When a 3.00-g sample of KCN is dissolved in water in a calorimeter that has a total heat capacity of 1.123 kJ·K–1, the temperature decreases by 0.480 K. Calculate the molar heat of solution of KCN.
q = mass sample x Ccal x delta T.
Divide by 3 to obtain q/1 g sample, and multiply by molar mass to find q for 1 mol KCN. That will give you q in kJ/mol.
To calculate the molar heat of solution of KCN, we can use the formula:
q = m × C × ΔT/moles
Where:
q is the heat released or absorbed by the reaction
m is the mass of the substance (in this case, KCN)
C is the heat capacity of the calorimeter
ΔT is the change in temperature
moles is the number of moles of the substance (in this case, KCN)
First, we need to determine the number of moles of KCN. The molar mass of KCN can be found from the periodic table:
Molar mass of K = 39.10 g/mol
Molar mass of C = 12.01 g/mol
Molar mass of N = 14.01 g/mol
Adding them up:
Molar mass of KCN = 39.10 + 12.01 + 14.01 = 65.12 g/mol
To find the number of moles, we can use the equation:
moles = mass / molar mass
moles = 3.00 g / 65.12 g/mol
moles = 0.0460 mol
Now, we can substitute the values into the heat equation:
q = (3.00 g) × (1.123 kJ·K^–1) × (0.480 K) / (0.0460 mol)
Simplifying the equation:
q = 6.56 kJ
The heat released by the reaction is 6.56 kJ.
Finally, to determine the molar heat of solution, divide the heat by the number of moles:
ΔH = q / moles
ΔH = 6.56 kJ / 0.0460 mol
Calculating:
ΔH = 142.6 kJ/mol
Therefore, the molar heat of solution of KCN is 142.6 kJ/mol.