Carbon is involved in inorganic compounds as well as organic compounds. Generally speaking, organic compounds contain carbon and hydrogen. This is not a firm rule. H2CO3 would be regarded as inorganic, while CCl4 would usually be regarded as organic.
Carbonates involve the carbonate ion, CO32-. Many carbonate compounds are found on earth's surface. Marble, for example, contains large amounts of calcium carbonate.
Carbonates generally react with acids to produce carbon dioxide, CO2. Aqueous solutions of CO2 are acidic:
H2O + CO2 H+ + HCO3-
Carbides may involve carbon atoms bounds into network structures, such as in silicon carbide (SiC) and boron carbide (B4C3). Both of these materials are very hard, and serve as abrasives. Quite a different situation exists for calcium carbide, CaC2. This substance can be thought of as the calcium salt of acetylene. When placed in water, solid calcium carbide reacts to produce acetylene gas.
CaC2 + 2H2O --> C2H2 + Ca(OH)2
Many metal carbides are known, such as tungsten carbide, WN. Cementite, Fe3C, is a very hard material. Steels containing Fe3C are very hard.
See jmol: Tungsten Carbide