Step-by-step Derivations

1. Identify the structure of the starting material: Cellulose. Cellulose is a polysaccharide, which is a long-chain polymer. It is composed of repeating monomer units of D-glucose. Specifically, these glucose units are linked together by β-1,4-glycosidic bonds. Each glucose monomer within the cellulose chain has three free hydroxyl (-OH) groups. These are located at the C-2, C-3, and C-6 positions.

   The basic repeating unit of cellulose looks like this (focusing on the hydroxyl groups):

2. Identify the reagents and the type of reaction.

   • Reactant: Cellulose.
   • Reagents: Acetic anhydride ((CH₃CO)₂O) in excess, and a catalytic amount of concentrated sulfuric acid (H₂SO₄).
   • Reaction Type: The reaction of an alcohol (-OH group) with acetic anhydride is called acetylation, which is a type of esterification. The acetyl group (-COCH₃) from acetic anhydride replaces the hydrogen atom of the hydroxyl group, forming an acetate ester (-O-CO-CH₃) and acetic acid as a byproduct.
   • The general reaction is: R-OH + (CH₃CO)₂O → R-O-COCH₃ + CH₃COOH.

3. Determine the product of the reaction. Since the question specifies that excess acetic anhydride is used, it implies that all available hydroxyl groups on the cellulose polymer will react. As each glucose unit has three -OH groups (at C-2, C-3, and C-6), all three will be converted to acetate ester groups.

   So, each -OH group will be transformed into a -O-CO-CH₃ group.

   The overall polymeric structure of cellulose, with its β-1,4-glycosidic linkages, remains intact under these conditions. The reaction only modifies the side groups.

   The resulting product is called cellulose triacetate, because three acetate groups are added per glucose monomer unit.

4. Analyze the given options.

   • Option A: This structure shows the correct cellulose backbone with β-1,4-glycosidic linkages. On each glucose unit, the hydroxyl groups at the C-2, C-3, and C-6 positions have been replaced by acetate ester groups (-O-CO-CH₃). This perfectly matches the expected structure of cellulose triacetate.

   • Option B: This structure shows the attachment of a keto group (-CO-CH₃) directly to the glucose ring, replacing the -OH group. This is incorrect. The oxygen atom from the original hydroxyl group is retained to form the ester linkage.

   • Option C: This structure shows α-1,4-glycosidic linkages. This is the structure of amylose (a component of starch), not cellulose. While it shows acetylation, it's the acetylation of starch, not cellulose.

   • Option D: This option shows the complete hydrolysis (breakdown) of the cellulose polymer into individual acetylated glucose monomers. While strong acid can hydrolyze glycosidic bonds, the primary reaction under these acetylation conditions is esterification, and the product, cellulose triacetate, is a polymer.

5. Conclusion. Based on the analysis, Option A is the only structure that correctly represents cellulose triacetate, which is formed by the complete acetylation of cellulose while preserving the β-1,4-linked polymeric backbone. The hydroxyl groups are converted to acetate ester groups.