Question

(a) How many chiral centers are there in (+)-fructose? (b) How many stereo isomeric 2-ketohexoses should there be? (c) Draw a "cross" formula of one enantiomer of each pair, placing \(\mathrm{C}=\mathrm{O}\) near the top, and \(-\mathrm{OH}\) on the right on the lowest chiral center \((\mathrm{C}-5)\).

Short answer

(a) There are 4 chiral centers in (+)-fructose, located at C2, C3, C4, and C5. (b) There are 8 stereoisomeric 2-ketohexoses, as calculated using the formula \( 2^n \), where \( n \) is the number of chiral centers (in this case, n=3). (c) The cross formula of one enantiomer for each pair of 2-ketohexoses with specified positions, according to the question: 1. D(+)-ribose: 2(R),3(S),4(R),5(S) 2. D(+)-altrose: 2(S),3(S),4(S),5(S) 3. D(+)-allose: 2(S),3(S),4(R),5(S) 4. D(+)-glucose: 2(R),3(R),4(R),5(S) 5. D(+)-idose: 2(R),3(S),4(S),5(S) 6. D(+)-galactose: 2(R),3(R),4(S),5(S) 7. D(+)-gulose: 2(S),3(R),4(S),5(S) 8. D(+)-mannose: 2(S),3(R),4(R),5(S)

Step-by-step solution

Part (a): Number of Chiral Centers in (+)-Fructose

The molecular formula of (+)-fructose is \( C_6H_{12}O_6 \). Fructose is a hexose sugar, which means it contains six carbon atoms. In order to find the chiral centers, we need to look at the structure of fructose. Fructose has four chiral centers, located at carbon 2 (C2), carbon 3 (C3), carbon 4 (C4), and carbon 5 (C5). All of these chiral centers have four different groups bonded to them, which give them the ability to create stereoisomers.

Part (b): Number of Stereoisomeric 2-ketohexoses

A 2-ketohexose is a hexose sugar (six-carbon sugar) with a ketone group on the second carbon atom. There are three chiral centers (C3, C4, and C5); for each chiral center, there are two possible configurations: either R or S configuration. To find the total number of stereoisomeric 2-ketohexoses, we can use the formula: Total stereoisomers = \( 2^n \), where \( n \) is the number of chiral centers. In this case, \( n = 3 \), Executing the formula, we get: Total stereoisomers = \( 2^3 \) = 8 There should be 8 stereoisomeric 2-ketohexoses.

Part (c): Drawing the Cross Formula of One Enantiomer of Each Pair

Following the instruction to place the C=O group near the top and -OH on the right on the lowest chiral center (C5), we can draw the cross formula of one enantiomer of each pair: 1. D(+)-ribose: 2(R),3(S),4(R),5(S) 2. D(+)-altrose: 2(S),3(S),4(S),5(S) 3. D(+)-allose: 2(S),3(S),4(R),5(S) 4. D(+)-glucose: 2(R),3(R),4(R),5(S) 5. D(+)-idose: 2(R),3(S),4(S),5(S) 6. D(+)-galactose: 2(R),3(R),4(S),5(S) 7. D(+)-gulose: 2(S),3(R),4(S),5(S) 8. D(+)-mannose: 2(S),3(R),4(R),5(S) Thus, we have drawn the cross formula of one enantiomer of each pair of 2-ketohexoses, with the specified positions of the C=O and -OH groups.

Key concepts

Chiral Centers

Chiral centers, also known as stereocenters, are carbon atoms within a molecule that have four different groups attached to them. This unique setup makes the carbon atom a point of asymmetry and enables the molecule to exist in different spatial arrangements known as stereoisomers. These chiral centers are the reason why many compounds, including carbohydrates, can have multiple forms that are mirror images of each other but cannot be superimposed.

Understanding chiral centers is crucial in the study of carbohydrates because their arrangement dictates the sugar's physical and biological properties. For instance, (+)-fructose, a common sugar found in fruits, has four chiral centers. Each of these can exist in different configurations, multiplying the possibilities for structural variation within the molecule.

2-Ketohexoses

2-Ketohexoses are sugars that contain six carbon atoms, with a ketone group located at the second carbon. This structural feature distinguishes them from other hexose sugars, such as those with an aldehyde group at the first carbon. The ketone group is crucial because it influences how the sugar interacts with other molecules and how it behaves in biological systems.

The presence of chiral centers in 2-ketohexoses allows for a variety of stereoisomers to exist. For every chiral center, two possible spatial arrangements can occur, often denoted as R (rectus) or S (sinister) configuration. Applying this to all the chiral centers results in a multiplicity of unique molecules. For example, a 2-ketohexose with three chiral centers can exist in eight possible stereo configurations.

Enantiomers

Enantiomers are a special type of stereoisomers that are mirror images of each other but are not superimposable. This means that no matter how you try to align them, they will never perfectly overlap—much like your left and right hands. Enantiomers have identical physical properties in a non-chiral environment, but they can interact with polarized light and biological systems in distinct ways.

In carbohydrate chemistry, enantiomers could have dramatically different tastes or metabolic effects. For example, the D-form of sugars is commonly found in nature and is biologically active for most organisms, while the L-form might not be. This distinction is essential in the development of pharmaceuticals and understanding the nutritional properties of different sugars.

Structural Isomerism

Structural isomerism is the occurrence of molecules that have the same molecular formula but differ in the way their atoms are connected. In carbohydrates, structural isomerism arises due to the different possible arrangements of the hydroxyl (-OH) groups and the placement of the carbonyl group (either as an aldehyde or ketone).

For instance, glucose and fructose both have the formula C6H12O6, but glucose has an aldehyde group at carbon 1, while fructose has a ketone group at carbon 2. This difference is not just a small detail—it affects the sugar's reactivity, how it tastes, and how it is metabolized by living organisms. Understanding structural isomerism helps to explain the diverse range of functions and properties that carbohydrates can have.

Carbohydrate Stereochemistry

Carbohydrate stereochemistry deals with the spatial arrangement of atoms within sugar molecules and is a key aspect in understanding how carbohydrates perform their functions in biological systems. The orientation of hydroxyl (-OH) groups on each chiral center can give rise to different properties, such as sweeteners versus non-sweeteners or digestible versus non-digestible carbohydrates.

When talking about carbohydrate stereochemistry, it's not only important to know the count and location of chiral centers but also the specific configuration at each center. For example, when referring to the 2-ketohexoses mentioned earlier, knowing that there are eight different stereo isomers is important, but it is equally critical to understand their specific arrangements to predict or explain their behavior in real-world applications, like food production or medicinal chemistry.