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 105kj of heat? Answer in kg.
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To calculate how much potassium nitrate needs to dissolve to absorb 105 kJ of heat, we need to use the heat of hydration value and convert the given units to match that value.
Given data:
Lattice energy of potassium nitrate = -163.8 kcal/mol
Heat of hydration of potassium nitrate = -155.5 kcal/mol
Heat to be absorbed = 105 kJ
First, let's convert the given heat of hydration to match the unit used for the heat to be absorbed:
-155.5 kcal/mol × (4.184 kJ/1 kcal) = -649.062 kJ/mol
Now, we can set up a ratio using the heat of hydration:
-649.062 kJ/mol (heat of hydration) corresponds to 1 mol of potassium nitrate.
We can use this ratio to find how much potassium nitrate is needed to absorb 105 kJ of heat:
105 kJ × (1 mol/-649.062 kJ) = -0.16139 mol
Since we want the answer in kg, we need to convert moles to kilograms. To do that, we need to know the molar mass of potassium nitrate. The molar mass of potassium nitrate (KNO3) can be calculated as follows:
Molar mass of K = 39.1 g/mol
Molar mass of N = 14.01 g/mol
3 × Molar mass of O = 3 × 16.00 g/mol
Molar mass of KNO3 = 39.1 g/mol + 14.01 g/mol + 3 × 16.00 g/mol = 101.1 g/mol
Now, we can convert moles to kilograms using the molar mass:
-0.16139 mol × (101.1 g/mol) × (1 kg/1000 g) = -0.016339 kg
However, we have a negative value due to the negative sign of the lattice energy and heat of hydration. In this context, we can disregard the negative sign as it only represents the direction of energy flow. Thus, the amount of potassium nitrate to dissolve in water to absorb 105 kJ of heat is approximately 0.016339 kg (or 16.34 grams).