Question

For the compound having molecular formula C$_4$H$_9$Br, write : (a) the isomer which is most reactive towards SN1 displacement. (b) the isomer which, on reacting with Na metal in the presence of dry ether, gives 2,5-Dimethylhexane.

Hint:

For SN1 reactions, always identify the most stable carbocation. For Wurtz reaction, split the product alkane symmetrically into two identical alkyl fragments and then attach halogen to the terminal carbon of each fragment.

Answer 1

Concept: The molecular formula \[ C_4H_9Br \] represents the bromobutane isomers. These isomers differ in the position of the bromine atom and the arrangement of the carbon skeleton. The possible isomers are:

• 1-Bromobutane

• 2-Bromobutane

• 1-Bromo-2-methylpropane (Isobutyl bromide)

• 2-Bromo-2-methylpropane (tert-Butyl bromide)
Different reactions favour different structural features. Therefore, we must analyze each part separately.

(a) Isomer most reactive towards SN1 displacement

Step 1: Principle of SN1 reaction. SN1 reactions proceed through the formation of a carbocation intermediate. The rate-determining step is: \[ R-Br \rightarrow R^+ + Br^- \] Hence, the stability of the carbocation formed determines the reactivity. The stability order of carbocations is: \[ 3^\circ \gt 2^\circ \gt 1^\circ \gt CH_3^+ \]

Step 2: Examine the carbocations formed. Among all the isomers of C$_4$H$_9$Br, tert-butyl bromide forms: \[ (CH_3)_3C^+ \] which is a tertiary carbocation. This carbocation is highly stabilized due to hyperconjugation and the +I effect of three methyl groups.

Step 3: Conclusion. Therefore, the isomer most reactive towards SN1 substitution is: \[ \boxed{\text{2-Bromo-2-methylpropane}} \] or \[ \boxed{(CH_3)_3CBr} \]

(b) Isomer which gives 2,5-Dimethylhexane on Wurtz reaction

Step 1: Recall Wurtz reaction. In the presence of sodium metal and dry ether: \[ 2R-X + 2Na \rightarrow R-R + 2NaX \] Two identical alkyl groups combine together to form a higher alkane.

Step 2: Analyze the required product. The product is: \[ 2,5\text{-Dimethylhexane} \] Its structure is: \[ CH_3-CH(CH_3)-CH_2-CH_2-CH(CH_3)-CH_3 \] This molecule can be obtained by joining two isobutyl groups. \[ (CH_3)_2CHCH_2- \] and \[ -CH_2CH(CH_3)_2 \]

Step 3: Identify the corresponding alkyl bromide. The required bromide is: \[ (CH_3)_2CHCH_2Br \] which is \[ \boxed{\text{1-Bromo-2-methylpropane}} \]

Final Answers: \[ \boxed{\text{(a) 2-Bromo-2-methylpropane}} \] \[ \boxed{\text{(b) 1-Bromo-2-methylpropane}} \]