They are called organic because hydrocarbons consist of hydrogen and carbon. Organic chemistry is the study of the compounds of hydrogen, carbon, nitrogen, and oxygen. The term organic in this case does not mean the living, but rather the four most common elements in the living.
Originally it was thought that organic chemicals could only be made by living beings until Whler changed Ammonium cyanate into Urea. Although still called organic it is now known that they can be made by inorganic means just as any other subtance including organic substances that do nor exist naturally like polyvinyl chloride.
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