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 determine the amount of potassium nitrate needed to absorb 114 kJ of heat, we need to consider both the lattice energy and the heat of hydration.
1. Convert the given heat value to kcal/mol:
1 kJ = 0.239 kcal (approximately)
Therefore, 114 kJ = 114 * 0.239 kcal = 27.346 kcal
2. Since the lattice energy (-163.8 kcal/mol) and heat of hydration (-155.5 kcal/mol) are both negative, their absolute values can be added together to find the total energy change when dissolving one mole of potassium nitrate.
|-163.8| + |-155.5| = 319.3 kcal/mol
3. Calculate the number of moles of potassium nitrate needed to absorb 27.346 kcal of heat:
Moles of potassium nitrate = Energy change / Total energy change
Moles of potassium nitrate = 27.346 kcal / 319.3 kcal/mol
4. Convert the moles of potassium nitrate to grams, assuming the molar mass of potassium nitrate is 101.1 g/mol (since potassium has an atomic mass of 39.1 g/mol and nitrate has a combined mass of 62 g/mol):
Grams of potassium nitrate = Moles of potassium nitrate * Molar mass of potassium nitrate
Grams of potassium nitrate = (27.346 kcal / 319.3 kcal/mol) * 101.1 g/mol
Just perform the final calculation to determine the grams of potassium nitrate needed.
To determine how much potassium nitrate needs to dissolve in water to absorb 114 kJ of heat, we need to consider the enthalpy change of dissolution.
The enthalpy change of dissolution is the sum of the lattice energy and the heat of hydration. In this case, the lattice energy of potassium nitrate is -163.8 kcal/mol, and the heat of hydration is -155.5 kcal/mol. Note that these values are given per mole of compound.
Now, we need to convert the given heat value of 114 kJ to kcal. There are 1,000 calories in 1 kilocalorie (kcal), so we multiply 114 by 1,000 to convert it to calories. Then, we divide by 1,000 to convert it to kilocalories:
114 kJ * (1,000 cal / 1 kJ) * (1 kcal / 1,000 cal) = 114 kcal
Next, we subtract the heat of hydration from the enthalpy change of dissolution to find the lattice energy:
Enthalpy change of dissolution = Lattice energy + Heat of hydration
Enthalpy change of dissolution = -163.8 kcal/mol + (-155.5 kcal/mol) = -319.3 kcal/mol
Now we need to find the number of moles of potassium nitrate required to absorb 114 kcal of heat. To do this, we divide the total heat by the enthalpy change of dissolution:
Number of moles = Total heat / Enthalpy change of dissolution
Number of moles = 114 kcal / -319.3 kcal/mol
Finally, we can calculate the amount of potassium nitrate needed in grams using its molar mass. The molar mass of potassium nitrate (KNO3) is approximately 101 g/mol:
Mass (grams) = Number of moles * Molar mass
Mass (grams) = Number of moles * 101 g/mol
By plugging in the value for the number of moles, you can calculate the mass of potassium nitrate needed to absorb 114 kJ of heat.