Understanding Monohalogen Derivatives

A monohalogen derivative is an organic molecule where exactly one hydrogen atom has been replaced by a halogen atom (like chlorine, bromine, etc.). To yield a single monohalogen derivative, all hydrogen atoms in the starting molecule must be equivalent in terms of their chemical environment. If the hydrogen atoms are not equivalent, replacing different hydrogen atoms with a halogen will result in different structural isomers, thus producing multiple monohalogen derivatives.

Analyzing the Options for Single Monohalogen Derivative Formation

Let's examine each option to see how many distinct monohalogen derivatives can be formed through substitution or addition reactions involving halogens.

• Propane ($\text{CH}_3\text{CH}_2\text{CH}_3$): Propane is an alkane. Free radical halogenation (substitution of hydrogen atoms with halogen atoms) is a common reaction for alkanes. Propane has two types of hydrogen atoms:
  • Six primary hydrogen atoms (attached to the terminal carbon atoms).
  • Two secondary hydrogen atoms (attached to the central carbon atom).

  Replacing a primary hydrogen yields 1-halopropane. Replacing a secondary hydrogen yields 2-halopropane. These are different compounds (structural isomers). Therefore, propane yields multiple monohalogen derivatives upon halogenation.

• Cyclopropane: Cyclopropane is a cyclic alkane with the formula $\text{C}_3\text{H}_6$. It has a strained three-membered ring structure.
  • All three carbon atoms in cyclopropane are equivalent due to the symmetry of the ring.
  • Each carbon atom is bonded to two hydrogen atoms. All six hydrogen atoms are equivalent.

  Substituting any one of these equivalent hydrogen atoms with a halogen atom will result in the same product, which is a monohalocyclopropane. Thus, cyclopropane yields a single monohalogen derivative.

• Propene ($\text{CH}_3\text{CH}=\text{CH}_2$): Propene is an alkene with a double bond. Reactions with halogens or hydrogen halides can involve addition across the double bond or substitution.
  • Addition of $\text{HX}$ (where $\text{X}$ is halogen) across the double bond typically follows Markovnikov's rule, leading primarily to 2-halopropane, but 1-halopropane can also be formed. This yields multiple monohalogen derivatives (or related products like dihalides upon further reaction).
  • Free radical allylic substitution (e.g., with $\text{NBS}$) can replace a hydrogen on the carbon adjacent to the double bond ($\text{CH}_3$ group), yielding 3-halopropene. This is different from the addition products.

  Propene yields multiple halogenated products, not a single monohalogen derivative easily under typical conditions.

• Propyne ($\text{CH}_3\text{C}\equiv\text{CH}$): Propyne is an alkyne with a triple bond. Reactions with halogens or hydrogen halides involve addition across the triple bond.
  • Addition reactions occur stepwise, adding one or two molecules of the reagent across the triple bond. For example, adding $\text{HX}$ can yield vinyl halides and then dihalides.
  • The molecule has different types of hydrogens (methyl hydrogens, acetylenic hydrogen). Substitution or addition reactions lead to various halogenated products.

  Propyne does not yield a single monohalogen derivative under typical halogenation conditions.

Conclusion on Single Monohalogen Derivative Formation

Comparing the possibilities, only cyclopropane has all its hydrogen atoms in equivalent positions. This equivalence ensures that replacing any one hydrogen atom with a halogen results in the identical monohalogen derivative.

Therefore, cyclopropane is the molecule among the options that would yield a single monohalogen derivative upon reaction with a halogen through substitution.