you are conducting a freezing-point determination in the laboratory by using an aqueous solution of KNO3. The observed freezing point of the solution is -1.15 C. Using a pure water sample, you recorded the freezing point of the pure solvent of the same thermometer as .25 C. Determine the molal concentration of KNO3. Assume that there are no forces of attraction between ions
To determine the molal concentration of KNO3, we will use the concept of freezing point depression. Freezing point depression occurs when a solute is added to a solvent, causing the freezing point of the resulting solution to be lower than that of the pure solvent. The change in freezing point is directly proportional to the molal concentration of the solute.
The formula to calculate freezing point depression (ΔTf) is given by:
ΔTf = Kf * m
Where:
- ΔTf is the change in freezing point (in this case, -1.15°C - 0.25°C = -1.4°C),
- Kf is the cryoscopic constant (provided for the solvent you're using),
- m is the molal concentration of the solute.
Given that the freezing point depression (ΔTf) is -1.4°C and the freezing point depression constant for water (Kf) is 1.86 °C kg/mol, we can rearrange the formula to solve for m:
m = ΔTf / Kf
Plugging in the values, we get:
m = -1.4°C / 1.86 °C kg/mol
Calculating this, we find that the molal concentration of KNO3 is approximately -0.75 mol/kg.
Note: The negative sign indicates a depression in the freezing point relative to the pure solvent due to the addition of the solute.