Which of the following statements concerning `3,4`-dibromo-`1`-pentane and `3,5`-dibromo-`2`-pentane are correct?
(I) They have same molecular formula `C_(5)H_(8)Br_(2)`
(II) They are positional isomers.
(III) They have similar chemical properties.

Options

A. `I` and `III`
B. `I` and `II`
C. `II` and `III`
D. `I,II` and `III`

Explanation

To determine which statements concerning `3,4`-dibromo-`1`-pentene and `3,5`-dibromo-`2`-pentene are correct, we will analyze each statement one by one.

### Step 1: Identify the molecular formula of both compounds
1. **Structure of `3,4`-dibromo-`1`-pentene**:
- The structure can be drawn as follows:
- CH2=CH-CH(Br)-CH(Br)-CH3
- This has a total of 5 carbon atoms (C) and 8 hydrogen atoms (H) and 2 bromine atoms (Br).
- Therefore, the molecular formula is C5H8Br2.

2. **Structure of `3,5`-dibromo-`2`-pentene**:
- The structure can be drawn as follows:
- CH3-CH(Br)-CH(Br)-CH2-CH3
- This also has a total of 5 carbon atoms (C), 8 hydrogen atoms (H), and 2 bromine atoms (Br).
- Therefore, the molecular formula is also C5H8Br2.

**Conclusion for Statement I**: Both compounds have the same molecular formula C5H8Br2.
**Result**: Statement I is **correct**.

### Step 2: Determine if they are positional isomers
- **Positional isomers** are compounds that have the same molecular formula but differ in the position of functional groups or substituents.
- In `3,4`-dibromo-`1`-pentene, the bromine atoms are located on the 3rd and 4th carbons.
- In `3,5`-dibromo-`2`-pentene, the bromine atoms are located on the 3rd and 5th carbons.
- Since the positions of the bromine atoms differ in these two compounds, they qualify as positional isomers.

**Conclusion for Statement II**: They are positional isomers.
**Result**: Statement II is **correct**.

### Step 3: Analyze their chemical properties
- **Chemical properties** can vary significantly among isomers due to differences in structure.
- Although both compounds contain bromine and have similar carbon skeletons, the position of the double bond and the bromine atoms will influence their reactivity.
- For example, the reactions involving elimination or substitution may occur differently due to the different positions of the bromine substituents.
- Therefore, we cannot conclude that they have similar chemical properties.

**Conclusion for Statement III**: They do not have similar chemical properties.
**Result**: Statement III is **incorrect**.

### Final Answer:
- The correct statements are: **I and II**.
- Therefore, the answer is **B** (I and II are correct).