
The problem asks for the number of oxygen atoms in the final major product 'P' of a two-step reaction sequence starting from but-2-yne.
The solution involves two sequential named organic reactions:
Step 1: Analyze the first step of the reaction sequence.
The starting material is but-2-yne (\( \text{CH}_3\text{C} \equiv \text{C}-\text{CH}_3 \)). The reagent is Na/liq. NH₃. This is the Birch reduction of an alkyne.
This reaction reduces the alkyne to an alkene with trans stereochemistry.
\[ \text{CH}_3\text{C} \equiv \text{C}-\text{CH}_3 \xrightarrow{\text{(i) Na/liq.NH}_3} \text{trans-But-2-ene} \]
The structure of the intermediate product, trans-but-2-ene, is:
Step 2: Analyze the second step of the reaction sequence.
The intermediate, trans-but-2-ene, is treated with dilute KMnO₄ at 273K (0 °C). This is a syn-dihydroxylation reaction (Baeyer's test).
Two hydroxyl (-OH) groups are added across the double bond on the same side. This reaction converts the alkene into a vicinal diol (a glycol).
\[ \text{trans-But-2-ene} \xrightarrow{\text{(ii) dil. KMnO}_4, 273\text{K}} \text{Butane-2,3-diol} \]
The reaction breaks the pi bond of the alkene and forms two new C-O sigma bonds.
The structure of the final product 'P', butane-2,3-diol, is:
\[ \text{CH}_3-\underset{\text{OH}}{\underset{|}{\text{CH}}}-\underset{\text{OH}}{\underset{|}{\text{CH}}}-\text{CH}_3 \]
(Note: The reaction of a trans-alkene with syn-addition results in a racemic mixture of (2R,3R) and (2S,3S) enantiomers, but the chemical constitution is butane-2,3-diol).
The question asks for the number of oxygen atoms present in the final product 'P'.
The final product is butane-2,3-diol, with the chemical formula \( \text{C}_4\text{H}_{10}\text{O}_2 \).
By inspecting the structure or the formula, we can see that the molecule contains two hydroxyl (-OH) groups. Each hydroxyl group has one oxygen atom.
Therefore, the total number of oxygen atoms in product 'P' is 2.
The reaction proceeds as follows:
Step 1: The triple bond in CH$_3$C$\equiv$C-CH$_3$ is reduced to a trans-alkene using Na/liq. NH$_3$:
\[\text{CH}_3\text{C} \equiv \text{C-CH}_3 \xrightarrow{\text{Na/liq. NH}_3} \text{CH}_3\text{CH} = \text{CHCH}_3\]
Step 2: The trans-alkene undergoes oxidation with dilute KMnO$_4$ at 273 K. This leads to the formation of a vicinal diol:
\[\text{CH}_3\text{CH} = \text{CHCH}_3 \xrightarrow{\text{dil. KMnO}_4} \text{CH}_3\text{CH(OH)CH(OH)CH}_3\]
The final product `P' contains two hydroxyl (-OH) groups, contributing two oxygen atoms.
Number of oxygen atoms in product `P':
\[2 \, (\text{from hydroxyl groups})\]
Identify A in the following reaction. 
For the reaction, \(N_{2}O_{4} \rightleftharpoons 2NO_{2}\) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is 5.40 kJ \(mol^{-1}\).
B. As \(\Delta G\) in graph is positive, \(N_{2}O_{4}\) will not dissociate into \(NO_{2}\) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \(N_{2}O_{4}\) changes into equilibrium mixture, value of \(\Delta G = -0.84 \text{ kJ mol}^{-1}\).
E. When 2 mole of \(NO_{2}\) changes into equilibrium mixture, \(\Delta G\) for equilibrium mixture is \(-6.24 \text{ kJ mol}^{-1}\).
Choose the correct answer from the following.

Method used for separation of mixture of products (B and C) obtained in the following reaction is: 
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 ___________.