Problem 69 - Chemistry The Central Science

Question

What is the empirical formula of cellulose? What is the unit that forms the basis of the cellulose polymer? What form of linkage joins these monomeric units?

Step-by-Step Solution

Answer

The empirical formula of cellulose is \(CH_2O\). The monomeric unit that forms the basis of the cellulose polymer is the anhydroglucose unit (AGU) with a molecular formula of \(C_6H_{10}O_5\). The linkage connecting these monomers is the β(1→4) glycosidic bond.

Step 1: Understand Empirical Formula and Monomeric Unit

An empirical formula represents the simplest ratio of the elements within a compound, while the monomeric unit refers to the single repeating unit that forms a polymer.

Step 2: Structure of Cellulose

Cellulose is an organic compound and a polysaccharide consisting of linear chains of β-D-glucose molecules linked together by β(1→4) glycosidic bonds. Cellulose is an important structural component of plant cell walls.

Step 3: Identify the Empirical Formula

To find the empirical formula of cellulose, we need to determine the ratio of carbon, hydrogen, and oxygen atoms in one glucose molecule. The molecular formula of glucoses is C6H12O6. The empirical formula can be determined by dividing the molecular formula by the greatest common factor of the subscripts, which in this case is 6. Hence, the empirical formula of cellulose is CH2O.

Step 4: Identify the Monomeric Unit

The monomeric unit that forms the basis of the cellulose polymer is the anhydroglucose unit or AGU. It is derived from the glucose molecule (C6H12O6) by the removal of one water molecule (H2O). The molecular formula of AGU is C6H10O5.

Step 5: Identify the Form of Linkage

The linkage between the monomeric units (AGUs) in cellulose is called β(1→4) glycosidic bond. It is formed between the hydroxyl group at the first carbon atom of one AGU and the hydroxyl group at the fourth carbon atom of another AGU, with the elimination of a water molecule. In conclusion, the empirical formula of cellulose is CH2O, the monomeric unit is the anhydroglucose unit (C6H10O5), and the linkage between these monomeric units is the β(1→4) glycosidic bond.

Key Concepts

Monomeric Unit of Polymers

In the world of polymers, the term 'monomeric unit' refers to the smallest repeating structure that makes up the larger polymer chain. Imagine it as a single link in a chain, where each link connects to form the extended structure that we recognize as the polymer. In the context of cellulose, which is a naturally occurring polymer, the monomeric unit is particularly special.

Each monomeric unit in cellulose originates from glucose, a simple sugar that is the energy currency in living organisms. However, in becoming part of cellulose, the glucose is transformed into an anhydroglucose unit, signifying a water molecule has been removed during polymerization. This change is pivotal because it allows cellulose to form strong fibrous structures crucial for plant cell walls. Understanding this unit is fundamental in grasping how large biological molecules are constructed from relatively simple building blocks.

β(1→4) Glycosidic Bond

The β(1→4) glycosidic bond represents the specific type of covalent link found between monomeric units of certain polysaccharides, including cellulose. It's like a strong handshake between two sugar molecules that connects them in a specific orientation and sequence.

Specifically, in a β(1→4) glycosidic bond, the 'β' denotes the configuration of the bond. This means the hydroxyl (OH) group on the first carbon (C1) of one sugar is pointing up, opposite to the oxygen bonded to the fourth carbon (C4). The bond is formed through a dehydration reaction where water is removed, joining the C1 of one anhydroglucose unit to the C4 of the next. This connection is what gives cellulose its unbranched, fibrous character, leading to the high tensile strength that is characteristic of plant cell walls. Without this specific type of bond, plants would not have the rigid structure necessary to stand upright and grow towards the light.

Anhydroglucose Unit

When we talk about the anhydroglucose unit (AGU), we're referring to the cornerstone of cellulose's structure. As implied by its name, an 'anhydro' form signifies the loss of water. An AGU is essentially a glucose molecule that has lost a molecule of water, converting from its usual C6H12O6 form to C6H10O5.

Through this slight but significant modification, the glucose molecule is prime for joining into the cellulose polymer chain. The AGUs repeat along the length of the chain, held together by the aforementioned β(1→4) glycosidic bonds, generating the lengthy, linear polymer that fortifies plant cell walls. The transformation into AGUs, and their subsequent linking, is key to the incredible stability and strength of cellulose, which plays a vital role in both the biology of plants and its myriad uses in humans' everyday lives, such as in paper production and textiles.