QuestionJune 18, 2025

Question 13 (9 points) Calculate the change in freezing point and boiling point if 5.75 gof NH_(4)NO_(3) is dissolved in 47.0 g of chloroform. Assume 100% dissociation of NH_(4)NO_(3) The molar mass of NH_(4)NO_(3) is 80.043g/mol The K_(f) and K_(b) for chloroform are 8.10^circ C/m and 5.24^circ C/m respectively.

Question 13 (9 points) Calculate the change in freezing point and boiling point if 5.75 gof NH_(4)NO_(3) is dissolved in 47.0 g of chloroform. Assume 100% dissociation of NH_(4)NO_(3) The molar mass of NH_(4)NO_(3) is 80.043g/mol The K_(f) and K_(b) for chloroform are 8.10^circ C/m and 5.24^circ C/m respectively.
Question 13 (9 points) Calculate the change in freezing point and boiling point if 5.75 gof NH_(4)NO_(3) is dissolved in 47.0 g of chloroform. Assume 100% dissociation of NH_(4)NO_(3) The molar mass of NH_(4)NO_(3) is 80.043g/mol The K_(f) and K_(b) for chloroform are 8.10^circ C/m and 5.24^circ C/m respectively.

Solution
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Answer

Change in freezing point: 24.76^{\circ}C, Change in boiling point: 16.01^{\circ}C Explanation 1. Calculate moles of solute Moles of NH_4NO_3 = \frac{5.75 \text{ g}}{80.043 \text{ g/mol}} = 0.0718 \text{ mol} 2. Calculate molality Molality m = \frac{\text{moles of solute}}{\text{kg of solvent}} = \frac{0.0718 \text{ mol}}{0.047 \text{ kg}} = 1.5277 \text{ mol/kg} 3. Determine van't Hoff factor For NH_4NO_3, which dissociates into NH_4^+ and NO_3^-, the van't Hoff factor i = 2. 4. Calculate change in freezing point \Delta T_f = i \cdot K_f \cdot m = 2 \cdot 8.10^{\circ}C/m \cdot 1.5277 \text{ mol/kg} = 24.76^{\circ}C 5. Calculate change in boiling point \Delta T_b = i \cdot K_b \cdot m = 2 \cdot 5.24^{\circ}C/m \cdot 1.5277 \text{ mol/kg} = 16.01^{\circ}C

Explanation

1. Calculate moles of solute<br /> Moles of $NH_4NO_3 = \frac{5.75 \text{ g}}{80.043 \text{ g/mol}} = 0.0718 \text{ mol}$<br /><br />2. Calculate molality<br /> Molality $m = \frac{\text{moles of solute}}{\text{kg of solvent}} = \frac{0.0718 \text{ mol}}{0.047 \text{ kg}} = 1.5277 \text{ mol/kg}$<br /><br />3. Determine van't Hoff factor<br /> For $NH_4NO_3$, which dissociates into $NH_4^+$ and $NO_3^-$, the van't Hoff factor $i = 2$.<br /><br />4. Calculate change in freezing point<br /> $\Delta T_f = i \cdot K_f \cdot m = 2 \cdot 8.10^{\circ}C/m \cdot 1.5277 \text{ mol/kg} = 24.76^{\circ}C$<br /><br />5. Calculate change in boiling point<br /> $\Delta T_b = i \cdot K_b \cdot m = 2 \cdot 5.24^{\circ}C/m \cdot 1.5277 \text{ mol/kg} = 16.01^{\circ}C$
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