To determine the general formula for a secondary amine, we must first understand what a secondary amine is.
An amine is a compound derived from ammonia (NH[tex]\(_3\)[/tex]) by replacing one or more hydrogen atoms with an alkyl or aryl group. Based on the number of hydrogen atoms replaced, amines are classified as primary, secondary, or tertiary:
- Primary Amine: One hydrogen atom is replaced by an alkyl or aryl group. The general formula is RNH[tex]\(_2\)[/tex].
- Secondary Amine: Two hydrogen atoms are replaced by alkyl or aryl groups. The general formula is R[tex]\(_2\)[/tex]NH.
- Tertiary Amine: All three hydrogen atoms are replaced by alkyl or aryl groups. The general formula is R[tex]\(_3\)[/tex]N.
Given this understanding:
1. [tex]$RNH _2$[/tex] represents a primary amine because it has one alkyl or aryl group attached to the nitrogen and two hydrogen atoms.
2. [tex]$H _2 NRNH _2$[/tex] is not a common notation and doesn't match the typical structure of any simple amine.
3. [tex]$RN _2 H$[/tex] is incorrect as it suggests the presence of two nitrogen atoms bonded to one hydrogen, which does not match the structure of a secondary amine.
4. [tex]$R _2 NH$[/tex] correctly represents a secondary amine because it has two alkyl or aryl groups attached to the nitrogen and one hydrogen atom.
Therefore, the general formula for a secondary amine is [tex]\(R_2NH\)[/tex].
