The reaction sequence is as follows:
(A) Reacts with KOH to form alkene [B] (Elimination of HBr).
(B) Reacts with Br\(_2\) to give dibromide [C].
(C) Dibromide reacts with NaNH\(_2\) to form [D] (Alkyne formation).
(D) The alkyne [D] undergoes hydration with mercuric sulfate to give [E].
The problem describes a series of reactions starting from an optically active alkyl halide, C\(_4\)H\(_9\)Br [A], and asks for the IUPAC name of the final product, [E]. We will identify each intermediate compound ([A], [B], [C], and [D]) to determine the structure of the final compound [E].
This problem involves several key organic reactions:
Step 1: Identify the structure of the starting alkyl halide [A].
The molecular formula is C\(_4\)H\(_9\)Br. The compound is stated to be optically active, which means it must contain a chiral carbon atom (a carbon atom bonded to four different groups). Let's examine the isomers of C\(_4\)H\(_9\)Br:
Since [A] is optically active, it must be 2-Bromobutane.
\[ \text{[A] = } \text{CH}_3\text{CH}_2\text{CH(Br)CH}_3 \]
Step 2: Identify the major product alkene [B].
Compound [A] (2-Bromobutane) reacts with hot alcoholic KOH, which is a strong base, causing an E2 elimination reaction. According to Zaitsev's rule, the major product is the more substituted alkene.
Elimination of HBr can form two possible alkenes:
The major product [B] is the more stable, disubstituted alkene, But-2-ene.
\[ \text{CH}_3\text{CH}_2\text{CH(Br)CH}_3 \xrightarrow[\text{heat}]{\text{alc. KOH}} \text{CH}_3\text{CH=CHCH}_3 \quad \text{(Major Product [B])} \]
Step 3: Identify the dibromide [C].
Alkene [B] (But-2-ene) reacts with bromine (Br\(_2\)) in an addition reaction. The double bond breaks, and a bromine atom adds to each carbon of the former double bond.
\[ \text{CH}_3\text{CH=CHCH}_3 + \text{Br}_2 \rightarrow \text{CH}_3\text{CH(Br)CH(Br)CH}_3 \quad \text{(Compound [C])} \]
The product [C] is 2,3-Dibromobutane.
Step 4: Identify the gas [D].
The vicinal dibromide [C] (2,3-Dibromobutane) is treated with alcoholic NaNH\(_2\), a very strong base. This causes double dehydrohalogenation to form an alkyne.
\[ \text{CH}_3\text{CH(Br)CH(Br)CH}_3 + 2 \text{NaNH}_2 \xrightarrow{\text{alcohol}} \text{CH}_3\text{C}\equiv\text{CCH}_3 + 2 \text{NaBr} + 2 \text{NH}_3 \]
The gaseous product [D] is But-2-yne.
Step 5: Identify the final compound [E].
The alkyne [D] (But-2-yne) undergoes hydration on warming with mercuric sulphate and dilute acid. This reaction adds a molecule of water across the triple bond. (Note: 18 grams of water is 1 mole, consistent with the 1:1 stoichiometry of the reaction).
The initial addition of H\(_2\)O forms an enol intermediate:
\[ \text{CH}_3\text{C}\equiv\text{CCH}_3 + \text{H}_2\text{O} \xrightarrow[\text{dil. H}_2\text{SO}_4]{\text{HgSO}_4, 333\text{K}} \left[ \text{CH}_3\text{C(OH)=CHCH}_3 \right] \quad \text{(Unstable enol)} \]
This enol immediately tautomerizes to the more stable keto form:
\[ \text{CH}_3\text{C(OH)=CHCH}_3 \rightleftharpoons \text{CH}_3\text{C(=O)CH}_2\text{CH}_3 \quad \text{(Compound [E])} \]
The final compound [E] is a ketone.
Step 6: Determine the IUPAC name of compound [E].
The structure of [E] is \( \text{CH}_3\text{COCH}_2\text{CH}_3 \). The longest carbon chain contains four carbon atoms (butane). The functional group is a ketone (suffix "-one"). Numbering from the left, the carbonyl group is at position 2. Therefore, the IUPAC name is Butan-2-one.
Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Consider the following reaction sequence: 
Given: Compound (x) has percentage composition \(76.6%\ \text{C}\), \(6.38%\ \text{H}\) and vapour density \(=47\). Compound (y) develops a characteristic colour with neutral \(\mathrm{FeCl_3}\) solution. Identify the {INCORRECT statement.}
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to