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 to absorb 114 kj of heat?
molesKNO3*(lattice energy+hydrationenergy)=114kj
solve for molesKNO3
To determine the amount of potassium nitrate needed to absorb 114 kJ of heat, we need to calculate the heat of solution. The heat of solution is the sum of the lattice energy and the heat of hydration.
Given:
Lattice energy of potassium nitrate (KNO3) = -163.8 kcal/mol
Heat of hydration of potassium nitrate (KNO3) = -155.5 kcal/mol
Heat to be absorbed = 114 kJ = 114,000 J
First, convert the heat of hydration and the heat to be absorbed to the same unit (Joules):
Heat of hydration = -155.5 kcal/mol = -155.5 kcal/mol x 4.18 J/cal x 1000 cal/kcal = -649,390 J/mol
Heat to be absorbed = 114 kJ = 114,000 J
Now, we can calculate the heat of solution:
Heat of solution = Lattice energy + Heat of hydration
Heat of solution = -163.8 kcal/mol + (-649,390 J/mol)
Heat of solution = -163.8 kcal/mol + (-649,390 J/mol)
Heat of solution = -163.8 kcal/mol - 649,390 J/mol
Heat of solution = -163.8 kcal/mol - 649,390 J/mol = -649,553.8 J/mol
Next, we can calculate the amount of potassium nitrate needed to absorb 114,000 J of heat:
Amount of potassium nitrate = Heat to be absorbed / Heat of solution
Amount of potassium nitrate = 114,000 J / -649,553.8 J/mol
Finally, calculate the amount of potassium nitrate needed in moles:
Amount of potassium nitrate = 0.1757 mol
Therefore, approximately 0.1757 moles of potassium nitrate would need to dissolve in water to absorb 114 kJ of heat.
(-163.8 + - 155.5) = - 319.3 kcal/mol
114kj/319.3 = -0.3570