Subtopic: Preservation of food by cooling and freezing
Question Statement:
An aqueous sucrose solution contains $17.1\text{ g}$ of sucrose ($M_w = 342.0\text{ g/mol}$) dissolved in $100.0\text{ g}$ of pure water. Taking the cryoscopic constant of water as $K_f = 1.86\text{ K}\cdot\text{kg/mol}$, the theoretical freezing point depression ($\Delta T_f = K_f \cdot m$) in $^\circ\text{C}$ is ________ (round off to 2 decimal places).
Answer Key:
0.93
Step-by-Step Solution & Explanation
1. Moles of sucrose:
$n = \frac{17.1\text{ g}}{342.0\text{ g/mol}} = 0.050\text{ mol}$
2. Molality $m$ (moles of solute per kg of solvent):
$m = \frac{0.050\text{ mol}}{0.100\text{ kg}} = 0.50\text{ mol/kg}$
3. Freezing point depression $\Delta T_f$:
$\Delta T_f = K_f \cdot m = 1.86\text{ K}\cdot\text{kg/mol} \times 0.50\text{ mol/kg} = 0.93^\circ\text{C}$