Question

Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol. You may want to reference (pages 551 - 555) section 12.3 while completing this problem. How much potassium nitrate has to dissolve in water to absorb 109 kJ of heat? Express your answer using two significant figures.

Answer 1

$\Delta H_{solution} = \Delta H_{lattice} + \Delta H _{hydration} = -163.8 kcal/mol -155.5 kcal/mol = - 319.3 kcal/mol$

Convert the unit from kcal/mol to kJ/mol
1 kcal = 4.184 kJ

$319.3 kcal/mol = 319.3 \times 4.184 = 1336 kJ/mol$

109 kJ of th heat corresponds to $\dfrac {109 kJ}{1336 kJ/mol} = 0.0816$ moles.

The molar mass of potassium nitrate is 101.1 g/mol.
0.0816 moles of potassium nitrate corresponds to $0.0816 mol \time 101.1 g/mol= 8.3 g = 0.0083$ kg
(because 1 kg = 1000 g)