Write the formula for the triacylglycerol formed from (a) glycerol and butanoic acid (b) glycerol and one molecule each of stearic \(\left(\mathrm{C}_{17} \mathrm{H}_{35} \mathrm{COOH}\right)\), palmitic \(\left(\mathrm{C}_{15} \mathrm{H}_{31} \mathrm{COOH}\right)\), and myristic \(\left(\mathrm{C}_{13} \mathrm{H}_{27} \mathrm{COOH}\right)\) acids

Glycerol is an organic compound commonly recognized by its capacity to form the backbone of lipid molecules such as triacylglycerols, also known as triglycerides. The glycerol structure contains three hydroxyl (OH) groups, one attached to each carbon atom in its three-carbon chain. This layout, scientifically denoted as \( C_3H_5(OH)_3 \), allows glycerol to be highly reactive with fatty acids, forming the ester bonds essential for triacylglycerol synthesis.

Understanding the glycerol structure is crucial because its functional groups provide the anchor points where fatty acids attach during the formation of triacylglycerols. It is this property that turns a simple molecule like glycerol into a fundamental building block for more complex lipids found within the cell membranes and stored fat in living organisms.

Fatty acids are the building blocks of lipids and are characterized by long hydrocarbon chains terminated with a carboxyl group (\( -COOH \)). These molecules are typically classified based on the length of their carbon chain and the presence of double bonds. Saturated fatty acids have no double bonds within the hydrocarbon chain, while unsaturated fatty acids contain one or more double bonds.

The example exercise mentions butanoic acid - a short-chain saturated fatty acid with four carbon atoms, and long-chain saturated fatty acids such as stearic acid (18 carbons), palmitic acid (16 carbons), and myristic acid (14 carbons). The carbon chain length and degree of saturation are significant because they influence the physical and functional properties of the fatty acid, such as melting point and the role they play within biological membranes.

The ester bond is a key chemical bond formed between the hydroxyl group of glycerol and the carboxyl group of a fatty acid. In biochemical terms, an ester bond is a type of covalent bond that results from a condensation reaction, which typically releases water as a byproduct. This is precisely the type of reaction that occurs during the synthesis of triacylglycerols.

In the formation process, each fatty acid's carboxyl group reacts with each of the three hydroxyl groups on the glycerol molecule. The removal of water molecules during this reaction is an integral part of esterification, and it results in the creation of three ester bonds, one for each fatty acid, ultimately leading to a complete triacylglycerol molecule.

The chemical formula of a substance is a representation of its molecular composition using elemental symbols and numerical subscripts. For triacylglycerols, the formula denotes the glycerol backbone, the fatty acids, and the ester linkages connecting them. For instance, the triacylglycerol formed from glycerol and three butanoic acid molecules might have a formula of \( C_3H_5(O(C_4H_7O)_3) \).

This formula indicates a molecule composed of a three-carbon glycerol backbone attached to three butanoic acid molecules, each by an ester bond. In mixed triacylglycerols, where various kinds of fatty acids are present, the chemical formula reflects the combination and sequence of different fatty acids as they are attached to the glycerol, such as in the example where glycerol combines with stearic, palmitic, and myristic acids to form \( C_3H_5(O(C_17H_{35}O)_1(O(C_{15}H_{31}O)_1(O(C_{13}H_{27}O)_1) \). It's essential to understand these formulas as they provide insight into the molecule's structure, which has direct implications for its physical properties and biological function.