In addition to filling in the blanks below, show all of your work for this problem on paper for later upload. Because you need water boiling at 100.0 °C for your recipe, how many grams of salt (NaCl(s)) would you need to add to 3.50 kg of water to raise the boiling point of water in Denver from the boiling point found in Problem 21 to 100.0 °C? Assume that the salt completely dissolves and fully dissociates in the water. If you did not get an answer for Problem 22, use 97.0 °C as the boiling point of water in Denver. Enter your value in the first box and an appropriate unit of measure in the second box.

Chemistry
10th Edition
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: Boiling Point Elevation Calculation**

**Instructions:**

In addition to filling in the blanks below, show all of your work for this problem on paper for later upload.

**Question:**

Because you need water boiling at 100.0 °C for your recipe, how many grams of salt (NaCl(s)) would you need to add to 3.50 kg of water to raise the boiling point of water in Denver from the boiling point found in Problem 21 to 100.0 °C? Assume that the salt completely dissolves and fully dissociates in the water. If you did not get an answer for Problem 22, use 97.0 °C as the boiling point of water in Denver.

**Step-by-Step Solution:**

1. **Identify the boiling point elevation equation:**
   \[
   \Delta T_b = i \cdot K_b \cdot m
   \]
   where:
   - \(\Delta T_b\) = Boiling point elevation
   - \(i\) = Van 't Hoff factor (number of particles the solute dissociates into)
   - \(K_b\) = ebullioscopic constant (for water, \(K_b = 0.512\) °C kg/mol)
   - \(m\) = Molality of the solution

2. **Calculate the boiling point elevation \( \Delta T_b \):**
   \[
   \Delta T_b = 100.0 \, °C - 97.0 \, °C = 3.0 \, °C
   \]

3. **Determine the Van 't Hoff factor (i) for NaCl:**
   NaCl dissociates into 2 ions (Na⁺ and Cl⁻), so \( i = 2 \).

4. **Calculate the molality (m):**
   \[
   m = \frac{\Delta T_b}{i \cdot K_b} = \frac{3.0}{2 \cdot 0.512} = \frac{3.0}{1.024} \approx 2.93 \, \text{mol/kg}
   \]

5. **Calculate the number of moles of NaCl needed:**
   \[
   \text{moles of NaCl} = m \times \text{mass of water in kg} = 2
Transcribed Image Text:**Problem: Boiling Point Elevation Calculation** **Instructions:** In addition to filling in the blanks below, show all of your work for this problem on paper for later upload. **Question:** Because you need water boiling at 100.0 °C for your recipe, how many grams of salt (NaCl(s)) would you need to add to 3.50 kg of water to raise the boiling point of water in Denver from the boiling point found in Problem 21 to 100.0 °C? Assume that the salt completely dissolves and fully dissociates in the water. If you did not get an answer for Problem 22, use 97.0 °C as the boiling point of water in Denver. **Step-by-Step Solution:** 1. **Identify the boiling point elevation equation:** \[ \Delta T_b = i \cdot K_b \cdot m \] where: - \(\Delta T_b\) = Boiling point elevation - \(i\) = Van 't Hoff factor (number of particles the solute dissociates into) - \(K_b\) = ebullioscopic constant (for water, \(K_b = 0.512\) °C kg/mol) - \(m\) = Molality of the solution 2. **Calculate the boiling point elevation \( \Delta T_b \):** \[ \Delta T_b = 100.0 \, °C - 97.0 \, °C = 3.0 \, °C \] 3. **Determine the Van 't Hoff factor (i) for NaCl:** NaCl dissociates into 2 ions (Na⁺ and Cl⁻), so \( i = 2 \). 4. **Calculate the molality (m):** \[ m = \frac{\Delta T_b}{i \cdot K_b} = \frac{3.0}{2 \cdot 0.512} = \frac{3.0}{1.024} \approx 2.93 \, \text{mol/kg} \] 5. **Calculate the number of moles of NaCl needed:** \[ \text{moles of NaCl} = m \times \text{mass of water in kg} = 2
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