4 statements are given below. Identify the incorrect statement:
(A) Phenol has lower \( pK_a \) value than \( \text{p} \)-cresol.
(B) 2-Chlorophenol is more acidic than phenol.
(C) Ortho and para nitrophenols can be separated by steam distillation since \( \text{p} \)-Nitrophenol is more steam volatile than \( o \)-Nitrophenol.
(D) Phenol on reaction with \( \text{Cr}_2\text{O}_7^{2-} / \text{H}^+ \) yields a conjugated diketone.
Let's analyze the statements:
1. (A) Phenol has lower \( pK_a \) value than \( \text{p} \)-cresol: This statement is true because \( \text{p} \)-cresol is a weaker acid compared to phenol.
The methyl group in \( \text{p} \)-cresol is an electron-donating group, which increases the electron density on the aromatic ring, making phenol less acidic than \( \text{p} \)-cresol.
2. (B) 2-Chlorophenol is more acidic than phenol: This statement is true. The chlorine atom in 2-chlorophenol is an electron-withdrawing group that stabilizes the negative charge on the oxygen atom after deprotonation, thus making 2-chlorophenol more acidic than phenol.
3. (C) Ortho and para nitrophenols can be separated by steam distillation since \( \text{p} \)-Nitrophenol is more steam volatile than \( o \)-Nitrophenol: This statement is incorrect. \( \text{p} \)-Nitrophenol has lower steam volatility compared to \( o \)-Nitrophenol due to the stronger intermolecular hydrogen bonding in \( \text{p} \)-nitrophenol, which makes it less volatile than \( o \)-nitrophenol. Therefore, they cannot be separated by steam distillation based on their volatility.
4. (D) Phenol on reaction with \( \text{Cr}_2\text{O}_7^{2-} / \text{H}^+ \) yields a conjugated diketone: This statement is true. The reaction of phenol with \( \text{Cr}_2\text{O}_7^{2-} / \text{H}^+ \) results in oxidation of phenol, and the product formed is a conjugated diketone, which is a product of the oxidation of phenol.
Thus, the incorrect statement is (C), and the correct answer is \( (A) \).
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: