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Chapter 5: Problem 63

Draw tetrahedral representations of the two enantiomers of the amino acid cysteine, \(\mathrm{HSCH}_{2} \mathrm{CH}\left(\mathrm{NH}_{2}\right) \mathrm{CO}_{2} \mathrm{H},\) and identify each as \(R\) or \(S .\)

Short Answer

Expert verified
Draw each enantiomer's tetrahedral representation, assigning R or S based on the priority path direction: clockwise for R, counterclockwise for S.

Step by step solution

01

Assign Priorities to Substituents

For the central carbon in cysteine, identify the four substituents: -SH (sulfur-containing group), -CH\(_3\) (methyl group), -NH\(_2\) (amino group), and -COOH (carboxyl group). Assign priorities based on atomic number. The order of priority is SH > COOH > NH\(_2\) > CH\(_3\).
02

Arrange Molecule for Visualization

Visualize the tetrahedral arrangement of the substituents around the central carbon atom such that the lowest priority group (often hydrogen, but here a group like CH\(_3\)) is oriented away from you. This can be visualized as if it is behind the plane of the paper or screen.
03

Determine Configuration Using Cahn-Ingold-Prelog Rules

When looking at the chiral center, trace a path from the highest to the lowest priority (excluding the one pointing away). If this path is clockwise, the configuration is R; if it is counterclockwise, it is S.
04

Analyze Each Enantiomer

Draw the structure of cysteine to represent each enantiomer. Start with one possible arrangement and assign R or S configuration based on the path traced. Draw the mirror image for the other form and assign the opposite configuration.
05

Label Each Enantiomer

Label one structure as R-cysteine if the path traced clockwise matches with R and label the other as S-cysteine when traced counterclockwise. Both configurations are always mirror images.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cahn-Ingold-Prelog priority rules
The Cahn-Ingold-Prelog (CIP) priority rules are essential for determining the configuration of chiral centers in molecules. These rules help us assign a priority to each of the four substituents attached to a chiral center, which is usually a central carbon atom.

Here's how the rules work:
  • Priority is assigned based on the atomic number of the atoms directly attached to the chiral center; the higher the atomic number, the higher the priority.
  • If two atoms attached to the center are the same, you compare the atoms bonded to these atoms, moving outward until a difference is found.
  • For isotopes, the heavier isotope gets priority.
  • Double and triple bonds are treated as if they are bonded to equivalent multiple three or four single-bonded atoms.
In the exercise on cysteine, the substituents around the central carbon are -SH, -COOH, -NH extsubscript{2}, and -CH extsubscript{3}. The priorities are determined as SH > COOH > NH extsubscript{2} > CH extsubscript{3}, based on sulfur, carbon, nitrogen, and carbon, respectively. Prioritizing these allows us to correctly determine molecular configurations.
Tetrahedral stereochemistry
Tetrahedral stereochemistry refers to the three-dimensional arrangement of atoms around a central atom, typically carbon, in organic molecules. A key aspect of stereochemistry is understanding how atoms are spatially oriented to affect molecular behavior, important when studying chiral molecules.

The tetrahedral geometry involves:
  • A central atom bonded to four different substituents.
  • The bonds radiate out from the central atom at 109.5掳 angles, forming a three-dimensional shape.
  • The molecule's orientation determines how light is rotated concerning the chiral centers within these structures.
When visualizing tetrahedral stereochemistry, it helps to use models or draw representations where the lowest priority group is oriented away from the viewer. In our cysteine example, arranging substituents like -CH extsubscript{3} at the back helps determine the configuration by looking at the sequence of priorities visible on the plane.
Chiral center configuration
A chiral center, often found in organic molecules, is a carbon atom bonded to four distinct substituents. The configuration at the chiral center determines whether the molecule is an enantiomer's "R" or "S" form.

To determine this configuration:
  • Assign priorities using the Cahn-Ingold-Prelog rules to each substituent.
  • Position the molecule so the lowest priority substituent is oriented away from you. It resembles having this group behind the plane of focus.
  • Observe the sequence from highest to the lowest priority group and trace the path. If the tracing path is clockwise, the configuration is "R" (rectus for "right"); if counterclockwise, it is "S" (sinister for "left").
In cysteine, this approach allows us to distinguish its enantiomers. For instance, trace starting from the -SH group through -COOH and -NH extsubscript{2} to determine each configuration and label appropriately. Understanding this is imperative as it affects the properties and behavior of the compound significantly.

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Most popular questions from this chapter

Draw examples of the following: (a) A meso compound with the formula \(\mathrm{C}_{8} \mathrm{H}_{18}\) (b) A meso compound with the formula \(\mathrm{C}_{9} \mathrm{H}_{20}\) (c) A compound with two chirality centers, one \(R\) and the other \(S\)

Draw all possible stereoisomers of 1,2 -cyclobutanedicarboxylic acid, and indicate the interrelationships. Which, if any, are optically active? Do the same for 1,3 -cyclobutanedicarboxylic acid.

Draw a tetrahedral representation of ( \(S\) )-2-pentanol (2-hydroxypentane).

cis--1,2-Dimethylcyclohexane is optically inactive even though it has two chirality centers. Explain.

What are the stereochemical configurations of the two diastereomers of \((2 S, 4 R)-2,4\) -octanediol? (A diol is a compound with two -OH groups.)
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