Metamerism is a phenomenon in organic chemistry in which compounds have the same molecular formula but different structures. This occurs when the carbon skeleton and the functional groups in the compounds are arranged differently.

Let`s analyze each option to see if it exhibit metamerism:

Option 1: Methyl propylether and diethyl ether. Both of these compounds belong to the class of ethers. In methyl propylether, the carbon skeleton consists of a methyl group attached to a propyl group. In diethyl ether, the carbon skeleton consists of two ethyl groups. These compounds have the same molecular formula (C5H12O), but different structures. Therefore, option 1 is correct.

Option 2: Ethyl alcohol and dimethyl ether. Ethyl alcohol is an alcohol compound, while dimethyl ether is an ether compound. Although they have different functional groups, the carbon skeleton in these compounds is the same, consisting of two carbon atoms. Therefore, they do not exhibit metamerism.

Option 3: Propionic acid and acetic acid. Both propionic acid and acetic acid belong to the class of carboxylic acids. They have the same carbon skeleton, consisting of three carbon atoms. Therefore, these compounds do not exhibit metamer