Chapter 15, Problem 15.21P

15-21 Answer true or false.

1. For a molecule with two stereocenters, 2² = 4 stereoisomers are possible.

For a molecule with three stereocenters, 3² = 9 stereoisomers are possible.

Enantiomers, like gloves, occur in pairs.

2-Pentanol and 3-pentanol are both chiral and show enantiomerism.

1-Methylcyclohexanol is achiral and does not show enantiomerism.

Diastereomers are stereoisomers that are not mirror images.

Interpretation Introduction

(a)

Interpretation:

To analyze whether the given statement- For a molecule with two stereocenters, 2² =4 stereoisomers are possible, is true or false.

Concept Introduction:

Stereoisomerism deals with the study of the spatial arrangements of the atoms in space. It does not mean to alter the connectivity of the atoms by mean of forming or breaking the bonds.

A molecule is said to be chiral if it cannot be superimposed on its mirror image and if it does not possess an alternate axis of symmetry.

A carbon atom bonded in a tetrahedral structure to four different substituents in a molecule, it is called as a chiral centre or stereocentre.

If an organic molecule has more than one chiral carbon or chiral centre then the molecule may be achiral or chiral and it is depend upon whether the molecule has element of symmetry or not.

Answer to Problem 15.21P

For a molecule with two stereocenters, 2² =4 stereoisomers are possible. Thus, given statement is true.

Explanation of Solution

According to van't Hoff rule, if a molecule contains n number of chiral carbons, provided it does not contain any elements of symmetry, and then the number of stereoisomers is given by- 2ⁿ.

Therefore for a molecule with 2 stereocenters, the possible isomer is given as-

2² =4.

Therefore, 4 stereoisomers are possible.

Interpretation Introduction

(b)

Interpretation:

To analyze whether the given statement- For a molecule with three stereocenters, 3² =9 stereoisomers are possible, is true or false.

Concept Introduction:

Stereoisomerism deals with the study of the spatial arrangements of the atoms in space. It does not mean to alter the connectivity of the atoms by mean of forming or breaking the bonds.

A molecule is said to be chiral if it cannot be superimposed on its mirror image and if it does not possess an alternate axis of symmetry.

A carbon atom bonded in a tetrahedral structure to four different substituents in a molecule, it is called as a chiral centre or stereocentre.

If an organic molecule has more than one chiral carbon or chiral centre then the molecule may be achiral or chiral and it is depend upon whether the molecule has element of symmetry or not.

Answer to Problem 15.21P

For a molecule with three stereocenters, 3² =9 stereoisomers are possible. Thus, given statement is true.

Explanation of Solution

According to van't Hoff rule, if a molecule contains n number of chiral carbons, provided it does not contain any elements of symmetry, and then the number of stereoisomers is given by- 2ⁿ.

Therefore for a molecule with 3 stereocenters, the possible isomer is given as-

3² =9.

Therefore, 9 stereoisomers are possible.

Interpretation Introduction

(c)

Interpretation:

To analyze whether the given statement- Enantiomers, like gloves, occur in pairs, is true or false.

Concept Introduction:

Stereoisomerism deals with the study of the spatial arrangements of the atoms in space. It does not mean to alter the connectivity of the atoms by mean of forming or breaking the bonds.

Compounds with a chiral centre exist in enantiomeric forms. The phenomenon of enantiomerism is called as optical isomerism. If the configuration at each stereocenter is changed, the enantiomer is converted into another enantiomer.

Answer to Problem 15.21P

Enantiomers, like gloves, occur in pairs.

Explanation of Solution

Isomers which are non-superimposable mirror images of each other are called Enantiomers.

Compounds with a chiral centre exist in enantiomeric forms. The phenomenon of enantiomerism is called as optical isomerism. If the configuration at each stereocenter is changed, the enantiomer is converted into another enantiomer.

Hence, Enantiomers, like gloves, occur in pairs.

Interpretation Introduction

(d)

Interpretation:

To analyze whether the given statement- 2-Pentanol and 3-Pentanol are both chiral and show enantiomerism, is true or false.

Concept Introduction:

Stereoisomerism deals with the study of the spatial arrangements of the atoms in space. It does not mean to alter the connectivity of the atoms by mean of forming or breaking the bonds.

Compounds with a chiral centre exist in enantiomeric forms. The phenomenon of enantiomerism is called as optical isomerism. If the configuration at each stereocenter is changed, the enantiomer is converted into another enantiomer.

Answer to Problem 15.21P

Only 2-Pentanol is chiral and show enantiomerism.

Explanation of Solution

Isomers which are non-superimposable mirror images of each other are called Enantiomers.

In 2-Pentanol, the carbon-2 is attached to four different groups namely- a methyl group, a propyl group, hydroxyl group and hydrogen.

Therefore it has a stereocenter, it forms a mirror image that is non-superimposable, and therefore they show isomerism.

has a mirror image as

In 3-Pentanol, the carbon-2 is attached to four groups namely- two ethyl group, hydroxyl group and hydrogen.

Therefore it does not have a stereocenter, it forms a mirror image that is superimposable, and therefore they do not show isomerism.

has a mirror image as

Interpretation Introduction

(e)

Interpretation:

To analyze whether the given statement- 1-Methylcyclohexanol is achiral and does not show enantiomerism, is true or false.

Concept Introduction:

Stereoisomerism deals with the study of the spatial arrangements of the atoms in space. It does not mean to alter the connectivity of the atoms by mean of forming or breaking the bonds.

Compounds with a chiral centre exist in enantiomeric forms. The phenomenon of enantiomerism is called as optical isomerism. If the configuration at each stereocenter is changed, the enantiomer is converted into another enantiomer.

Answer to Problem 15.21P

1-Methylcyclohexanol is achiral and does not show enantiomerism.

Explanation of Solution

1- Methylcyclohexanol has a plane of symmetry due to which it is not optically active.

1- Methylcyclohexanol is achiral and doesn’t show enantiomerism.

Interpretation Introduction

(f)

Interpretation:

To analyze whether the given statement- Diastereomers are stereoisomers that are not mirror images, is true or false.

Concept Introduction:

Stereoisomerism deals with the study of the spatial arrangements of the atoms in space. It does not mean to alter the connectivity of the atoms by mean of forming or breaking the bonds.

Compounds with a chiral centre exist in enantiomeric forms. The phenomenon of enantiomerism is called as optical isomerism. If the configuration at each stereocenter is changed, the enantiomer is converted into another enantiomer.

Answer to Problem 15.21P

Diastereomers are Stereoisomers that are not mirror images.

Explanation of Solution

Stereoisomers which don't have any mirror image relationship are called Diastereomers.

Diastereomers are non-enantiomeric stereoisomers which have two or more stereocenter and differ only in configuration of at least one of them.

Example-

In tartaric acid,

and are diastereomers.