Question

Compound 'X' with molecular formula \(C_4H_9Br\) reacts with aqueous KOH to give an alcohol. The rate of this reaction depends only on the concentration of the compound 'X'. When an optically active isomer 'Y' of the compound 'X' was treated with aqueous KOH solution, the rate of reaction was found to be dependent on concentration of compound 'Y' and aqueous KOH both.

(a) Write down the structural formula of both 'X' and 'Y'.

(b) Out of 'X' and 'Y', which one will undergo racemisation and why?

(c) Out of 'X' and 'Y', which one will form product with inversion of configuration and why?

Hint:

The order of the reaction tells us the mechanism. A reaction whose rate depends only on the alkyl halide follows \(S_N1\) (first order) and is favoured by tertiary halides.

Answer 1

Step 1: Read the clues for X.
Compound X is \(C_4H_9Br\), and its reaction with aqueous KOH depends only on the concentration of X. A rate depending only on the halide means a first order \((S_N1)\) reaction.

Step 2: Identify X.
\(S_N1\) is favoured by tertiary halides because they give a stable tertiary carbocation. So X is tert-butyl bromide, \((CH_3)_3C\text{-}Br\) (2-bromo-2-methylpropane).

Step 3: Read the clues for Y.
Y is an optically active isomer of X, and its reaction rate depends on both Y and KOH. A rate depending on two species means a second order \((S_N2)\) reaction.

Step 4: Identify Y.
For optical activity, the carbon bearing bromine must be a chiral centre (four different groups). The \(C_4H_9Br\) isomer that is optically active and a secondary halide is sec-butyl bromide, \(CH_3CH_2CH(Br)CH_3\) (2-bromobutane). Its chiral carbon carries \(-H, -Br, -CH_3\) and \(-C_2H_5\).

Step 5: Match mechanisms.
X (tertiary) goes by \(S_N1\) (first order). Y (secondary, chiral) goes by \(S_N2\) (second order), which fits the rate depending on both Y and KOH.

Answer: X is 2-bromo-2-methylpropane \((CH_3)_3CBr\), which reacts by \(S_N1\). Y is 2-bromobutane \(CH_3CH_2CHBrCH_3\), which is optically active and reacts by \(S_N2\).