Which of the noncyclic isomers of \(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{F}\) are optically active?

First, let's list all the noncyclic isomers of C4H7F: 1. 1-fluorobut-1-ene 2. 1-fluorobut-2-ene 3. 2-fluorobut-1-ene 4. 2-fluorobut-2-ene 5. 3-fluorobut-1-ene

A chiral center (stereocenter) is an atom with four different groups attached to it, making it non-superimposable on its mirror image. For these molecules, we are looking for a carbon atom with four different substituents attached to it. 1. 1-fluorobut-1-ene: There are no chiral centers, as the second carbon has two hydrogen atoms attached to it. 2. 1-fluorobut-2-ene: The second carbon is a chiral center, as it has a fluorine atom, an ethyl group, a hydrogen atom, and a vinyl group attached to it. 3. 2-fluorobut-1-ene: There are no chiral centers, as the second carbon has two hydrogen atoms attached to it. 4. 2-fluorobut-2-ene: The second carbon is a chiral center, as it has a fluorine atom, a methyl group, a hydrogen atom, and a vinyl group attached to it. 5. 3-fluorobut-1-ene: There are no chiral centers, as the second carbon has two hydrogen atoms attached to it.

Optically active isomers are those that have one or more chiral centers. Based on our analysis in Step 2, we can conclude that 1-fluorobut-2-ene (isomer 2) and 2-fluorobut-2-ene (isomer 4) are optically active, as they both contain a chiral center.