Question

The structural formula for the linear form of D-mannose is: (a) How many chiral carbons are present in the molecule? (b) Draw the structure of the six-member-ring form of this sugar.

Short answer

(a) There are 4 chiral carbons in D-mannose located at positions \(C_2, C_3, C_4\), and \(C_5\). (b) To draw the six-membered ring form of D-mannose, form a pyranose ring by connecting the oxygen atom on carbon \(C_5\) to the carbon \(C_1\). Place the OH groups according to the configuration of D-mannose: OH groups on \(C_2, C_4\) and \(C_5\) should be on the right side of the ring, while the OH group on \(C_3\) is on the left side of the ring. Add a CH2OH group above the ring at the \(C_6\) position. The resulting structure is the α-D-mannopyranose.

Step-by-step solution

Understanding Chiral Carbon Atoms

Chiral carbon atoms are carbon atoms with four different substituents attached to them. They are also commonly referred to as stereogenic centers or asymmetric carbons. When we identify a chiral carbon in a molecule, we look for a carbon atom that has four different groups or atoms attached to it. This gives the molecule an ability to exhibit optical isomerism, resulting in enantiomers (mirror image isomers).

Counting Chiral Carbons in D-mannose

D-mannose has the following structural formula: \(C_6 H_{12} O_6\), which means it has six carbon atoms, twelve hydrogen atoms and six oxygen atoms. The linear form of D-mannose can be written as: H-(CHOH)_4-CHO. Now, we look for chiral carbons in this structure by checking for carbon atoms with four different substituents. We can see that there are 4 chiral carbons, each located at: \( C_2, C_3, C_4\) and \(C_5\). So, the answer to question (a) is 4 chiral carbons.

Drawing the Six-membered Ring Form of D-mannose

To draw the six-membered ring form of D-mannose, we will first create a 6-membered ring system containing one five-carbon ring and one oxygen atom, known as the pyranose ring. We form this ring by connecting the oxygen atom on carbon \(C_5\) to the carbon \(C_1\). Here is the step-by-step process to draw the six-membered ring structure: 1. Draw a hexagon, which represents the six atoms in the ring (5 carbons and 1 oxygen). Place the oxygen atom in one of the corners. Number the carbon atoms clockwise, beginning with the carbon atom next to the oxygen atom. This gives the position of the carbon atoms in the ring. 2. Add the OH (hydroxyl) groups to the chiral carbon atoms (C2, C3, C4, and C5) making sure to place them according to the configuration of D-mannose: OH groups on C2, C4 and C5 should be on the right side of the ring, while the OH group on C3 is on the left side of the ring. 3. Draw the remaining substituents (hydrogen atoms) on each chiral carbon atom. 4. Add a CH2OH group above the ring at the C6 position to complete the D-mannose structure in its six-membered ring form. The structure formed is called the α-D-mannopyranose (α-D-mannose six-membered ring form). Following these steps, you should be able to draw the six-membered ring form of D-mannose, as requested in question (b).

Key concepts

D-mannose structure

D-mannose is an essential sugar that falls within the category of monosaccharides and is crucial in various biological systems. Understanding its structure is paramount for students studying biochemistry or molecular biology.

At its core, the D-mannose structure can be represented in several ways, including the Fischer projection and the Haworth projection. In its linear form, it resembles glucose but differs at the C-2 position. D-mannose has a chain of six carbon atoms with hydroxyl (-OH) groups and hydrogen atoms attached. This configuration implies four of those carbon atoms are chiral, meaning they are connected to four distinct groups, leading to isomerism.

To determine how many chiral carbons D-mannose has, we count each carbon center that is bound to four different substituents. In D-mannose's case, four such chiral centers are identified: on the second, third, fourth, and fifth carbons. These chiral carbons are significant because they grant D-mannose the property of chirality, meaning it exists in two enantiomeric forms that are non-superimposable mirror images of each other.

Optical Isomerism

Optical isomerism is a fascinating concept in stereochemistry where two or more compounds, known as isomers, share the same molecular formula but differ in the spatial arrangement of atoms. These isomers are termed optical isomers or enantiomers.

An everyday analogy to help understand enantiomers is to think of your hands; they are mirror images of one another, yet they cannot be perfectly overlapped. In a chemical context, this characteristic exhibits specific implications when we interact with light. Enantiomers have the unique property to rotate plane-polarized light in different directions; one isomer will rotate light to the right (dextrorotary), while the other rotates it to the left (levorotary)

For D-mannose, the presence of chiral carbons means it can exist as two enantiomers. Even though these isomers might share the same physical and chemical properties, they can have drastically different interactions with biological systems. These differences often result in varying tastes, smells, and drug activities. Hence, comprehending optical isomerism is critical for designing pharmaceuticals and understanding metabolic pathways.

Pyranose Ring Form

The pyranose ring form represents a monosaccharide that has adopted a cyclic structure, incorporating a six-membered ring consisting of five carbon atoms and one oxygen atom. This depiction is well-illustrated in the Haworth projection, which gives a more realistic three-dimensional perspective of the molecule's spatial arrangement.

In the case of D-mannose, to achieve the pyranose ring form, a chemical reaction occurs within the molecule itself. The hydroxyl group on the fifth carbon atom reacts with the aldehyde group on the first carbon, creating a hemiacetal and forming the ring structure known as a pyranose, since it's related to the six-membered oxygen-containing heterocycle pyran.

The pyranose form of D-mannose, specifically, is referred to as D-mannopyranose. When drawing this structure, care must be taken to represent the orientation of the hydroxyl groups as per D-mannose's configuration. The accurate depiction of these groups is vital since it affects the sugar's reactivity and interaction with other molecules. In biochemistry, the ring form of sugars like D-mannose is crucial, as it represents the biologically relevant form in which these molecules generally exist and perform their functions in living organisms.