A certain liquid X has a normal boiling point of 117.50 °C and a boiling point elevation constant K= 1.51 °C kg'mol Calculate the boiling point of a solution made of 52.3g of urea (CH N,O) dissolved in 650. g of X. Round your answer to 5 significant digits.
A certain liquid X has a normal boiling point of 117.50 °C and a boiling point elevation constant K= 1.51 °C kg'mol Calculate the boiling point of a solution made of 52.3g of urea (CH N,O) dissolved in 650. g of X. Round your answer to 5 significant digits.
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![### Boiling Point Elevation Calculation
**Problem:**
A certain liquid X has a normal boiling point of 117.50 °C and a boiling point elevation constant \( K_b = 1.51 \, °C \cdot kg \cdot mol^{-1} \). Calculate the boiling point of a solution made of 52.3 g of urea (CH\(_4\)N\(_2\)O) dissolved in 650. g of X.
**Solution:**
Given:
- Normal boiling point of liquid X, \( T_b = 117.50 \, °C \)
- Boiling point elevation constant, \( K_b = 1.51 \, °C \cdot kg \cdot mol^{-1} \)
- Mass of urea, \( m_{\text{urea}} = 52.3 \, \text{g} \)
- Mass of solvent (liquid X), \( m_{\text{solvent}} = 650. \, \text{g} \)
The boiling point elevation (\( \Delta T_b \)) is calculated using the formula:
\[ \Delta T_b = K_b \cdot m \]
where \( m \) is the molality of the solution. Molality (m) is calculated as:
\[ m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \]
**Step 1: Calculate the moles of urea.**
- Molar mass of urea (CH\(_4\)N\(_2\)O):
\[
M_{\text{urea}} = 12.01 (\text{C}) + 4 \times 1.01 (\text{H}) + 2 \times 14.01 (\text{N}) + 16.00 (\text{O}) = 60.06 \, \text{g/mol}
\]
- Moles of urea:
\[
\text{moles of urea} = \frac{52.3 \, \text{g}}{60.06 \, \text{g/mol}} = 0.8704 \, \text{mol}
\]
**Step 2: Calculate the molality (m).**
- Mass of solvent (in kg):
\[
\text{mass of solvent](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe361a5c2-e3a6-4cd8-bee8-5dcb720cb10b%2F5e6ce5a7-b170-45d4-bf4e-6bf15e2abba6%2Frdosqm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Boiling Point Elevation Calculation
**Problem:**
A certain liquid X has a normal boiling point of 117.50 °C and a boiling point elevation constant \( K_b = 1.51 \, °C \cdot kg \cdot mol^{-1} \). Calculate the boiling point of a solution made of 52.3 g of urea (CH\(_4\)N\(_2\)O) dissolved in 650. g of X.
**Solution:**
Given:
- Normal boiling point of liquid X, \( T_b = 117.50 \, °C \)
- Boiling point elevation constant, \( K_b = 1.51 \, °C \cdot kg \cdot mol^{-1} \)
- Mass of urea, \( m_{\text{urea}} = 52.3 \, \text{g} \)
- Mass of solvent (liquid X), \( m_{\text{solvent}} = 650. \, \text{g} \)
The boiling point elevation (\( \Delta T_b \)) is calculated using the formula:
\[ \Delta T_b = K_b \cdot m \]
where \( m \) is the molality of the solution. Molality (m) is calculated as:
\[ m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \]
**Step 1: Calculate the moles of urea.**
- Molar mass of urea (CH\(_4\)N\(_2\)O):
\[
M_{\text{urea}} = 12.01 (\text{C}) + 4 \times 1.01 (\text{H}) + 2 \times 14.01 (\text{N}) + 16.00 (\text{O}) = 60.06 \, \text{g/mol}
\]
- Moles of urea:
\[
\text{moles of urea} = \frac{52.3 \, \text{g}}{60.06 \, \text{g/mol}} = 0.8704 \, \text{mol}
\]
**Step 2: Calculate the molality (m).**
- Mass of solvent (in kg):
\[
\text{mass of solvent
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