Draw structural formulas for the three secondary amines with the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{11} \mathrm{~N}\).

The nitrogen atom is connected to two carbon atoms in a secondary amine. Let's denote these two carbon atoms as \(C_{1}\) and \(C_{2}\).

As there are 4 carbon atoms in the molecular formula, we have 2 carbon atoms remaining. We can distribute these carbon atoms between \(C_{1}\) and \(C_{2}\) in three possible ways: 1. \(C_{1}\) has 0 remaining carbon atoms and \(C_{2}\) has 2 remaining carbon atoms. 2. \(C_{1}\) has 1 remaining carbon atom and \(C_{2}\) has 1 remaining carbon atom. 3. \(C_{1}\) has 2 remaining carbon atoms and \(C_{2}\) has 0 remaining carbon atoms.

Now we need to configure the remaining hydrogen atoms for each case in order to satisfy the valency requirement for each carbon atom. 1. In the first case, \(C_{1}\) has 0 remaining carbon atoms and \(C_{2}\) has 2 remaining carbon atoms. As there are 11 hydrogen atoms in the molecular formula, \(C_{1}\) has 3 hydrogen atoms and \(C_{2}\) has 8 hydrogen atoms. The structural formula is: H | N - \(C_{1}\) - \(C_{2}\) - \(C_{3}\) - \(C_{4}\) | H 2. In the second case, \(C_{1}\) has 1 remaining carbon atom and \(C_{2}\) has 1 remaining carbon atom. As there are 11 hydrogen atoms in the molecular formula, the hydrogen atoms are distributed between \(C_{1}\) and \(C_{2}\) as follows: - \(C_{1}\) has 2 hydrogen atoms - \(C_{1'}\) (attached to \(C_{1}\)) has 3 hydrogen atoms - \(C_{2}\) has 2 hydrogen atoms - \(C_{2'}\) (attached to \(C_{2}\)) has 3 hydrogen atoms The structural formula is: H | N - \(C_{1}\) - \(C_{1'}\) - \(C_{2}\) - \(C_{2'}\) | H 3. In the third case, \(C_{1}\) has 2 remaining carbon atoms and \(C_{2}\) has 0 remaining carbon atoms. As there are 11 hydrogen atoms in the molecular formula, \(C_{1}\) has 8 hydrogen atoms and \(C_{2}\) has 3 hydrogen atoms. The structural formula is: H | N - \(C_{1}\) - \(C_{2}\) - \(C_{3}\) - \(C_{4}\) | H So our three structural formulas for the given molecular formula are: 1. N - (\(C_{1}\))3H - \(C_{2}\) - \(C_{3}\) - \(C_{4}\) 2. N - \(C_{1}\)-(\(C_{1'}\))3H - \(C_{2}\)-(\(C_{2'}\))3H 3. N - \(C_{1}\) - \(C_{2}\) - \(C_{3}\) - (\(C_{4}\))3H