Solution:
Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol.
Therefore,
Latice Energy: K⁺(g) + NO₃⁻(g) → KNO₃(s) . . . ∆H = –163.8 kcal/mol
Hydration:
K⁺(g) + NO₃⁻(g) + excess H₂O → K⁺(aq) + NO₃⁻(aq) . . . ∆H = –155.5 kcal/mol
Flip the first equation and add them together:
KNO₃(s) + excess H₂O → K⁺(aq) + NO₃⁻(aq) . . . ∆H = +8.3 kcal/mol = +34. 73 kJ/mol
(110kJ)/(34. 73 kJ/mol) = 3.16729 mol must be dissolved to absorb 110 kJ