Write the equation representing the formation of a soap molecule from stearic acid, \(\mathrm{C}_{17} \mathrm{H}_{35} \mathrm{COOH},\) and sodium hydroxide.

Stearic acid is a type of fatty acid that can be found in various animal and vegetable fats. It is a long-chain saturated fat with 18 carbon atoms, making it solid at room temperature. Having the chemical formula \(\text{C}_{17}\text{H}_{35}\text{COOH}\), stearic acid is commonly used in the production of soaps, cosmetics, and candles. Its structure includes a long hydrocarbon chain connected to a carboxyl group \(\text{-COOH}\). This carboxyl group is very reactive and participates in many chemical reactions, including saponification. Stearic acid is known for producing a hard, white soap with excellent consistency and lathering properties.

Sodium hydroxide, also known as lye or caustic soda, is a highly reactive base often used in soap making. It has the chemical formula \(\text{NaOH}\). When dissolved in water, it dissociates into sodium ions (Na^+) and hydroxide ions (OH^-). Sodium hydroxide is very corrosive, so it's important to handle it with care.
In the context of saponification, sodium hydroxide reacts with the fatty acids in fats and oils to produce soap. This process involves the nucleophilic attack of the hydroxide ion on the carbon of the carboxyl group in the fatty acid, leading to the formation of the carboxylate salt (soap) and water. Sodium hydroxide is crucial in breaking down the lipid molecules to form the soap.

Soap formation occurs via a chemical process called saponification. During saponification, a fatty acid reacts with a strong base, usually sodium hydroxide, to produce soap and water. The general equation for saponification is:
\[ \text{RCOOH} + \text{NaOH} \rightarrow \text{RCOONa} + \text{H}_{2}\text{O} \]
In the specific case of stearic acid and sodium hydroxide, the reaction can be written as:
\[ \text{C}_{17}\text{H}_{35}\text{COOH} + \text{NaOH} \rightarrow \text{C}_{17}\text{H}_{35}\text{COONa} + \text{H}_{2}\text{O} \]
The product, \(\text{C}_{17}\text{H}_{35}\text{COONa}\), is known as sodium stearate, which is a common type of soap. The main components in soap molecules are hydrophobic (water-repelling) tail and hydrophilic (water-attracting) head. This amphiphilic structure enables soap to emulsify oils, allowing them to be washed away with water. Soap is thus essential for effective cleaning as it helps remove grease, dirt, and grime from surfaces and skin.