Organic Chemistry: A Comprehensive Guide

Organic chemistry, the study of carbon-based compounds, is the foundation of life and modern technology. Carbon’s ability to form stable, diverse structures through single, double, and triple bonds creates millions of compounds, from methane (\( \ce{CH4} \)) to DNA. This MathMultiverse guide explores hydrocarbons, functional groups, IUPAC nomenclature, and applications in energy, medicine, and materials, enriched with examples, equations, and visualizations.

Since Friedrich Wöhler’s 1828 synthesis of urea (\( \ce{NH2CONH2} \)), organic chemistry has revealed carbon’s tetravalency and hybridization (\( sp^3, sp^2, sp \)) as keys to its versatility. This article covers molecular structures, reactions, and their real-world impact.

Hydrocarbons

Hydrocarbons, composed of carbon and hydrogen, are classified by bonding and structure, serving as fuels and chemical precursors.

Alkanes

Saturated hydrocarbons with single bonds, general formula:

\[ \ce{C_nH_{2n+2}} \]

Examples: Methane (\( \ce{CH4} \)), propane (\( \ce{C3H8} \)).

Alkenes

Contain at least one double bond, formula:

\[ \ce{C_nH_{2n}} \]

Example: Ethene (\( \ce{CH2=CH2} \)).

Alkynes

Feature a triple bond, formula:

\[ \ce{C_nH_{2n-2}} \]

Example: Ethyne (\( \ce{HC#CH} \)).

Aromatic Hydrocarbons

Benzene (\( \ce{C6H6} \)) with a stable ring structure.

Hydrocarbon Molar Masses

Molar masses of alkanes, alkenes, alkynes (\( n=1 \) to 5).

Functional Groups

Functional groups define a molecule’s reactivity and properties.

Alcohols (\( \ce{-OH} \))

Example: Ethanol (\( \ce{CH3CH2OH} \)).

Carboxylic Acids (\( \ce{-COOH} \))

Example: Acetic acid (\( \ce{CH3COOH} \)).

Amines (\( \ce{-NH2} \))

Example: Methylamine (\( \ce{CH3NH2} \)).

Esters (\( \ce{-COOR} \))

Example: Ethyl acetate (\( \ce{CH3COOCH2CH3} \)).

Aldehydes (\( \ce{-CHO} \))

Example: Formaldehyde (\( \ce{HCHO} \)).

Ketones (\( \ce{>C=O} \))

Example: Acetone (\( \ce{CH3COCH3} \)).

IUPAC Nomenclature

IUPAC rules ensure consistent naming.

Alkanes

Example: \( \ce{CH3CH2CH2CH3} \) is butane.

Alkenes

Example: \( \ce{CH3CH=CHCH3} \) is 2-butene.

Alkynes

Example: \( \ce{CH3CH2C#CH} \) is 1-butyne.

Functional Groups

Example: \( \ce{CH3CH(OH)CH2COOH} \) is 3-hydroxybutanoic acid.

Examples

Molar Mass of Butane

For \( \ce{C4H10} \):

\[ M = (4 \times 12) + (10 \times 1) = 48 + 10 = 58 \, \text{g/mol} \]

Esterification Reaction

Acetic acid and ethanol:

\[ \ce{CH3COOH + CH3CH2OH <=> CH3COOCH2CH3 + H2O} \]

Equilibrium constant: \( K \approx 4 \).

Combustion of Ethyne

Balanced reaction:

\[ \ce{2C2H2 + 5O2 -> 4CO2 + 2H2O} \]

Naming Branched Alkane

For \( \ce{CH3C(CH3)2CH3} \):

\[ \text{2,2-Dimethylpropane} \]

Boiling Points of Alcohols

Boiling points of alcohols vs. alkanes (n=1 to 4).

Applications

Energy: Fuels

Octane (\( \ce{C8H18} \)) combustion:

\[ \ce{2C8H18 + 25O2 -> 16CO2 + 18H2O} \]

Medicine: Drugs

Aspirin (\( \ce{C9H8O4} \)), molar mass:

\[ M = (9 \times 12) + (8 \times 1) + (4 \times 16) = 180 \, \text{g/mol} \]

Materials: Polymers

Polyethylene synthesis:

\[ n \ce{CH2=CH2 -> -(CH2CH2)_n-} \]

Food: Flavors

Ethyl butanoate (\( \ce{CH3CH2CH2COOCH2CH3} \)):

\[ M = 116 \, \text{g/mol} \]