Solutions

The correct statement is: Relative lowering of vapor pressure is independent of T.

Here's why:

• Relative Lowering of Vapor Pressure: According to Raoult's Law, the relative lowering of vapor pressure is equal to the mole fraction of the solute: where:
  • P₀ is the vapor pressure of the pure solvent
  • P_s is the vapor pressure of the solution
  • x_solute is the mole fraction of the solute
• Osmotic Pressure: Osmotic pressure (π) is given by: While molarity (M) and temperature (T) are involved, the van't Hoff factor (i) *can* be affected by the nature of the solute (e.g., whether it's an electrolyte or a nonelectrolyte), but it isn't *always* dependent on the nature of solute. Strong electrolytes dissociate completely into ions, but weak electrolytes only partially dissociate, and non-electrolytes do not dissociate at all. Furthermore, even for electrolytes, *ion pairing* becomes significant at higher concentrations.
• Elevation of Boiling Point: The elevation of the boiling point (ΔT_b) is given by: where:
  • K_b is the ebullioscopic constant, which *depends on the solvent*
  • m is the molality of the solution
• Lowering of Freezing Point: The depression of the freezing point (ΔT_f) is given by: where:
  • K_f is the cryoscopic constant, which depends on the *solvent*
  • m is the molality of the solution. While, at lower concentrations, molality is approximately equal to molarity, the phrase "molar concentration" is less accurate than "molality". This is a more subtle point, and the more relevant point is that Kf depends on the solvent.

Correct Answer: Relative lowering of vapor pressure is independent of T.

The correct answer is option (B): 82000 g/mol

Explanation: The osmotic pressure formula is given by:

Where:

• = osmotic pressure = atm
• V = volume of solution = 4.0 L
• T = temperature = 27°C = 300 K
• R = gas constant = 0.08206 L·atm/mol·K
• n = number of moles = , where M is the molar mass (since mass = 4 g)

Substitute into the formula:

Multiply both sides by 4:

Solve for M:

Hence, the molar mass of the polymer is approximately 82000 g/mol.