Problem 62 - Chemistry Matter and Change

Question

Draw the structure of the open-chain form of fructose. Circle all chiral carbons, and then calculate the number of stereoisomers with the same formula as fructose.

Step-by-Step Solution

Answer

The open-chain form of fructose has the following structure: O || H-C-OH | H C-OH | C-OH | H-C-OH | CH2OH There are three chiral carbons, as indicated by asterisks (*): O || H-C-OH * | H C-OH * | C-OH * | H-C-OH | CH2OH Using the equation 2^n, where n is the number of chiral carbons (3 in this case), there are 2^3 = 8 possible stereoisomers with the same formula as fructose.

Step 1: Drawing the open-chain form of fructose

Fructose, also called D-fructose or dextro-fructose, is a monosaccharide with the chemical formula C6H12O6. In its open-chain form, fructose has a structure as follows: O || H-C-OH | H C-OH | C-OH | H-C-OH | CH2OH

Step 2: Identifying and circling the chiral carbons

A chiral carbon atom is a carbon that has four different groups attached to it. In the structure of fructose, there are three chiral carbons which can be marked as follows: O || H-C-OH * | H C-OH * | C-OH * | H-C-OH | CH2OH Each asterisk (*) represents a chiral carbon atom.

Step 3: Calculating the number of stereoisomers

To find the total number of stereoisomers for fructose, we will use the equation 2^n, where n is the number of chiral carbons. In fructose, we have identified three chiral carbons: Number of stereoisomers = 2^n = 2^3 = 8 So, there are 8 possible stereoisomers with the same formula as fructose.

Key Concepts

Chiral Carbon

A chiral carbon, also known as an asymmetric carbon, is a carbon atom that is bonded to four different atoms or groups of atoms. This unique structural feature makes it capable of existing in two non-superimposable mirror image forms, known as enantiomers. In the open-chain form of fructose, certain carbon atoms meet these criteria and thereby become chiral.

• For fructose, each chiral carbon is represented with an asterisk in the molecular structure.
• These chiral centers are crucial for the molecule's stereochemistry and significantly impact its biological properties and functions.

Understanding chiral carbons is fundamental because they determine how the molecule interacts with other substances, including enzymes and receptors, and thus influence metabolic and physiological processes.

Stereoisomers

Stereoisomers are molecules that have the same molecular formula and sequence of bonded atoms, but they differ in the three-dimensional orientations of these atoms in space. They can exhibit very different properties despite having similar structures.

• Two main types of stereoisomers are enantiomers and diastereomers.
• Enantiomers are mirror images of each other and cannot be superimposed, like left and right hands.
• Diastereomers, on the other hand, are not mirror images.

In the case of fructose in its open-chain form, the molecule can exist in 8 different stereoisomers, as determined by the formula \( 2^n \), where \( n \) is the number of chiral carbons. Fructose has three chiral carbons, leading to \( 2^3 = 8 \) stereoisomers.

Open-Chain Form

The open-chain form of fructose is one way in which the molecule can appear, depicting its structure with a linear arrangement of atoms. In this form, fructose shows its backbone consisting of carbon atoms, each bonded with hydrogen and hydroxyl (OH) groups.

• The open-chain structure is important for understanding the molecule's potential to form ring structures, such as the five-membered furanose ring typical of fructose.
• It also aids students in identifying the location of the chiral carbons more easily, as displayed in the linear form of the molecule.

This representation helps simplify the identification of structural aspects, including functional groups and chiral centers, which can otherwise be more challenging to visualize in the ring form.

Monosaccharide

Monosaccharides are the simplest form of carbohydrates, consisting of a single sugar molecule. They serve as building blocks for more complex sugars like disaccharides and polysaccharides. Fructose is a prime example of a monosaccharide, characterized by its sweetness and role in various biological processes.

• Monosaccharides can exist in different forms, such as the open-chain and cyclic ring structures.
• They can combine through glycosidic bonds to form disaccharides, like sucrose, or polysaccharides, which are important for energy storage and structural components of cells.

Understanding monosaccharides includes recognizing their fundamental characteristics: their molecular formula, presence of chiral centers, and ability to create diverse structures crucial for biological functions.