Step 1: Understanding the Concept:
The question requires the determination of all possible isomers for the molecular formula \(C_3H_5Br\).
In organic chemistry, the term "isomers" encompasses both constitutional (structural) isomers and stereoisomers (geometrical and optical).
Structural isomers have the same molecular formula but different connectivity of atoms.
Stereoisomers have the same connectivity but different spatial arrangements.
To start, we must determine the Degree of Unsaturation (DU) to understand the structural features allowed by the formula.
Step 2: Key Formula or Approach:
The Degree of Unsaturation (DU) or Double Bond Equivalent (DBE) is calculated as:
\[ DU = C + 1 - \frac{H + X}{2} \]
For \(C_3H_5Br\):
\[ DU = 3 + 1 - \frac{5 + 1}{2} = 4 - 3 = 1 \]
A DU value of 1 indicates that the molecule contains either one double bond (acyclic) or one ring (cyclic).
Step 3: Detailed Explanation:
Let's systematically construct the possible isomers:
1. Acyclic Isomers (Alkenes):
We have a three-carbon chain with one double bond. The base molecule is propene (\(CH_2=CH-CH_3\)).
We substitute one hydrogen with a bromine atom at different positions:
- Position 1 (C1): This gives 1-bromoprop-1-ene (\(CHBr=CH-CH_3\)).
This compound possesses a double bond where each carbon has two different groups. Thus, it exhibits geometrical isomerism.
- (i) cis-1-bromoprop-1-ene (or (Z)-1-bromoprop-1-ene).
- (ii) trans-1-bromoprop-1-ene (or (E)-1-bromoprop-1-ene).
- Position 2 (C2): This gives 2-bromoprop-1-ene (\(CH_2=CBr-CH_3\)).
- (iii) 2-bromoprop-1-ene. There are no geometrical isomers here as C1 has two identical H atoms.
- Position 3 (C3): This gives 3-bromoprop-1-ene (\(CH_2=CH-CH_2Br\)), commonly known as allyl bromide.
- (iv) 3-bromoprop-1-ene. No stereoisomerism is possible here.
2. Cyclic Isomers:
With three carbons and DU=1, we can form a three-membered ring.
- (v) Bromocyclopropane. This is formed by substituting one H on the cyclopropane ring with Br.
Counting them all: 2 (cis/trans) + 1 (2-bromo) + 1 (3-bromo) + 1 (cyclic) = 5 isomers in total.
Failing to recognize the geometrical isomers of 1-bromoprop-1-ene is a common error that leads to an incorrect count of 4.
Step 4: Final Answer:
The total number of isomers for \(C_3H_5Br\) is 5, which matches option (D).