A certain substance X has a normal freezing point of 1.5 °C and a molal freezing point depression constant K₁=4.89 °C-kg-mol. A solution is prepared by dissolving some urea ((NH₂)2CO) in 750. g of X. This solution freezes at 0.2 °C. Calculate the mass of urea that was dissolved. Round your answer to 2 significant digits.
A certain substance X has a normal freezing point of 1.5 °C and a molal freezing point depression constant K₁=4.89 °C-kg-mol. A solution is prepared by dissolving some urea ((NH₂)2CO) in 750. g of X. This solution freezes at 0.2 °C. Calculate the mass of urea that was dissolved. Round your answer to 2 significant digits.
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![**Problem Statement:**
A certain substance \( X \) has a normal freezing point of 1.5 °C and a molal freezing point depression constant \( K_f = 4.89 \, °\text{C} \cdot \text{kg} \cdot \text{mol}^{-1} \). A solution is prepared by dissolving some urea \(\left( \text{NH}_2\right)_2 \text{CO} \) in 750. g of \( X \). This solution freezes at 0.2 °C. Calculate the mass of urea that was dissolved.
Round your answer to 2 significant digits.
**Input Section:**
A text box and a keypad are displayed for inputting the answer. The text box has "g" next to it, indicating the unit in grams.
**Calculation Details:**
1. Determine the freezing point depression:
\[
\Delta T_f = T_f^\circ - T_f
\]
Where:
- \( T_f^\circ \) is the normal freezing point of pure substance \( X \) (1.5 °C).
- \( T_f \) is the observed freezing point of the solution (0.2 °C).
\[
\Delta T_f = 1.5 \, \text{°C} - 0.2 \, \text{°C} = 1.3 \, \text{°C}
\]
2. Apply the freezing point depression equation:
\[
\Delta T_f = K_f \cdot m
\]
Solving for \( m \) (molality):
\[
m = \frac{\Delta T_f}{K_f} = \frac{1.3}{4.89} \, \text{mol} \cdot \text{kg}^{-1} \approx 0.266 \, \text{mol/kg}
\]
3. Calculate moles of urea:
Molality \( m \) is given as:
\[
m = \frac{\text{moles of solute}}{\text{kg of solvent}}
\]
Using mass of solvent \( X \) as 750. g (0.750 kg):
\[
\text{moles of urea} = m \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2dc05801-0f2f-4b82-9bd0-eb38a3fb827a%2F9585d71d-6c06-4267-9d78-6d7773f1d8e8%2Fgykrmkv_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A certain substance \( X \) has a normal freezing point of 1.5 °C and a molal freezing point depression constant \( K_f = 4.89 \, °\text{C} \cdot \text{kg} \cdot \text{mol}^{-1} \). A solution is prepared by dissolving some urea \(\left( \text{NH}_2\right)_2 \text{CO} \) in 750. g of \( X \). This solution freezes at 0.2 °C. Calculate the mass of urea that was dissolved.
Round your answer to 2 significant digits.
**Input Section:**
A text box and a keypad are displayed for inputting the answer. The text box has "g" next to it, indicating the unit in grams.
**Calculation Details:**
1. Determine the freezing point depression:
\[
\Delta T_f = T_f^\circ - T_f
\]
Where:
- \( T_f^\circ \) is the normal freezing point of pure substance \( X \) (1.5 °C).
- \( T_f \) is the observed freezing point of the solution (0.2 °C).
\[
\Delta T_f = 1.5 \, \text{°C} - 0.2 \, \text{°C} = 1.3 \, \text{°C}
\]
2. Apply the freezing point depression equation:
\[
\Delta T_f = K_f \cdot m
\]
Solving for \( m \) (molality):
\[
m = \frac{\Delta T_f}{K_f} = \frac{1.3}{4.89} \, \text{mol} \cdot \text{kg}^{-1} \approx 0.266 \, \text{mol/kg}
\]
3. Calculate moles of urea:
Molality \( m \) is given as:
\[
m = \frac{\text{moles of solute}}{\text{kg of solvent}}
\]
Using mass of solvent \( X \) as 750. g (0.750 kg):
\[
\text{moles of urea} = m \times
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