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Organic chemistry is the scientific study of the structure, properties, composition, reactions, and synthesis of organic compounds.
Organic nomenclature is the system established for naming and grouping organic compounds.
Hydrocarbons - Alkanes - Alkenes - Dienes or Alkadienes - Alkynes - Halogenoalkanes - Alcohols - Mercaptans - Ethers - Aldehydes - Ketones - Carboxylic acids - Esters - Carbohydrates - Alicyclic compounds - Amides - Amines - Lipids - Nitriles
Benzene - Toluene - Xylene - Aniline - Phenol - Acetophenone - Benzonitrile - Halogenoarenes - Naphthalene - Anthracene - Phenanthrene - Benzopyrene - Coronene - Azulene - Biphenyl
Pyridine - Pyrrole - Thiophene - Furan - Imidazole
Polymers are a special kind of molecule. Generally considered "large" molecules, polymers are get their reputation regarding size because they are molecules that consist of multiple smaller segments. The segments could be chemically identical, which would make such a molecule a homopolymer. Or the segments could be vary in chemical structure, which would make that molecule a heteropolymer. Polymers are a subset of "macromolecules" which is just a classification for all molecules that are considered large.
Polymers can be organic or inorganic. Commonly-encountered polymers are usually organic (eg. polyethylene, polypropylene, Plexiglas, etc). But inorganic polymers are also familiar to everyday items (eg. silly putty, silicone, etc).
Organic nomenclature - Chemical formula - Structural formula - Skeletal formula - Organic reaction
The reason that there are so many carbon compounds is that carbon has the ability to form many carbon chains of different lengths, and rings of different sizes (catenation). Many carbon compounds are extremely sensitive to heat, and generally decompose below 300'C. They tend to be less soluble in water compared to many inorganic salts. In contrast to such salts, they tend to be much more soluble in organic solvents such as ether or alcohol. Organic compounds are covalently bonded.
The single most useful tool to characterize the molecular structure of an organic compound is nuclear magnetic resonance (NMR). Proton NMR tells how hydrogen atoms are grouped in an organic molcule and how they are situated relative to one another and to other atoms. Carbon-13 NMR tells similarly about carbon atoms in a molecule and how they are connected to hydrogens. For a molecule of moderate size (<30 atoms), a single NMR spectrum is what it takes to figure out the structure.
Organic chemistry as a science is generally agreed to have started in 1828 with Friedrich Woehler's synthesis of the organic, biologically significant compound urea by accidentally evaporating an aqueous solution of ammonium cyanate(NH4OCN).