The question asks to identify the metamer of the given compound (X), which is N-phenylcyclohexanecarboxamide, from the given options.
Concept Used:
Metamers are a type of structural isomer that have the same molecular formula and the same polyvalent functional group, but differ in the nature of the alkyl or aryl groups attached to the sides of the functional group. In this case, the polyvalent functional group is the amide linkage \((-NH-C(=O)-)\).
To be a metamer of compound (X), a molecule must:
Have the same molecular formula as (X).
Contain the same amide functional group.
Have a different arrangement of alkyl/aryl groups attached to the nitrogen and the carbonyl carbon of the amide group.
Step-by-Step Solution:
Step 1: Analyze the structure and determine the molecular formula of the given compound (X).
The compound (X) is N-phenylcyclohexanecarboxamide. It consists of a phenyl group (\(C_6H_5\)) attached to the nitrogen atom and a cyclohexyl group (\(C_6H_{11}\)) attached to the carbonyl carbon.
\[
\text{Molecular formula of (X)} = (C_6H_5) + (NH) + (CO) + (C_6H_{11})
\]
\[
= C_{(6+1+6)}H_{(5+1+11)}NO = C_{13}H_{17}NO
\]
The groups attached to the amide linkage are: Phenyl on the N-side and Cyclohexyl on the C=O side.
Step 2: Analyze each option to check its molecular formula and structure.
Option (1): N-phenylbenzamide
Structure: \(C_6H_5-NH-CO-C_6H_5\)
Molecular formula: \(C_{(6+1+6)}H_{(5+1+5)}NO = C_{13}H_{11}NO\). The molecular formula is different from (X). Thus, it is not an isomer.
Option (2): 4-(cyclohexylamino)benzaldehyde
Structure: \(OHC-C_6H_4-NH-C_6H_{11}\). This compound has an amide-like linkage but also contains an aldehyde functional group (\(-CHO\)).
Although the molecular formula is the same, the functional group is different (it is an amino-aldehyde). Therefore, it is a functional isomer, not a metamer.
Option (3): N-cyclohexylcyclohexanecarboxamide
Structure: \(C_6H_{11}-NH-CO-C_6H_{11}\)
Molecular formula: \(C_{(6+1+6)}H_{(11+1+11)}NO = C_{13}H_{23}NO\). The molecular formula is different from (X). Thus, it is not an isomer.
The molecular formula is the same as that of compound (X).
Step 3: Compare compound (4) with compound (X) based on the definition of metamers.
Both (X) and (4) have the same molecular formula: \(C_{13}H_{17}NO\).
Both (X) and (4) have the same amide functional group.
In compound (X), the groups are Phenyl (\(C_6H_5\)) on the N-side and Cyclohexyl (\(C_6H_{11}\)) on the C=O side.
In compound (4), the groups are Cyclohexyl (\(C_6H_{11}\)) on the N-side and Phenyl (\(C_6H_5\)) on the C=O side.
Since the arrangement of the aryl and alkyl groups around the amide functional group is different, compounds (X) and (4) are metamers of each other.
Final Computation & Result:
Based on the analysis, compound (4) has the same molecular formula and the same functional group as compound (X) but differs in the arrangement of the groups attached to the amide linkage.
Therefore, option (4) is the metamer of the given compound (X).
