Two solutions contain the same amount of water as a solvent. One solution contains 0.5 mol glucose (C₆H₁₂O₆) while the other one contains 0.2 mol of CaCl₂ . If the freezing points of both solutions are the same, determine the van't Hoff i factor for CaCl₂ solution. A) 2.50 B) 3 C) 1.50 D) 2.75 E) 0.75

Question

Quizplus · Accepted Answer

The van't Hoff factor (i) is a measure of the number of particles a solute dissociates into in solution. For glucose (C6H12O6), i = 1 because it does not dissociate in water. For CaCl2, i = 3 because it dissociates into three ions (Ca2+ and 2 Cl-) in water. The freezing point depression is given by the equation: ΔTf = Kf * i * m, where ΔTf is the freezing point depression, Kf is the cryoscopic constant of the solvent, i is the van't Hoff factor, and m is the molality of the solution. Since the freezing points of both solutions are the same, we can set the two equations equal to each other and solve for i: Kf * i * m(glucose) = Kf * i * m(CaCl2). Since Kf and m are the same for both solutions, we can cancel them out and solve for i: i(glucose) = i(CaCl2). Substituting the values of i for glucose and CaCl2, we get: 1 = i(CaCl2). Therefore, the van't Hoff factor for the CaCl2 solution is 1.

Two Solutions Contain the Same Amount of Water as a Solvent