The depression in freezing point of a solution is

ANS:C - both (a) and (b).

The correct answer is: directly proportional to the mole of solute. The depression in freezing point of a solution is given by the equation: Δ𝑇𝑓=𝑖⋅𝐾𝑓⋅𝑚ΔTf​=i⋅Kf​⋅m Where:

• Δ𝑇𝑓ΔTf​ is the depression in freezing point,
• 𝑖i is the van't Hoff factor (a measure of the number of particles into which a solute dissociates in a solution),
• 𝐾𝑓Kf​ is the cryoscopic constant (a property of the solvent),
• 𝑚m is the molality of the solute (the number of moles of solute per kilogram of solvent).

From this equation, it's evident that the depression in freezing point is directly proportional to the molality of the solute (𝑚m). Therefore, the statement "directly proportional to the mole of solute" is correct. The statement "inversely proportional to the mass of solvent" is not generally true in the context of depression of freezing point; it would apply to colligative properties like osmotic pressure. So, the correct answer is not "both (a) and (b)."