Final answer:
The cryoscopic constant of glacial acetic acid is calculated using the enthalpy of fusion and the melting point, resulting in a value of 12.14 J/(g°C).
Step-by-step explanation:
To calculate the cryoscopic constant (Kf) of glacial acetic acid, we use its melting point and the enthalpy of fusion. The Kf is a proportionality constant that relates the amount by which the freezing point of a solvent is depressed by the addition of a solute to the molal concentration of the solute. Using the formula Kf = (enthalpy of fusion) / (melting point * molar mass), we can calculate the cryoscopic constant for glacial acetic acid.
The given values are an enthalpy of fusion of 11.7 kJ/mol, a melting point of 16.0°C, and a molar mass of 60.05 g/mol. To use these in the formula, we first need to adjust the units of the melting point from °C to K by adding 273.15 to the melting point, resulting in 289.15 K. However, for the cryoscopic constant, we actually do not need to convert to Kelvin as both the change in temperature and melting point are in degrees Celsius, which would cancel each other out. So, we use the values as they are, and the cryoscopic constant formula becomes:
Kf = (11.7 kJ/mol) / (16.0°C * 60.05 g/mol)
First, convert kJ to J: 11.7 kJ/mol = 11700 J/mol. Then plug in the values:
Kf = (11700 J/mol) / (16.0°C * 60.05 g/mol)
Kf = 12.14 J/(g°C)
This is the cryoscopic constant for glacial acetic acid, which is a measure of how much the freezing point of the acid would be lowered by the addition of a solute.