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Chapter 28: Problem 61

Projection formulas impose certain limitations and care must be taken in drawing and manipulating them. Use (R)-(+)-glyceraldehyde as an example and show that: (a) Rotating the Fischer projection by \(90^{\circ}\) in the plane of the paper produces the opposite absolute configuration. What is the effect of rotation by \(180^{\circ}\) and \(270^{\circ}\) in the plane of the paper? (b) Interchanging two substituents converts one enantiomer into the other. What is the effect of two such interchanges?

Short Answer

Expert verified
Rotating the Fischer projection by \(90^{\circ}\) or \(270^{\circ}\) inverts the configuration of the molecule while \(180^{\circ}\) rotation retains the same configuration. Interchanging two substituents inverts the configuration, but two such interchanges restore the original configuration.

Step by step solution

01

Understanding Chiral Centers and Fischer Projections

A chiral center is a carbon atom that is attached to four different types of atoms or groups of atoms. (R)-(+)-glyceraldehyde, in this case, is represented using Fischer projections, which is a 2D representation of a 3D molecule. In the Fischer projection, the vertical lines represent bonds that point into the plane of the paper (away from the viewer) while horizontal lines represent bonds coming out of the plane of the paper (towards the viewer).
02

Rotation of the Fischer Projection

In the first part, rotating the Fischer projection by \(90^{\circ}\) in the plane of the paper will reverse the configuration, turning an (R) structure into an (S) structure, or vice versa. Rotating by \(180^{\circ}\) will give the mirror image, but will retain the same configuration due to inversion, i.e., it remains (R)-(+)-glyceraldehyde. Similarly, a rotation of \(270^{\circ}\) will again invert the configuration; for example, from (R) to (S) or vice versa.
03

Interchanging Substituents

In the second part, interchanging two substituents on the chiral center converts one enantiomer to another, i.e., it alters the configuration from (R) to (S) or vice versa. If two such interchanges are made, it would restore the original configuration since each interchange inverts the configuration.

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Most popular questions from this chapter

The structure of the DNA molecule is best described as (a) a random coil; (b) a double helix; (c) a pleated sheet; (d) partly coiled; (e) a branched chain.

The following terms are all related to stereoisomers and their optical activity. Explain the meaning of each: (a) dextrorotatory; (b) levorotatory; (c) racemic mixture; (d) \((R)\).

In your own words, define the following terms or symbols: (a) \((+) ;\) (b) \(\mathrm{L} ;\) (c) sugar; (d) \(\alpha\) -amino acid; (e) isoelectric point.

If \(\mathrm{D}-(+)\) -glyceraldehyde is treated with \(\mathrm{HCN}\) in aqueous solution under basic conditions for three days at room temperature, cyanohydrins are formed (see Chapter 27). The cyanohydrins are not isolated, but are hydrolyzed to hydroxyacids in the same reaction mixture using dilute sulfuric acid. In this process, a new stereocenter is formed in the molecule. The products are diastereomers, formed in unequal amounts, and separable from each other by recrystallization because of their different physical properties, including solubilities. The trihydroxybutanoic acids are separated and then oxidized to tartaric acid with dilute nitric acid, which oxidizes only the primary alcohol group. (a) Ignoring stereochemistry, draw the reaction sequence for the transformations described above and hence deduce the structure of tartaric acid. (b) Starting from the Fischer projection of \(\mathrm{D}-(+)-\) glyceraldehyde and using the reaction scheme from part (a), draw Fischer projections of the two trihydroxybutanoic acids formed and designate the chiral centers as \(R\) or \(S\). (c) Starting from the Fischer projection of \(\mathrm{D}-(+)-\) glyceraldehyde and using the reaction scheme from part (a), draw Fischer projections of the two forms of tartaric acid formed and designate the chiral centers as \(R\) or \(S\). (d) One form of tartaric acid obtained is optically active, rotating the plane of polarized light in a negative sense \((-) .\) The other isomer formed, called meso-tartaric acid, is not optically active. Explain why the other isomer is not optically active. Draw the dashed-wedged line structure that corresponds to the Fischer projection of meso-tartaric acid. Can you describe how the two halves of the molecule are related? Using Fischer projections, write equations for the conversion of \(L-(-)-\) glyceraldehyde to tartaric acid. Show clearly the stereochemistry of the tartaric acids that are formed, and indicate whether you expect them to be optically active.

Briefly describe each of the following ideas, phenomena, or methods: (a) saponification; (b) chiral carbon atom; (c) racemic mixture; (d) denaturation of a protein.
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