The given conversion involves the bromination of propanoic acid $CH_3CH_2COOH$ to 2-bromopropanoic acid $CH_3CHBrCOOH$. The bromine atom is introduced at the $\alpha$-carbon (the carbon adjacent to the carboxyl group). This type of $\alpha$-halogenation of carboxylic acids is known as the Hell-Volhard-Zelinsky (HVZ) reaction.
The Hell-Volhard-Zelinsky reaction proceeds in two steps:
Step 1: The carboxylic acid reacts with bromine (\(Br_2\)) in the presence of red phosphorus (P red.). The red phosphorus reacts with bromine to form phosphorus tribromide (\(PBr_3\)), which then converts the carboxylic acid to an acyl bromide. The acyl bromide undergoes tautomerization to form an enol, which is then brominated at the $\alpha$-position.
Step 2: The $\alpha$-bromoacyl bromide is hydrolyzed with water (\(H_2O\)) to yield the $\alpha$-bromocarboxylic acid.
The overall reaction sequence is:
$$CH_3CH_2COOH \xrightarrow{Br_2/P} \, red.CH_3CHBrCOBr \xrightarrow{H_2O} CH_3CHBrCOOH$$
Therefore, the reagent 'X' required for this conversion is (i) Br$_2$/P red., followed by (ii) H$_2$O.
Analyzing the other options:
Option (2) Br$_2$/CCl$_4$ is used for the bromination of alkenes or alkanes (radical substitution), not for $\alpha$-halogenation of carboxylic acids.
Option (3) Br$_2$ / OH$^-$ is used for the haloform reaction with methyl ketones or secondary alcohols that can be oxidized to methyl ketones.
Option (4) PBr$_3$ is used to convert carboxylic acids to acyl bromides or alcohols to alkyl bromides, but it does not directly introduce a bromine at the $\alpha$-position of a carboxylic acid.
Thus, the correct reagent 'X' is $ \boxed{(i) Br_2/P \, red., (ii) H_2O} $.
Convert Ethanal to But-2-enal
If the ratio of the terms equidistant from the middle term in the expansion of \((1 + x)^{12}\) is \(\frac{1}{256}\), then the sum of all the terms of the expansion \((1 + x)^{12}\) is:
A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )