13. A sample of ice at 0°C melts after absorbing 300,000J of heat. How many moles of H,0 are contained in the sample? Assume that the heat of fusion of ice is 333 J/g

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**Thermodynamics Practice Problem: Heat Absorption by Melting Ice**

**Problem 13:**

A sample of ice at 0°C melts after absorbing 300,000 J of heat. How many moles of \( H_2O \) are contained in the sample? Assume that the heat of fusion of ice is 333 J/g.

---

**Solution Steps:**

1. **Identify the given values:**
   - Heat absorbed (\( Q \)): 300,000 J
   - Heat of fusion of ice (\( \Delta H_f \)): 333 J/g

2. **Calculate the mass of ice melted using the formula:**
   
   \[
   Q = m \cdot \Delta H_f
   \]
   
   Rearrange to solve for mass (\( m \)):
   
   \[
   m = \frac{Q}{\Delta H_f} = \frac{300,000 \text{ J}}{333 \text{ J/g}} = 900.9 \text{ g}
   \]

3. **Convert the mass to kilograms:**
   
   \[
   900.9 \text{ g} = 0.9009 \text{ kg}
   \]

4. **Find the number of moles of \( H_2O \):**
   
   The molar mass of water (\( H_2O \)) is approximately 18.015 g/mol. Thus, the number of moles (\( n \)) is:
   
   \[
   n = \frac{900.9 \text{ g}}{18.015 \text{ g/mol}} \approx 50 \text{ moles}
   \]

**Answer:**

Approximately 50 moles of \( H_2O \) are contained in the sample that absorbed 300,000 J of heat to melt at 0°C.
Transcribed Image Text:**Thermodynamics Practice Problem: Heat Absorption by Melting Ice** **Problem 13:** A sample of ice at 0°C melts after absorbing 300,000 J of heat. How many moles of \( H_2O \) are contained in the sample? Assume that the heat of fusion of ice is 333 J/g. --- **Solution Steps:** 1. **Identify the given values:** - Heat absorbed (\( Q \)): 300,000 J - Heat of fusion of ice (\( \Delta H_f \)): 333 J/g 2. **Calculate the mass of ice melted using the formula:** \[ Q = m \cdot \Delta H_f \] Rearrange to solve for mass (\( m \)): \[ m = \frac{Q}{\Delta H_f} = \frac{300,000 \text{ J}}{333 \text{ J/g}} = 900.9 \text{ g} \] 3. **Convert the mass to kilograms:** \[ 900.9 \text{ g} = 0.9009 \text{ kg} \] 4. **Find the number of moles of \( H_2O \):** The molar mass of water (\( H_2O \)) is approximately 18.015 g/mol. Thus, the number of moles (\( n \)) is: \[ n = \frac{900.9 \text{ g}}{18.015 \text{ g/mol}} \approx 50 \text{ moles} \] **Answer:** Approximately 50 moles of \( H_2O \) are contained in the sample that absorbed 300,000 J of heat to melt at 0°C.
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