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 105 kJ of heat?
DrBob the end of your explanation is vague as all sweet mercy
To determine how much potassium nitrate needs to dissolve in water to absorb 105 kJ of heat, we need to use the heat of hydration value.
The heat of hydration is the amount of heat released or absorbed when one mole of a solute dissolves in water.
Given that the heat of hydration of potassium nitrate is -155.5 kcal/mol, we need to convert this value to kJ/mol:
1 kcal = 4.184 kJ
-155.5 kcal/mol = -155.5 * 4.184 kJ/mol = -649.382 kJ/mol
Now, we can set up a proportion to solve for the amount of potassium nitrate needed to absorb 105 kJ of heat:
(-649.382 kJ/mol) / x mol = 105 kJ
To solve for x, we can cross-multiply:
-649.382 kJ * x = 105 kJ * 1 mol
x = (105 kJ * 1 mol) / (-649.382 kJ)
x ≈ -0.161 mol
Since we can't have a negative number of moles, we discard the negative sign and obtain approximately 0.161 mol.
Therefore, approximately 0.161 moles of potassium nitrate need to dissolve in water to absorb 105 kJ of heat.
To determine how much potassium nitrate needs to dissolve in water to absorb 105 kJ of heat, we need to calculate the amount of heat released or absorbed during the dissolution process.
The total heat absorbed during the dissolution of potassium nitrate can be calculated by summing the lattice energy and the heat of hydration:
Total heat absorbed = lattice energy + heat of hydration
To convert the given values from kcal/mol to kJ/mol, we can multiply by 4.184, since 1 kcal is equal to 4.184 kJ:
Lattice energy = -163.8 kcal/mol * 4.184 kJ/kcal = -684.5692 kJ/mol
Heat of hydration = -155.5 kcal/mol * 4.184 kJ/kcal = -649.012 kJ/mol
Total heat absorbed = -684.5692 kJ/mol + (-649.012 kJ/mol)
= -1333.5812 kJ/mol
Now, we can use stoichiometry to calculate the amount of potassium nitrate required to absorb 105 kJ of heat. The molar heat absorbed per mole of potassium nitrate is given by the total heat absorbed.
Molar heat absorbed = Total heat absorbed / moles of potassium nitrate
To calculate the amount of potassium nitrate required for 105 kJ of heat absorption, we can use the following equation:
(105 kJ / -1333.5812 kJ/mol) * (1 mol/average molar mass of potassium nitrate) = moles of potassium nitrate
The average molar mass of potassium nitrate (KNO3) is calculated by adding the atomic masses of potassium (K), nitrogen (N), and three oxygen (O) atoms.
Average molar mass of KNO3 = (1 * atomic mass of K) + (1 * atomic mass of N) + (3 * atomic mass of O)
Substituting the atomic masses of each element:
= (1 * 39.10 g/mol) + (1 * 14.01 g/mol) + (3 * 16.00 g/mol)
= 101.10 g/mol
Now, we can calculate the amount of potassium nitrate required:
(105 kJ / -1333.5812 kJ/mol) * (1 mol/101.10 g) = moles of potassium nitrate
Finally, to obtain the mass of potassium nitrate in order to absorb 105 kJ of heat, we multiply the moles of potassium nitrate by the molar mass of KNO3:
Mass of potassium nitrate = moles of potassium nitrate * molar mass of KNO3
dHsoln = dHhydration - lattice energy
dHsoln = -155 kcal/mol -(-164.8 kcal/mol
Solve for dHsoln = about 8 kcal/mol and I would convert that to J/mol. Then
1 mol KNO3 x (105,000/converted 8.3, then convert mols KNO3 to grams KNO3. If I didn't slip on my calculator that is about 300 g KNO3 but check my work carefully.