Question

How much potassium nitrate has to dissolve in water to absorb 105 kj of heat? there are 4.184 kj/kcal. also note the answer is to be reported in kg?

Answer 1

Lattice energy of potassium nitrate (KNO3) = -163.8 kcal/mol

Hydration energy of KNO3 = -155.5 kcal/mole

Heat of solution is the amount of heat absorbed by water when 1 mole of KNO3 is dissolved in it

Heat of solution = Hydration energy - Lattice energy

                           = -155.5 -(-163.8) = 8.3 kcal/mol

1 kcal/mol = 4.184 kJ/mole

Therefore, 8.3 kcal/mole = 4.184 * 8.3 = 34.73 kJ/mol

Now,  34.73 kJ of heat is absorbed when 1 mole of KNO3 is dissolved

The given 105 kJ of heat would correspond to : 105/34.73 = 3.023 moles of KNO3

Molar mass of KNO3 = 101.1 g/mole

Mass of KNO3 = Molar mass * moles

                       = 101.1 * 3.023 = 305.63 g = 0.3056 kg