
Step 1: Understanding the Formation of P
The oxidation of iso-propylbenzene (cumene) in the presence of \( O_2 \) and acidic hydrolysis leads to the formation of phenol and acetone (P).
Step 2: Formation of Q
Reaction of P (acetone) with three equivalents of chlorine (\( Cl_2 \)) leads to the formation of trichloroacetone (Q).
Step 3: Formation of R and S
Treatment of Q with \( Ca(OH)_2 \) results in hydrolysis to form:
Step 4: Verifying the Statements
Conclusion:
The statements have been analyzed, and the correct ones are identified.
To solve the problem, we need to analyze the reaction sequence starting from iso-propylbenzene and verify the statements about compounds P, Q, R, and S.
1. Reaction of iso-propylbenzene with O2 and H3O+:
Iso-propylbenzene undergoes oxidation to form phenol and a by-product P (which is likely trichloromethylphenol or related compound).
2. Reaction of P with 3 equivalents of Cl2 to give Q:
P reacts with chlorine to form compound Q containing trichloromethyl groups (CCl3).
3. Treatment of Q with Ca(OH)2 produces R and calcium salt S:
This reaction yields compound R, which has chloroform-like structure, and S, the calcium salt of a carboxylic acid.
4. Verifying the given statements:
(A) Reaction of P with R in the presence of KOH followed by acidification gives the compound shown with a CCl3 and hydroxyl groups:
This is correct as it corresponds to the haloform reaction forming trichloromethyl derivatives.
(B) Reaction of R with O2 in presence of light gives phosgene gas (COCl2):
This is correct because R contains chloroform-like structure that can yield phosgene under these conditions.
(C) Q reacts with aqueous NaOH to produce Cl3CCH2OH and Cl3CCOO-Na+:
This is incorrect as Q is expected to form other products, not the ones stated.
(D) Heating S gives back P:
This is correct as the calcium salt S decomposes upon heating to give P.
Final Answer:
Statements (A), (B), and (D) are correct.
Given below are two statements:
Statement I: Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in water to a very small extent.
Statement II: Sodium metal can be used to dry diethyl ether and not ethyl alcohol.
In the light of the given statements, choose the correct answer from the options given below:
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.