Answer:
291.07 g potassium nitrate has to dissolve in water, at room temperature, to absorb 1.00 x 102 kJ of heat
Explanation:
Given that,
Lattice energy of Potassium nitrate (KNO3) = -163.8 kcal/mol
Heat of hydration of KNO3 = -155.5 kcal/mol
Heat to absorb by KNO3 = 100kJ
Mass of KNO3 to dissolve in water = ?
Solution:
Heat of solution = Hydration energy - Lattice energy
= -155.5 -(-163.8)
= 8.3 kcal/mol
since,
1 kcal/mol = 4.184 kJ/mole
Therefore,
= 4.184 kJ/mol x 8.3 kcal/mol
= 34.73 kJ/mol
Now, 34.73 kJ of heat is absorbed when 1 mole of KNO3 is dissolved in water.
For 100 kJ of heat would be
= 100/34.73
= 2.879 moles of KNO3
Molar mass of KNO3 = 101.1 g/mole
Mass of KNO3 = Molar mass x moles
= 101.1 g/mole x 2.879
= 291.07 g
= 0.291 kg
291.07 g potassium nitrate has to dissolve in water, at room temperature, to absorb 1.00 x 102 kJ of heat
The mass of potassium nitrate is 295 g.
We know that;
Heat of solution = Hydration energy - lattice energy
Hydration energy = -155.5 kcal /mol
lattice energy = -163.8 kcal/mol
Heat of solution = (-155.5 kcal /mol) - (-163.8 kcal/mol)
Heat of solution = 8.3 kcal/mol
But
1 kcal/mol = 4.184 kJ/mole
Hence;
8.3 kcal/mol × 4.184 kJ/mole = 34.2 kJ/mole
So;
1 mole of Potassium nitrate evolves 34.2 kJ of heat
x moles of Potassium nitrate evolves 1.00 x 102 kJ
x = 1.00 x 102 kJ/34.2 kJ
x = 2.92 moles
Mass of Potassium nitrate = 2.92 moles x 101.1 g/mole = 295 g
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