Chapter 5, Problem 5.27P

The amino acid $\left(S\right)\text{-alanine}$ has the physical characteristics listed under the structure.

(S)-alanine

$\left[\text{α}\right]=+8.5$

$\text{mp}=297°\text{C}$

a. What is the melting point of $\left(R\right)\text{-alanine}$?

b. How does the melting point of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ compare to the melting point of $\left(S\right)\text{-alanine}$?

c. What is the specific rotation of $\left(R\right)\text{-alanine}$, recorded under the same conditions as the reported rotation of $\left(S\right)\text{-alanine}$?

d. What is the optical rotation of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$?

e. Label each of the following as optically active or inactive: a solution of pure $\left(S\right)\text{-alanine}$; an equal mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$; a solution that contains $75\%\left(S\right)\text{-}\text{and}25\%\left(R\right)\text{-alanine}$.

Interpretation Introduction

(a)

Interpretation: The melting point of $\left(R\right)\text{-alanine}$ is to be predicted.

Concept introduction: Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. Diastereomers are the stereoisomers that have the opposite $R,S$ notations for at least one stereogenic center and the same $R,S$ notations for at least one stereogenic center. Enantiomers have identical physical properties, whereas diastereomers have different physical properties.

Answer to Problem 5.27P

The melting point of $\left(R\right)\text{-alanine}$ is $297°\text{C}$.

Explanation of Solution

The given melting point of $\left(S\right)\text{-alanine}$ is $297°\text{C}$. The $\left(R\right)\text{-alanine}$, and $\left(S\right)\text{-alanine}$ are the enantiomers. Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. Therefore, the melting point of $\left(R\right)\text{-alanine}$ is also $297°\text{C}$.

Conclusion

The melting point of $\left(R\right)\text{-alanine}$ is $297°\text{C}$.

Interpretation Introduction

(b)

Interpretation: The melting point of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is to be compared with the melting point of $\left(S\right)\text{-alanine}$.

Concept introduction: Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. A racemic mixture is obtained when $\left(R\right)\text{- and}\left(S\right)$ enantiomers are mixed in equal amount. Their racemic mixture possess different physical properties than parent one.

Answer to Problem 5.27P

The melting point of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is different with the melting point of $\left(S\right)\text{-alanine}$.

Explanation of Solution

The given melting point of $\left(S\right)\text{-alanine}$ is $297°\text{C}$. The $\left(R\right)\text{-alanine}$, and $\left(S\right)\text{-alanine}$ are the enantiomers. Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. A racemic mixture is obtained when $\left(R\right)\text{-}\text{and}\left(S\right)$ enantiomers are mixed in equal amount. Their racemic mixture possess different physical properties than parent one.

Therefore, the melting point of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is different with the melting point of $\left(S\right)\text{-alanine}$.

Conclusion

The melting point of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is different with the melting point of $\left(S\right)\text{-alanine}$.

Interpretation Introduction

(c)

Interpretation: The specific rotation of $\left(R\right)\text{-alanine}$ is to be predicted.

Concept introduction: Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. Their specific rotation values are opposite in sign but equal in magnitude, when they are recorded under same condition.

Answer to Problem 5.27P

The specific rotation of $\left(R\right)\text{-alanine}$ is $-8.5$.

Explanation of Solution

The specific rotation of $\left(S\right)\text{-alanine}$ is $+8.5$. The $\left(R\right)\text{-alanine}$, and $\left(S\right)\text{-alanine}$ are the enantiomers. Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. Their specific rotation values are opposite in sign but equal in magnitude, when they are recorded under same condition.

Thus, the specific rotation of $\left(R\right)\text{-alanine}$ is $-8.5$.

Conclusion

The specific rotation of $\left(R\right)\text{-alanine}$ is $-8.5$.

Interpretation Introduction

(d)

Interpretation: The optical rotation of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is to be calculated.

Concept introduction: Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. A racemic mixture is obtained when $\left(R\right)\text{- and}\left(S\right)$ enantiomers are mixed in equal amount.

Answer to Problem 5.27P

The optical rotation of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is zero.

Explanation of Solution

The specific rotation of $\left(S\right)\text{-alanine}$ is $+8.5$.

The specific rotation of $\left(R\right)\text{-alanine}$ is $-8.5$.

The $\left(R\right)\text{-alanine}$, and $\left(S\right)\text{-alanine}$ are the enantiomers. Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. A racemic mixture is obtained when $\left(R\right)\text{-}\text{and}\left(S\right)$ enantiomers are mixed in equal amount.

Thus, the optical rotation of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is zero $\left(-8.5+8.5=0\right)$.

Conclusion

The optical rotation of a racemic mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is zero.

Interpretation Introduction

(e)

Interpretation: The solutions of pure $\left(S\right)\text{-alanine}$, an equal mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$, $75\%\left(S\right)\text{- and}25\%\left(R\right)\text{-alanine}$ are to be labeled as optically active or inactive.

Concept introduction: Enantiomers are the stereoisomers that have exactly opposite $R,S$ notations. They possess identical physical properties. A racemic mixture is obtained when $\left(R\right)\text{-}\text{and}\left(S\right)$ enantiomers are mixed in equal amount. Their racemic mixture possess different physical properties than parent one.

Answer to Problem 5.27P

The pure $\left(S\right)\text{-alanine}$ is labeled as optically active, an equal mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is labeled as optically inactive, $75\%\left(S\right)\text{- and}25\%\left(R\right)\text{-alanine}$ is labeled as optically active.

Explanation of Solution

The pure $\left(S\right)\text{-alanine}$ is an enantiomer. Enantiomers are optically active compounds. Thus, $\left(S\right)\text{-alanine}$ is optically active compound.

A racemic mixture is obtained when $\left(R\right)\text{-}\text{and}\left(S\right)$ enantiomers are mixed in equal amount. Thus, an equal mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is optically inactive.

A $75\%\left(S\right)\text{- and}25\%\left(R\right)\text{-alanine}$ solution is optically active. Because, in solution $25\%\left(R\right)\text{-alanine}$ cancel only $25\%\left(S\right)\text{-alanine}$ and still $50\%$ of $\left(S\right)\text{-alanine}$ is left. Therefore, $75\%\left(S\right)\text{-}\text{and}25\%\left(R\right)\text{-alanine}$ solution is optically active.

Thus, the pure $\left(S\right)\text{-alanine}$ is labeled as optically active, an equal mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is labeled as optically inactive, $75\%\left(S\right)\text{-}\text{and}25\%\left(R\right)\text{-alanine}$ is labeled as optically active.

Conclusion

The pure $\left(S\right)\text{-alanine}$ is labeled as optically active, an equal mixture of $\left(R\right)\text{-}\text{and}\left(S\right)\text{-alanine}$ is labeled as optically inactive, $75\%\left(S\right)\text{-}\text{and}25\%\left(R\right)\text{-alanine}$ is labeled as optically active.