Q.57. - Organic Chemistry

Question

Question: Answer the following questions about compound A, which contains a $\mathbf{-}\mathit{C}{\mathit{H}}_{\mathbf{3}}$ group and OH group bonded to the carbon skeleton that consists of three six-membered rings in the conformation shown.

a. Are the $\mathbf{-}\mathit{C}{\mathit{H}}_{\mathbf{3}}$ and OH groups oriented cis or trans to each other?

b. Is a substituent on ${\mathit{C}}_{\mathbf{a}}$ that is cis to the $\mathit{C}{\mathit{H}}_{\mathbf{3}}$  group located in the axial or equatorial position?

c. Is an equatorial Br at ${\mathit{C}}_{\mathbf{b}}$ oriented cis or trans to the OH group?

d. Is the H atom on ${\mathit{C}}_{\mathbf{c}}$ located cis or trans to the OH group?

e. Is a substituent on ${\mathit{C}}_{\mathbf{d}}$ that is trans to the OH group located in the axial or equatorial position?

Step-by-Step Solution

Answer

Answer

1. The $C{H}_3$ and the OH groups are trans to each other.
2. The group on $C_a$ has to be in an equatorial position to remain cis to the  $C{H}_3$ group.
3. The equatorial Br at $C_b$ is cis to the OH group. 
4. The H atom on $C_c$ is cis to the OH group.
5. The $C_d$  substituent trans to the OH group is at the axial position. 

Step 1: Cis and Trans conformations

In stereoisomerism, the groups aligned either up or down the ring on either side of the axial or equatorial position are said to be in cis conformation. 

If one of the two groups is assigned up and the other down the ring, they are said to be in trans conformation.

Cis and trans positions of   groups

Step 2: Axial and equatorial positions

All axial groups and hydrogen atoms are located along the perpendicular axis, either up or down the ring. 

All equatorial groups and hydrogen atoms are aligned either up or down the plane (near the equator) of the ring.

Representation of axial and equatorial positions

Step 3: Cis and Trans groups in the given compound

a. The  $C{H}_3$ group is aligned on the axial up position of the ring and the OH group is aligned on the equatorial down position of the ring. Hence, both groups are trans to each other. 

 

b. The $C{H}_3$  group is aligned on the axial up position of the ring. So, a group on  $C_a$  has to be on the upper side of the ring to be in a cis alignment with the  $C{H}_3$ group.

 

Since carbon $C_a$  is down the ring, so a group on the axial position will also be at the same position. Hence, the group has to be in an equatorial position to remain cis to the  $C{H}_3$ group.

$C_a$ group cis to the $C{H}_3$  group

 

c. The  $C_b$ carbon is on the upper side. Hence, the axial group on $C_b$  will also be on the upper side of the ring. Hence, the equatorial Br group will be down at  $C_b$ carbon.

 

Since both OH and Br groups are down the ring, both are cis to each other. 

Equatorial Br cis to the OH group

 

d. The OH group is located on the equatorial down position. $C_c$ is located down the ring. Hence, the axial group will also be down the ring. The equatorial position of  $C_c$ is bonded to another ring. 

 

Hence, H will be on the axial down position on $C_c$ . So, H and OH groups will be cis to each other.

H atom located cis to the OH group

 

e. The OH group is located on the equatorial down position. For a group on $C_d$ to be trans to the OH group, it has to be on the upper side of the ring.

Since $C_d$ is the up carbon, the axial group will be on the upper side of the ring. 

 

Hence, a group on $C_d$  has to be in an axial position to be trans to the OH group.

Substituent on $C_d$ trans to OH