Potassium has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol. How much potassium nitrate needs to dissolve in water to absorb 114 kJ of heat?

To find out how much potassium nitrate needs to dissolve in water to absorb 114 kJ of heat, we need to use the equation:

ΔHsol = ΔHlattice + ΔHhydration

where:
ΔHsol is the enthalpy of solution or heat absorbed when a solute dissolves in a solvent,
ΔHlattice is the lattice energy, which represents the energy required to break apart the crystal lattice of the solid,
ΔHhydration is the heat of hydration, which represents the heat released when the solute ions are hydrated or dissolved in water.

Given:
ΔHlattice = -163.8 kcal/mol
ΔHhydration = -155.5 kcal/mol
ΔHsol = 114 kJ (which needs to be converted to kcal by dividing by 4.184 since 1 kJ = 4.184 kcal)

First, let's convert the heat of solution from kJ to kcal:

ΔHsol = 114 kJ ÷ 4.184 = 27.28 kcal

Now, we can substitute the values into the equation:

27.28 kcal = -163.8 kcal/mol + (-155.5 kcal/mol)

Next, we need to solve for the number of moles of potassium nitrate (KNO3), which is the solute. To do this, we can rearrange the equation and solve for the moles:

27.28 kcal = (-163.8 - 155.5) kcal/mol * moles

moles = 27.28 kcal ÷ (-163.8 - 155.5) kcal/mol

moles ≈ 0.0869 mol

Therefore, approximately 0.0869 moles of potassium nitrate need to dissolve in water to absorb 114 kJ of heat.