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

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Quizplus · Accepted Answer

The freezing point depression ($\Delta T_f$) is directly proportional to the molality ($m$) of the solute:
$$\Delta T_f = K_f\cdot m\cdot i$$
where $K_f$ is the freezing point depression constant for the solvent and $i$ is the van't Hoff factor. Since both solutions contain the same amount of water as a solvent and have the same freezing point, we can write:
$$K_f\cdot m_{	ext{glucose}}\cdot i_{	ext{glucose}}=K_f\cdot m_{	ext{CaCl}_2}\cdot i_{	ext{CaCl}_2}$$
Dividing the two equations, we have:
$$\frac{i_{	ext{CaCl}_2}}{i_{	ext{glucose}}}=\frac{m_{	ext{glucose}}}{m_{	ext{CaCl}_2}}\approx2.50$$
since $m_{	ext{glucose}}/m_{	ext{CaCl}_2}=0.5/0.2=2.5$. Therefore, the van't Hoff factor for CaCl$_2$ is approximately 2.50, giving the answer choice A.

Two Solutions Contain the Same Amount of Water as a Solvent.One