Choose the correct statements from the following:

(A) two different solutions of sucrose of same molality prepared in different solvents will have the same depression in freezing point.
(B) the osmotic pressure of a solution is given by the equation П = CRT (where C is the molarity of the solution)
(C) decreasing order of osmotic pressure for 0.01 M aqueous solution of $BaCl_2, KCl, CH_3COOH$ and sucrose is $BaCl_2> KCl > CH_3COOH$ > sucrose
(D) according to Raoult's law the vapor pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution

Choose the correct answer from the options given below:

(B), (C) and (D) only

The correct answer is Option (3) → (B), (C) and (D) only

Let's analyze each statement carefully:

(A) Two different solutions of sucrose of same molality prepared in different solvents will have the same depression in freezing point.

• Freezing point depression is given by $\Delta T_f = K_f \cdot m$, where $K_f$​ is the cryoscopic constant of the solvent.
• Since $K_f$​ depends on the solvent, the depression will not be the same in different solvents.
  ❌ Incorrect

(B) The osmotic pressure of a solution is given by the equation $\Pi = CRT$ (where C is the molarity of the solution).

• This is correct for ideal dilute solutions.
  ✅ Correct

(C) Decreasing order of osmotic pressure for 0.01 M aqueous solution of BaCl₂, KCl, CH₃COOH, and sucrose is BaCl₂ > KCl > CH₃COOH > sucrose

• Osmotic pressure depends on the number of solute particles.
• BaCl₂ → dissociates into 3 ions → 0.01 × 3 = 0.03 M particles
• KCl → 2 ions → 0.01 × 2 = 0.02 M particles
• CH₃COOH → weak acid, partially ionized, fewer particles → <0.01 M
• Sucrose → nonelectrolyte → 0.01 M
  ✅ The order BaCl₂ > KCl > CH₃COOH > sucrose is correct

(D) According to Raoult's law, the vapor pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution.

• This is correct.
  ✅ Correct