Carbon (C)

Common allotropes include diamond (each C is sp³ tetrahedrally bonded; hardest natural material; electrical insulator), graphite (planar sp² sheets with delocalized \(\pi\)-electrons; lubricating, electrically conductive), graphene (single sheet of graphite; exceptional strength and mobility), fullerenes (closed cages like C₆₀), and carbon nanotubes (rolled graphene; high tensile strength).

Different bonding (\(\mathrm{sp^3}\) vs \(\mathrm{sp^2}\)) explains contrasting hardness and conductivity.

Carbon forms three key hybrid states:

• sp: linear, bond angle \(180^\circ\); example: \(\mathrm{HC\equiv CH}\).
• sp²: trigonal planar, \(120^\circ\); example: \(\mathrm{H_2C{=}CH_2}\).
• sp³: tetrahedral, \(\approx 109.5^\circ\); example: \(\mathrm{CH_4}\).

Hybridization governs geometry, bond lengths/strengths, and the presence of \(\pi\)-bonds.

In graphite, each carbon is sp²-hybridized with one electron in a p-orbital forming a delocalized \(\pi\)-system across the sheet, enabling electron mobility (conductivity). In diamond, all four valence electrons are localized in \(\mathrm{sp^3}\) \(\sigma\)-bonds, leaving no free carriers, so it is an insulator.

Carbon shows a wide range of oxidation states:

• −4: \(\mathrm{CH_4}\) (methane)
• 0: elemental carbon (graphite, diamond)
• +2: \(\mathrm{CO}\) (carbon monoxide)
• +4: \(\mathrm{CO_2}\), carbonates like \(\mathrm{CaCO_3}\)

The versatility of C results from its ability to form multiple bonds and stable chains/rings.

Complete combustion (excess oxygen):

• \(\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)}\)
• \(\mathrm{CH_4(g) + 2\,O_2(g) \rightarrow CO_2(g) + 2\,H_2O(l)}\)

Limited oxygen can produce CO:

\(\mathrm{2\,C(s) + O_2(g) \rightarrow 2\,CO(g)}\)

Dissolved CO₂ establishes a series of equilibria that buffer pH:

\(\mathrm{CO_2(aq) + H_2O(l) \rightleftharpoons H_2CO_3(aq) \rightleftharpoons HCO_3^-(aq) + H^+(aq) \rightleftharpoons CO_3^{2-}(aq) + 2H^+(aq)}\)

This system is central to blood buffering and natural waters (e.g., hard water, cave formation).

\(^{14}\!\mathrm{C}\) is produced in the atmosphere and incorporated into living organisms. After death, \(^{14}\!\mathrm{C}\) decays (\(T_{1/2} \approx 5730\,\text{yr}\)). Age is estimated by:

\(\displaystyle t = \frac{1}{\lambda}\ln\!\left(\frac{N_0}{N}\right)\), where \(\lambda = \frac{\ln 2}{T_{1/2}}\).

\(N_0\) is the initial activity and \(N\) the measured activity of the sample.

Fullerenes (e.g., C₆₀) are closed carbon cages with delocalized \(\pi\)-systems; they show interesting redox/host–guest chemistry. Carbon nanotubes are cylindrical graphene sheets with exceptional mechanical strength and tunable electrical properties (metallic or semiconducting), enabling applications in composites, nanoelectronics, and sensing.

Carbon–carbon bonds are strong and directional; C can form single (\(\sigma\)), double (\(\sigma+\pi\)), and triple (\(\sigma+2\pi\)) bonds. Catenation (C–C chain/ring formation) and valency 4 allow an immense diversity of structures—the basis of organic chemistry.

The carbon cycle moves carbon among atmosphere (CO₂), biosphere (organic matter), hydrosphere (dissolved inorganic/organic carbon), and geosphere (carbonates, fossil fuels). Key steps include photosynthesis:

\(\mathrm{6\,CO_2 + 6\,H_2O \xrightarrow{light} C_6H_{12}O_6 + 6\,O_2}\)

and respiration/combustion returning CO₂ to the atmosphere.