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(B) The freezing point depression $\Delta T_f$ is a colligative property,which depends on the molality $(m)$ of the solution. $\Delta T_f = K_f 	imes

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$6 \ g$ urea in $100 \ g \ H_2O$ and $18 \ g$ glucose in $100 \ g \ H_2O$

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(B) The freezing point depression $\Delta T_f$ is a colligative property,which depends on the molality $(m)$ of the solution. $\Delta T_f = K_f 	imes m$. For the freezing points to be equal,the molality of the two solutions must be equal. Molality $m = \frac{	ext{moles of solute}}{	ext{mass of solvent in kg}}$. For option $B$: Moles of urea $= \frac{6 \ g}{60 \ g/mol} = 0.1 \ mol$. Moles of glucose $= \frac{18 \ g}{180 \ g/mol} = 0.1 \ mol$. Since the mass of the solvent $(100 \ g \ H_2O)$ is the same for both,and the number of moles of solute is the same $(0.1 \ mol)$,the molality of both solutions is identical. Therefore,they will have the same freezing point.

Under identical conditions,which aqueous solutions have the same freezing point? (Molecular mass of urea $= 60 \ u$ and glucose $= 180 \ u$)

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