how much potassium nitrate has to dissolve in water to absorb 103 kj of heat

To determine how much potassium nitrate (\( \text{KNO}_3 \)) needs to dissolve in water to absorb 103 kJ of heat, we'll need to use the concept of enthalpy of solution (ΔH_sol), which is the amount of heat absorbed or released when a substance dissolves in a solvent. 

### Steps:
1. **Find the enthalpy of solution (ΔH_sol) for potassium nitrate**: The enthalpy of solution for \( \text{KNO}_3 \) is approximately \( +34.89 \, \text{kJ/mol} \). This positive value indicates that the dissolution of potassium nitrate is endothermic, meaning it absorbs heat.

2. **Use the formula**:
   \[
   q = n \times \Delta H_{\text{sol}}
   \]
   Where:
   - \( q \) is the heat absorbed (in kJ)
   - \( n \) is the number of moles of \( \text{KNO}_3 \)
   - \( \Delta H_{\text{sol}} \) is the enthalpy of solution per mole (in kJ/mol)

   Rearranging for \( n \):
   \[
   n = \frac{q}{\Delta H_{\text{sol}}}
   \]

3. **Calculate the number of moles**:
   \[
   n = \frac{103 \, \text{kJ}}{34.89 \, \text{kJ/mol}} \approx 2.95 \, \text{mol}
   \]

4. **Convert moles to mass**: 
   The molar mass of \( \text{KNO}_3 \) is approximately \( 101.1 \, \text{g/mol} \).
   \[
   \text{Mass} = n \times \text{Molar mass}
   \]
   \[
   \text{Mass} \approx 2.95 \, \text{mol} \times 101.1 \, \text{g/mol} \approx 298.2 \, \text{g}
   \]

### Answer:
You need to dissolve approximately **298.2 grams** of potassium nitrate in water to absorb 103 kJ of heat.

Would you like any further details or have any questions about this calculation? Here are some related questions to consider:

1. What is the significance of the enthalpy of solution being positive or negative?
2. How does temperature affect the solubility of potassium nitrate in water?
3. What are some common uses of potassium nitrate in various industries?
4. How would the required mass change if the enthalpy of solution were lower?
5. What would happen if you tried to dissolve more potassium nitrate than the water can hold?

**Tip:** Always ensure that the temperature at which you dissolve a substance is appropriate, as the solubility and enthalpy of solution can vary with temperature.

Learn how much potassium nitrate needs to dissolve in water to absorb 103 kJ of heat. Detailed step-by-step calculation using the enthalpy of solution concept. Suitable for advanced high school students and beyond.

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