Problem 69 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) What is the empirical formula of cellulose? (b) What is the monomer that forms the basis of the cellulose polymer? (c) What bond connects the monomer units in cellulose: amide, acid, ether, ester, or alcohol?

Step-by-Step Solution

Answer

(a) The empirical formula of cellulose is \(C_6H_{10}O_5\) for each repeating unit. (b) The monomer that forms the basis of the cellulose polymer is β-D-glucose. (c) The bond connecting the monomer units in cellulose is an ether bond, specifically a β(1→4)-glycosidic bond.

Step 1: (a) Empirical formula of cellulose

Cellulose is a polysaccharide that consists of a long chain of β-D-glucose monomer units. The empirical formula for glucose is C6H12O6. However, in cellulose, the monomer units are connected through glycosidic linkages, causing the loss of a water molecule (H2O) for each linkage formed between two glucose units. Thus, the empirical formula of cellulose becomes C6H10O5 for each repeating unit.

Step 2: (b) Monomer of cellulose

Since cellulose is formed from glucose monomer units, the monomer that forms the basis of the cellulose polymer is β-D-glucose.

Step 3: (c) Bond connecting the monomer units in cellulose

The bond that connects the monomer units in cellulose is an ether bond. This is also called a glycosidic bond when referring to carbohydrates. In cellulose, the glucose monomers are connected by a β(1→4)-glycosidic bond specifically. This bond is formed between the hydroxyl groups on the 1st and 4th carbons of adjacent glucose molecules, resulting in an oxygen bridge that acts as the ether bond.

Key Concepts

Empirical Formula of Cellulose

Cellulose is a structural polysaccharide found in the cell walls of plants. To understand its empirical formula, we need to look at the building blocks that make up cellulose. Each unit of cellulose is a glucose molecule, but in cellulose, these glucose units are connected in such a way that a water molecule (H₂O) is lost for each linkage formed. This happens because cellulose is composed of β-D-glucose molecules connected by glycosidic linkages.

The empirical formula is a simplified representation of the types and numbers of atoms in a compound, showing the lowest whole-number ratio. For glucose, this formula is C₆H₁₂O₆, but due to the removal of a water molecule stable linkage, the formula shifts to C₆H₁₀O₅ for each repeating unit of cellulose.

• Glucose empirical formula: C₆H₁₂O₆
• Cellulose empirical adjustment: C₆H₁₀O₅ (due to dehydration during polymerization)

Understanding this transformation helps in grasping how cellulose is structured chemically.

Glycosidic Bond in Cellulose

Glycosidic bonds are a type of covalent bond that connect carbohydrate molecules, specifically found in polysaccharides like cellulose. In the realm of carbohydrates, glycosidic bonds are pivotal for creating complex sugar structures.

In cellulose, these bonds are specifically β(1→4)-glycosidic bonds. This indicates the position and orientation of the linkage between glucose units:

• The number 1 refers to the carbon number in one glucose molecule.
• The number 4 indicates the carbon number in the adjacent glucose molecule.

The β orientation signifies a specific geometric configuration in this bond. It links the hydroxyl group on the first carbon of one glucose to the fourth carbon of another, creating a bridge with an oxygen atom, which is why it is also referred to as an ether bond in cellulose.

These bonds are crucial for the rigidity and strength of cellulose, making them crucial for plant structure and stability.

β-D-glucose: The Basic Unit of Cellulose

β-D-glucose is the monomer that serves as the building block for cellulose. Structurally, glucose is a simple sugar with the formula C₆H₁₂O₆, but β-D-glucose specifically refers to one of the stereoisomers of glucose. This means it has the same chemical formula but a different orientation in space.

The 'β' in β-D-glucose indicates the orientation of the hydroxyl (OH) group on the first carbon (anomeric carbon) is above the plane of the sugar ring. This specific stereochemistry allows for the formation of β(1→4)-glycosidic bonds when connecting to other glucose units, resulting in the linear chains that are characteristic of cellulose.

• Basic chemical formula: C₆H₁₂O₆
• Stabilizes plant cell walls due to its unique linkage

Understanding β-D-glucose's role in forming cellulose is key to appreciating how this polysaccharide contributes to the structural integrity of plant cells.