading to increased basic strength.

• Amphoteric Reactions of Alumina:

  • With Base: $Al_2O_3 + 2NaOH \rightarrow 2NaAlO_2 + H_2O$ (Sodium meta-aluminate).

  • With Acid: $Al_2O_3 + 3H_2SO_4 \rightarrow Al_2(SO_4)_3 + 3H_2O$.

Halides and Structures

• Trihalides ($MX_3$) are the standard; monohalides ($MX$) are generally unstable except for Thallium.

• Boron Halides: Exist as monomers in the vapour phase with trigonal planar geometry. They are covalent ($BF_3$, $BCl_3$, $BBr_3$, $BI_3$).

• Aluminium Halides: $AlF_3$ is ionic. $AlCl_3$, $AlBr_3$, and $AlI_3$ are covalent.

• Dimerization of Aluminium Chloride: In the vapour state and non-polar solvents, $AlCl_3$ exists as a dimer ($Al_2Cl_6$). Each Aluminium is tetrahedrally coordinated by four Chlorine atoms. Two Chlorines are "bridged," acting as donors to form coordinate bonds with the vacant orbitals of Al atoms.

• Solid $AlCl_3$ has a closely packed layer structure where Aluminium has a coordination number of six (octahedral arrangement).

• Boron trihalides do not dimerize because the Boron atom is too small to fit four large halogen ions around it. Even $BF_3$ remains a monomer due to the high energy required to break strong $p\pi - p\pi$ back bonds.

• Lower Halides: Boron forms dihalides like $B_2Cl_4$. Thallium halides like $TlI_3$ are ionic, containing $Tl^+$ and the linear triiodide ion $I_3^-$.

Anomalous Behaviour of Boron and Diagonal Similarities with Silicon

• Boron differs from its group due to its small size, high ionization energy, high electronegativity, and absence of d-orbitals.

• Comparisons with Aluminium:

  • Boron is a non-metal and a bad conductor; Aluminium is a metal and a good conductor.

  • Boron has much higher melting and boiling points.

  • Boron shows maximum covalency of four; Aluminium can reach six.

  • Boron trihalides are monomers; Aluminium trihalides are dimers.

• Diagonal Relationship with Silicon:

  • Both are non-metals with high melting points and are semiconductors.

  • Both form volatile, easily hydrolysed hydrides.

  • Both form solid, weakly acidic oxides ($B_2O_3$, $SiO_2$) and weak acids ($H_3BO_3$, $H_4SiO_4$).

  • Both form binary metal compounds (borides and silicides) that hydrolyse to give hydrides.

  • Both chlorides fume in air and hydrolyse similarly: $BCl_3 + 3H_2O \rightarrow H_3BO_3 + 3HCl$ and $SiCl_4 + 4H_2O \rightarrow H_4SiO_4 + 4HCl$.

Orthoboric Acid ($H_3BO_3$)

• Preparation:

  • From Borax: Treating a hot concentrated borax solution with $HCl$ or $H_2SO_4$. $Na_2B_4O_7 + 2HCl + 5H_2O \rightarrow 4H_3BO_3 + 2NaCl$.

  • From Colemanite ($Ca_2B_6O_{11} \cdot 5H_2O$): Pass $SO_2$ through a boiling suspension of powdered colemanite mineral. $Ca_2B_6O_{11} + 11H_2O + 4SO_2 \rightarrow 2Ca(HSO_3)_2 + 6H_3BO_3$.

• Physical and Chemical Properties:

  • White lustrous crystalline solid with a soapy touch. Sparingly soluble in cold water, fairly soluble in hot water.

  • Action of Heat:

    • $100^\circ\text{C}$: Forms metaboric acid ($HBO_2$).

    • $160^\circ\text{C}$: Forms tetraboric acid ($H_2B_4O_7$).

    • Red Heat: Forms boron trioxide ($B_2O_3$).

  • Acidity: Boric acid is a weak monobasic Lewis acid, not a protonic acid. It accepts $OH^-$ from water: $B(OH)_3 + 2H_2O \rightleftharpoons [B(OH)_4]^- + H_3O^+$. Dissociation constant $K \approx 1.0 \times 10^{-9}$.

  • Titration with $NaOH$ has a sharp end point only in the presence of polyhydroxy compounds (glycerol, mannitol, catechol) which form stable complexes with the borate ion, preventing back-hydrolysis.

• Structure: Consists of $BO_3^{3-}$ units linked by hydrogen bonds into a two-dimensional sheet structure. Boron is $sp^2$ hybridised in a trigonal planar geometry.

