Chapter 5, Problem 36P

(a)

Interpretation Introduction

Interpretation: Whether the indicated cyclohexane derivative is chiral or not should be identified.

  

Concept introduction: Four kinds of symmetry elements that may be present are tabulated as follows:

  $\begin{array}{ccc}\text{S}\text{.No}& \text{Symmetry element}& \text{Notatio}n\\ 1.& \text{Axis of symmetry}& C_n\\ 2.& \text{Plane of symmetry}& \sigma \\ 3.& \begin{array}{l}\text{Alternating axis of }\\ \text{symmetry}\end{array}& S_n\\ 4.& \text{Center of symmetry}& i\end{array}$

The enantiomers are identical chemical compounds that have a mirror-image relationship to each other while diastereomers do not hold mirror image relationships. The former are chiral and optically active while the latter can be chiral or achiral.

Any organic compound must have no plane of symmetry in order to be optically active. The compounds with any plane of symmetry are achiral and optically inactive.

(b)

Interpretation Introduction

Interpretation: Whether the indicated cyclohexane derivative is chiral or not should be identified.

  

Concept introduction: Four kinds of symmetry elements that may be present are tabulated as follows:

  $\begin{array}{ccc}\text{S}\text{.No}& \text{Symmetry element}& \text{Notatio}n\\ 1.& \text{Axis of symmetry}& C_n\\ 2.& \text{Plane of symmetry}& \sigma \\ 3.& \begin{array}{l}\text{Alternating axis of }\\ \text{symmetry}\end{array}& S_n\\ 4.& \text{Center of symmetry}& i\end{array}$

The enantiomers are identical chemical compounds that have a mirror-image relationship to each other while diastereomers do not hold mirror image relationships. The former are chiral and optically active while the latter can be chiral or achiral.

Any organic compound must have no plane of symmetry in order to be optically active. The compounds with any plane of symmetry are achiral and optically inactive.

(c)

Interpretation Introduction

Interpretation: Whether the indicated cyclohexane derivative is chiral or not should be identified.

  

Concept introduction: Four kinds of symmetry elements that may be present are tabulated as follows:

  $\begin{array}{ccc}\text{S}\text{.No}& \text{Symmetry element}& \text{Notatio}n\\ 1.& \text{Axis of symmetry}& C_n\\ 2.& \text{Plane of symmetry}& \sigma \\ 3.& \begin{array}{l}\text{Alternating axis of }\\ \text{symmetry}\end{array}& S_n\\ 4.& \text{Center of symmetry}& i\end{array}$

The enantiomers are identical chemical compounds that have a mirror-image relationship to each other while diastereomers do not hold mirror image relationships. The former are chiral and optically active while the latter can be chiral or achiral.

Any organic compound must have no plane of symmetry in order to be optically active. The compounds with any plane of symmetry are achiral and optically inactive.

(d)

Interpretation Introduction

Interpretation: Whether the indicated cyclohexane derivative is chiral or not should be identified.

  

Concept introduction: Four kinds of symmetry elements that may be present are tabulated as follows:

  $\begin{array}{ccc}\text{S}\text{.No}& \text{Symmetry element}& \text{Notatio}n\\ 1.& \text{Axis of symmetry}& C_n\\ 2.& \text{Plane of symmetry}& \sigma \\ 3.& \begin{array}{l}\text{Alternating axis of }\\ \text{symmetry}\end{array}& S_n\\ 4.& \text{Center of symmetry}& i\end{array}$

The enantiomers are identical chemical compounds that have a mirror-image relationship to each other while diastereomers do not hold mirror image relationships. The former are chiral and optically active while the latter can be chiral or achiral.

Any organic compound must have no plane of symmetry in order to be optically active. The compounds with any plane of symmetry are achiral and optically inactive.