Two grand themes tie Groups 13 and 14 together: the inert pair effect that governs oxidation-state stability, and the anomalous behaviour of the first member (boron, carbon) compared with its heavier congeners. A third recurring idea — the diagonal relationship — links the first element of each group with the second element of the next group.
The inert pair effect. Heavy p-block elements have an outer ns2npx configuration. As we descend a group, the ns2 (‘inert’) electrons become increasingly reluctant to participate in bonding. The reason is two-fold: the intervening d- and f-electrons shield the ns2 pair poorly, so it is held tightly; and the M-X bond energy falls down the group, so the energy released by forming two extra bonds no longer compensates for the energy needed to unpair and promote the ns2 electrons. The result is that the lower oxidation state (+1 in Group 13, +2 in Group 14) becomes more stable as we go down: Tl+ > Tl3+ in stability, and Pb2+ > Pb4+. Consequently the higher-state species of the heavy elements (Tl3+, Pb4+) are good oxidising agents.
Anomalous behaviour of boron and carbon. The first member of each p-block group differs from the rest because of its small atomic size, high ionisation enthalpy and electronegativity, and the absence of valence d-orbitals. For boron: it is a metalloid (the others are metals), forms only covalent and electron-deficient compounds (Lewis acids like BF3), and has a maximum covalency of 4 (it cannot expand its octet). For carbon: it shows the strongest catenation, forms stable pπ-pπ multiple bonds (so CO2 is molecular while SiO2 is a network), and is limited to a covalency of 4.
Diagonal relationships. Because moving right increases and moving down decreases the same properties (size, electronegativity, charge density), the first element of a group resembles the second element of the next group lying diagonally below-right. Thus boron resembles silicon: both are hard, refractory metalloids, form weakly acidic oxides (B2O3, SiO2), volatile covalent halides hydrolysed by water, and macromolecular hydrides/oxides. (Similarly, in nearby groups, lithium resembles magnesium and beryllium resembles aluminium.)
Group 13 vs Group 14 — a comparison. Group 13 has three valence electrons (ns2np1), shows +3 and (lower down) +1, and its trihalides/hydrides tend to be electron-deficient Lewis acids. Group 14 has four valence electrons (ns2np2), shows +4 and (lower down) +2, and its tetravalent compounds are electron-precise. Both groups show the non-metal-to-metal trend down the column, both have anomalous first members, and both obey the inert pair effect in the heavier elements.
Uses worth remembering. Boron compounds: borax (washing, glass, borosilicate Pyrex), boric acid (mild antiseptic), boron filaments (light, stiff composites). Aluminium: aircraft, cables, foil, thermite welding. Carbon: diamond (abrasives, jewellery), graphite (electrodes, lubricant, pencil ‘lead’), activated charcoal (adsorbent). Silicon: semiconductors and computer chips; silica and silicates in glass and ceramics; silicones as sealants; zeolites as catalysts and water softeners; tin and lead in solders, alloys and storage batteries.