Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol. How much potassium nitrate has to dissolve in water to absorb 1.00⨉10² kJ of heat?

Verified step by step guidance

1. Convert the given heat absorption from kilojoules to kilocalories using the conversion factor: 1 kcal = 4.184 kJ.
2. Calculate the enthalpy change for the dissolution of potassium nitrate using the formula: $\mathrm{\Delta }{H}_{\text{solution}}=\text{Lattice Energy}+\text{Heat of Hydration}$.
3. Determine the amount of heat absorbed per mole of potassium nitrate dissolved by using the calculated $\mathrm{\Delta }{H}_{\text{solution}}$.
4. Use the converted heat absorption value to find the number of moles of potassium nitrate needed by dividing the total heat to be absorbed by the heat absorbed per mole.
5. Convert the number of moles of potassium nitrate to grams using its molar mass (101.1 g/mol).

Key Concepts

Lattice Energy

Lattice energy is the amount of energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. In the case of potassium nitrate, a lattice energy of -163.8 kcal/mol indicates that this amount of energy is released when one mole of potassium nitrate is formed from its constituent ions.

Heat of Hydration

The heat of hydration refers to the energy change that occurs when ions are surrounded by water molecules and solvate. For potassium nitrate, the heat of hydration is -155.5 kcal/mol, meaning that this amount of energy is released when one mole of potassium nitrate dissolves in water. This process is crucial for understanding how much energy is absorbed or released during the dissolution of ionic compounds.

Thermodynamics of Dissolution

The thermodynamics of dissolution involves the balance between lattice energy and heat of hydration to determine the overall energy change when a solute dissolves in a solvent. In this scenario, the dissolution of potassium nitrate absorbs heat from the surroundings, which can be calculated by considering the total energy changes involved. Understanding this concept is essential for calculating how much potassium nitrate is needed to absorb a specific amount of heat.