What is metamerism

Question

According to metamerism in polyvalent functional groups, if both alkyl groups' around functional group are different then they are considered as metamers but in few books it is given that if one of the alkyl group is different then it is a metamer.

In my opinion, for e.g. diethyl ether and methyl propyl ether are metamers. But methyl propyl ether and methyl isopropyl ether should be position isomers and not metamers.

Which is true?

Answer 1

The terms metamerism, or metamer, in a sense of chemical isomerism (there are other meanings in zoology and colorimetry), are very old. Presently, they are not used nor mentioned in authoritative chemistry texts.

Even the old Watts’ Dictionary of Chemistry from 1892 states the related terms do not have conclusive definition:

ISOMERISM. Even a superficial reader of chemical literature will soon become aware that the term isomeric and the kindred expressions allotropic, metameric, and polymeric are by no means always used in consistent senses, and he will have considerable difficulty in clearly realising their exact and relative import; (…)

(…)

METAMERISM. This term is generally applied to those cases if isomerism wherein compounds show identity of elementary composition, but belong to different types of classes (…).

(…)

(…) For example, it has long been a question whether ethylic acetoacetate is to be represented as $\ce{CH3-CO-CH2-CO2Et}$ or by the formula $\ce{CH3-C(OH)=CH-CO2Et}$. A discussion of such causes has been given by Laar (…), who proposes to term such isomerides tautomeric. But, as he practically himself admits, the use of such a term savours of tautology. V. Meyer subsequently brought forward a suggestion of Jacobson's to substitute desmotropic for tautomeric. Hantzsch and Herrmann (…), while using the term tautomerism when speaking of compounds capable of passing from the one type into the other, proposed to limit the term desmotropic to each of the states. As the phenomena in question are the outcome of mobility and not of fixity, the new term also appears to be particularly ill chosen, and bearing in mind the intention of Berzelius in introducing the term metameric (see p. 81), it would appear that this old term is a peculiarly appropriate one to use in such cases. (…)

Or S. A. Norton, The elements of chemistry: inorganic and organic (1884)

Isomerism.

Two or more compounds which contain the same elements, and have the same percentage composition, but differ in properties, are said to be isomeric. There are several varieties if Isomerism:

1. Bodies are physically isomeric when they differ only in certain physical properties, as their odors or their relation to polarized light. Over twenty volatile oils have the composition, $\ce{C10H16}$ (lemons, orange, bergamotte).
2. Bodies are isomeric in the strict sense of the word when they have the same vapor density, the same percentage composition, and exhibit similar chemical changes under similar circumstances. Thus there are two primary butyl alcohols which are strictly isomeric: $\ce{CH3CH2CH2CH2OH}$, and $\ce{(CH3)2CHCH2OH}$, and which give rise to other compounds, acids, ethers, etc., which are also isomeric.

3. In general use of the word, metameric bodies are also called isomers. Bodies are metameric when they have the same percentage composition and the same molecular weight, but exhibit dissimilar chemical properties under similar circumstances.

   Propionic acid, methyl acetate, and ethyl formate have the same molecular formula, $\ce{C3H6O2}$, but when acted upon by caustic potash yield very dissimar products:
   (…)

   Some metamers are so totally different that no resemblances of structure have been imagined to exist. Such are starch and gum arabic, which are pseudo-isomers.

   Metamers are found in all terms above $\ce{C3}$, and increase in number very rapidly with each addition of $\ce{CH2}$. There are four butyl alcohols known, two primary, which are strictly isomeric with each other, and two others metameric with these, which do not form corresponding acids and ethers.

4. Polymeric bodies agree in percentage composition, but do not have the same molecular weight. Their formulæ are multiples of some empirical formulæ common to all, as the $\ce{CH2}$ in the olefines, $\ce{C_nH_{2n}}$.

So, the historical meaning of mesomers is that they are isomers with very diferent properties, different functional groups.

Contrarily, there are several organic chemistry textbooks (mostly Indian provenience), with somewhat contrary definition, e.g. Tewari & Vishnoi: A Textbook of Organic Chemistry, 4th Edition:

Metamerism

Compounds of the same homologous series show this type of isomerism because of unequal distribution of carbon atoms (…)

(…)

(ii) Metamerism. The carbonyl group may occupy different position in the carbon chain to give metamers.

$\ce{CH3CH2COCH2CH3}$      $\ce{CH3CH2CH2COCH3}$

Therefore I think that these terms should not be used.

Answer 2

The question is ill posed. Both alkyl groups are different.... (from each other?) if one alkyl group is different (from what?)... Metamers are isomers which differs by the structural carbon atoms distribution at the sides of a polivalent functional group. As such given a linear chain they are positional isomers too, with respect to the position of the polivalent functional group. All four ethers you posed as example are metamers. Personally I never heard of metamers except in an introductory course, for that matter.