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 107 kJ of heat?
To determine how much potassium nitrate needs to dissolve in water to absorb 107 kJ of heat, we will use the concept of enthalpy change.
Enthalpy change (ΔH) is the heat absorbed or released during a chemical process, such as dissolution. For a process where a solute dissolves in a solvent, the enthalpy change can be calculated as the sum of the lattice energy (ΔHlattice) and the heat of hydration (ΔHhydration).
First, let's convert the units to be consistent:
Lattice energy = -163.8 kcal/mol
Heat of hydration = -155.5 kcal/mol
Heat to be absorbed = 107 kJ
1 kcal = 4.184 kJ (conversion factor)
-163.8 kcal/mol = -163.8 * 4.184 kJ/mol ≈ -684.79 kJ/mol (approximated to 3 significant figures)
-155.5 kcal/mol = -155.5 * 4.184 kJ/mol ≈ -649.34 kJ/mol (approximated to 3 significant figures)
Now we can calculate the total enthalpy change (ΔHtotal):
ΔHtotal = ΔHlattice + ΔHhydration
ΔHtotal = (-684.79 kJ/mol) + (-649.34 kJ/mol)
ΔHtotal = -1334.13 kJ/mol
The negative sign indicates that the process is exothermic, meaning heat is released during dissolution.
To find out how much potassium nitrate needs to dissolve to absorb 107 kJ of heat, we can use a proportion based on the enthalpy change:
ΔHtotal / x = ΔHgiven / mass
where x is the molar mass of potassium nitrate (KNO3), and mass is the amount in grams.
The molar mass of potassium nitrate can be calculated as:
K: 39.10 g/mol (from periodic table)
N: 14.01 g/mol (from periodic table)
O: 3 × 16.00 g/mol = 48.00 g/mol (from molecular formula)
Total molar mass = 39.10 + 14.01 + 48.00 = 101.11 g/mol (approximated to 3 significant figures)
Now, we can rearrange the proportion to solve for mass:
mass = (ΔHgiven * x) / ΔHtotal
mass = (107 kJ * 101.11 g/mol) / -1334.13 kJ/mol
Solving this equation gives us the mass of potassium nitrate needed to absorb 107 kJ of heat in water.