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, at room temperature, to absorb 1.00 x 102 kJ of heat

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