To determine which compound exhibits metamerism, we need to understand the concept of metamerism in organic chemistry. Metamerism is a type of isomerism where compounds (metamers) have the same molecular formula but differ in the alkyl groups attached to a functional group or the same multivalent atom.
Let's analyze each of the given options:
\(C _{5} H _{12}\): This is the molecular formula for alkanes such as pentane. Alkanes do not exhibit metamerism as there is no functional group or heteroatom for chain variation.
\(C _{3} H _{8} O\): This is the molecular formula for alcohols like propanol and ethers such as methoxyethane. However, with only three carbons, there isn't enough variability in chain structure to exhibit metamerism.
\(C _{3} H _{6} O\): This corresponds to aldehydes and ketones, like propanal and acetone, but again, similar to the previous case, there are not enough distinct chains to exhibit metamerism with this small number of total carbons.
\(C _{4} H _{10} O\): This formula can correspond to ethers like diethyl ether (CH3CH2OCH2CH3) and methyl propyl ether (CH3OCH2CH2CH3). These represent structural isomers with different alkyl groups on either side of the oxygen atom, thus displaying metamerism.
Thus, the correct answer is \(C _{4} H _{10} O\), as it can form metamers with different alkyl group arrangements around the ether functional group.
In simple words, multiple compounds having the same molecular formulae but different structural formulae are referred to as isomers and this entire phenomenon is described as ‘Isomerism’. ‘Isos’ and ‘meros’ are Greek words that translate to ‘equal parts’.
Types of Isomerism:
Isomerism can be differentiated by primary types and their subtypes.
Structural Isomerism
Ring Chain Isomerism, Chain Isomerism, Tautomerism, Functional Isomerism, Metamerism, and Positional Isomerism are the subtypes of Structural Isomerism.
Stereoisomerism
Optical Isomerism & Geometric Isomerism are the two subtypes of Stereoisomerism.
The phenomenon when the compounds start showing isomerism because of their different structure is termed Structural Isomerism. Example - Isobutane and n-butane
Structural Isomerism can further be classified into various types such as chain isomerism, positional isomerism, functional isomerism, metamerism, ring-chain isomerism, and tautomerism.
Ring Chain isomerism
In the ring chain isomerism, there will be an open-chain structure in any one of the isomers and the remaining will have a closed chain or a ring structure. These kinds of compounds are known as ring chain isomers and this phenomenon is termed ring chain isomerism. The number of pi bonds in ring chain isomers will be different. Example - Cyclopropane and Propene. Their molecular formula is C3H6
Chain isomerism
In chain isomerism, there will be different branches of carbon atoms in multiple isomers compounds but still, their molecular formula remains the same. Skeleton isomerism is the other term used to refer to chain isomerism. Example- 2 methyl butane, 2-2 dimethyl propane, and n-pentane. Their molecular formula is C5H12
Tautomerism
In tautomerism, there will be a difference in isomer compounds only in the position of electrons, protons, and atoms. Tautomers take place in an equilibrium state as they can easily interchange. Example - Keto-enol tautomerism
Functional Isomerism
In functional isomerism, the isomer compounds with different functional groups have the same molecular formula. Example - dimethyl ether and ethanol. They both have the same molecular formula C2H6 O. The functional group of Ethanol is ‘OH’ while the Functional group of dimethyl ether is ‘R-O-R’.
Metamerism
In metamerism, each side of the functional group has the presence of different alkyl chains. Compared with other types of isomerism, metamerism is rarely found and is constrained to molecules with atoms. Example - Methoxy-propane (CH3OC3H7) & ethoxyethane (C2H5OC2H5)
Positional Isomerism
In Positional isomerism, the functional groups and substituents of a structural isomer will have different positions. Example - 1-Chloropropane and 2-Chloropropane
Stereoisomerism
The phenomenon when compounds start showing different spatial arrangements of atoms even when their molecular formula is the same is termed Stereoisomerism. Example - 1,2 - dichloroethene (C2H2CI2)
Optical isomerism
In optical isomerism, the isomer Compounds differ in terms of optical activity but are mirror images of each other. In this subtype of Stereoisomerism, carbon atoms are connected to four different groups and this is known as the chiral center. Enantiomers is the term mostly used to refer to optical isomers.
In Dextro optical isomers plane of polarized light is rotated to the right. In Laevo optical Isomers, the plane of polarized light is rotated to the left.
Geometric isomerism
In geometric isomerism, the spatial positions of molecules are locked because of the presence of a double bond or ring structure. It is often referred to as Cis-Trans isomerism. Groups connected to ring structure carbon atom must be different in geometric isomerism.
are isomeric compounds. 
are functional group isomers.
