Acetone has a Kf value of 2.40 ºC/m. The freezing point of pure acetone is –94.80ºC. Calculate the molality of a solution containing acetone and an unknown solute. This solution freezes at -96.20°C. Be sure to round your answer to three significant figures. Do not include your units in your answer.
The Correct Answer and Explanation is :
To calculate the molality of the solution, we will use the formula that relates the freezing point depression to the molality of a solution:
[
\Delta T_f = K_f \times m
]
Where:
- (\Delta T_f) is the freezing point depression (in °C),
- (K_f) is the cryoscopic constant (freezing point depression constant) of the solvent, and
- (m) is the molality of the solution (in mol/kg).
Step 1: Determine the Freezing Point Depression ((\Delta T_f))
The freezing point depression is the difference between the freezing point of the pure solvent and the freezing point of the solution.
[
\Delta T_f = T_f(\text{pure solvent}) – T_f(\text{solution})
]
[
\Delta T_f = -94.80^\circ C – (-96.20^\circ C)
]
[
\Delta T_f = 1.40^\circ C
]
Step 2: Use the Freezing Point Depression Equation to Find Molality
Now that we know the freezing point depression (\Delta T_f = 1.40^\circ C) and the cryoscopic constant (K_f = 2.40^\circ C/m), we can solve for molality (m).
Rearranging the formula:
[
m = \frac{\Delta T_f}{K_f}
]
Substitute the known values:
[
m = \frac{1.40^\circ C}{2.40^\circ C/m}
]
[
m = 0.5833 \, \text{mol/kg}
]
Step 3: Round the Answer to Three Significant Figures
The molality of the solution is approximately:
[
m = 0.583 \, \text{mol/kg}
]
Explanation
Freezing point depression occurs because the presence of a solute lowers the freezing point of the solvent. The magnitude of this depression depends on the amount of solute particles in the solution and is proportional to the molality of the solution. In this case, we were given the freezing points of pure acetone and the solution, which allowed us to calculate the freezing point depression. Using the formula with the provided (K_f) value for acetone, we were able to find the molality of the solution.