When a 4.00-g sample of KCN is dissolved in water in a calorimeter that has a total heat capacity of 1.797 kJ·K–1, the temperature decreases by 0.400 K. Calculate the molar heat of solution of KCN.
q = 1.797 kJ/K x 0.4 K = ? kJ.
q in kJ/g = q/4.00
q in kJ/mol = (q/4.00) x molar mass KCN.
To calculate the molar heat of solution of KCN, we need to use the formula:
q = mCΔT
Where:
q = heat transfer in Joules (J)
m = mass of the sample in grams (g)
C = heat capacity of the calorimeter in J/K
ΔT = change in temperature in Kelvin (K)
First, convert the mass of KCN from grams to moles. The molar mass of KCN is:
molar mass of K = 39.10 g/mol
molar mass of C = 12.01 g/mol
molar mass of N = 14.01 g/mol
molar mass of KCN = 39.10 g/mol + 12.01 g/mol + 14.01 g/mol = 65.12 g/mol
moles of KCN = mass of KCN / molar mass of KCN
moles of KCN = 4.00 g / 65.12 g/mol = 0.0613 mol
Next, calculate the heat transfer (q):
q = mCΔT
q = (0.0613 mol)(1.797 kJ·K–1)(0.400 K)
Since the heat capacity given is in kJ, we need to convert it to J by multiplying by 1000:
q = (0.0613 mol)(1.797 kJ·K–1)(0.400 K)(1000 J/1 kJ)
q = 44.22 J
Finally, calculate the molar heat of solution of KCN:
Molar heat of solution of KCN = q / moles of KCN
Molar heat of solution of KCN = 44.22 J / 0.0613 mol
Molar heat of solution of KCN ≈ 720 J/mol
To calculate the molar heat of solution of KCN, we need to use the equation:
q = mCΔT
where:
- q is the heat absorbed or released by the solution (in this case, it is the negative value of heat released)
- m is the mass of the KCN sample (4.00 g)
- C is the heat capacity of the calorimeter (1.797 kJ·K–1)
- ΔT is the change in temperature (-0.400 K).
First, let's convert the mass of KCN to moles. To do this, we need the molar mass of KCN, which is the sum of the atomic masses of potassium (K), carbon (C), and nitrogen (N).
Molar mass of K = 39.10 g/mol
Molar mass of C = 12.01 g/mol
Molar mass of N = 14.01 g/mol
Molar mass of KCN = (39.10 g/mol) + (12.01 g/mol) + (14.01 g/mol) = 65.12 g/mol
Next, let's calculate the moles of KCN:
moles of KCN = mass of KCN / molar mass of KCN
moles of KCN = 4.00 g / 65.12 g/mol ≈ 0.061 mol
Now, we can calculate the heat released by the solution:
q = mCΔT
q = (4.00 g) × (1.797 kJ·K–1) × (-0.400 K)
q ≈ -2.8792 kJ
Since the question states that the temperature decrease is negative, we need to make the heat released positive.
q = -(-2.8792 kJ) = 2.8792 kJ
Finally, we calculate the molar heat of solution:
molar heat of solution = q / moles of KCN
molar heat of solution = (2.8792 kJ) / 0.061 mol ≈ 47.18 kJ/mol
Therefore, the molar heat of solution of KCN is approximately 47.18 kJ/mol.