Borates and Borax

• Borates are formed by linking $BO_3$ (planar) or $BO_4$ (tetrahedral) units via shared oxygen atoms.

• Common units include:

  • $BO_3^{3-}$ (e.g., $Ca_3(BO_3)_2$).

  • $(BO_2)_n^{n-}$ (metaborates).

• Borax ($Na_2B_4O_7 \cdot 10H_2O$): Contains the structural anion $[B_4O_5(OH)_4]^{2-}$. This unit contains two tetrahedral $BO_4$ units and two trigonal $BO_3$ units. It is formulated as $Na_2[B_4O_5(OH)_4] \cdot 8H_2O$.

Diborane ($B_2H_6$)

• Preparation:

  • Lab scale: $2NaBH_4 + I_2 \xrightarrow{\text{Diglyme}} B_2H_6 + 2NaI + H_2$.

  • Industry scale: $2BF_3 + 6NaH \xrightarrow{180^\circ\text{C}} B_2H_6 + 6NaF$.

• Reactions:

  • Flammable: $B_2H_6 + 3O_2 \rightarrow B_2O_3 + 3H_2O$ ($\Delta H^\circ = -2008\,kJ\,mol^{-1}$).

  • Hydrolysis: $B_2H_6 + 6H_2O \rightarrow 2H_3BO_3 + 6H_2$.

  • With Ammonia:

    • Low temp: Forms $[(NH_3)_2BH_2]^+ [BH_4]^-$.

    • High temp ($180^\circ\text{C}$): Forms Borazine ($B_3N_3H_6$).

  • Hydroboration: Addition of Diborane to alkenes to form alkylboranes, which can be converted to primary alcohols with alkaline $H_2O_2$.

• Structure and Bonding:

  • It is an electron-deficient compound with 12 valence electrons.

  • Contains four terminal B-H bonds (standard 2-centre 2-electron bonds) and two bridged B-H-B bonds.

  • The bridged bonds are "banana bonds" or 3-centre 2-electron bonds, involving three nuclei ($B$, $H$, and $B$) and one electron pair.

  • Each Boron atom is $sp^3$ hybridised.

  • Terminal hydrogens lie in one plane with the Boron atoms, while bridging hydrogens lie in a plane at right angles above and below.

Borazine and Boron Nitride

• Borazine ($B_3N_3H_6$):

  • Known as "inorganic benzene" because it is isoelectronic and isostructural with benzene.

  • Preparation: $3B_2H_6 + 6NH_3 \xrightarrow{250-300^\circ\text{C}} 2B_3N_3H_6 + 12H_2$.

  • Structure involves alternate Boron and Nitrogen atoms in a ring. Both are $sp^2$ hybridised. Nitrogen donates its lone pair into the empty p-orbital of Boron ($dative$ bond).

  • Reacts with water, alcohols, and halides to form 1:3 addition products.

• Boron Nitride ($BN$):

  • Known as "inorganic graphite". White crystalline polymeric solid with a high melting point ($3270^\circ\text{C}$).

  • Layered structure identical to graphite, where Boron and Nitrogen alternate in the lattice. B-N bond length is 1.45\,\text{&}.

  • Prepared by pyrolysis of boron amide ($B(NH_2)_3$) at $750^\circ\text{C}$.

Boron Trihalides and Lewis Acidity

• Relative Lewis acid strength: BBr_3 > BCl_3 > BF_3.

• This order is explained by $p\pi - p\pi$ back bonding. In $BF_3$, the filled 2p-orbital of fluorine overlaps effectively with the empty 2p-orbital of Boron because they are similar in size and energy. This dative back bonding partially satisfies Boron's electron deficiency, making it a weaker Lewis acid.

• As halogens get larger ($Cl$, $Br$), the overlap between their 3p/4p orbitals and Boron's 2p orbital becomes less efficient, increasing the Lewis acid character.

Alumina ($Al_2O_3$)

• Common forms:

  • $\alpha-Al_2O_3$ (Corundum): Extremely hard, rhombohedral structure. Oxygen atoms are hexagonally close-packed with 2/3 of octahedral sites occupied by $Al^{3+}$.

  • $\gamma-Al_2O_3$ (Activated Alumina): Defect spinel structure, obtained by dehydrating $Al(OH)_3$ below $450^\circ\text{C}$. More reactive and used as an absorbent.

• Properties: White solid, high melting point ($2072^\circ\text{C}$), good thermal conductivity, and amphoteric.

• Uses: Aluminium production, abrasives (sandpaper, grinding wheels), refractory bricks, furnace linings, and medical implants (dental and orthopedic).