The freezing point of a solution can be calculated using the formula:
ΔT = Kf * m
where ΔT is the change in freezing point, Kf is the freezing point depression constant (for water, it is 1.86 °C/m), and m is the molality of the solution.
First, we need to calculate the molality (m) of the sucrose solution:
m = moles of solute / kilograms of solvent
m = 3.8 mol / 1 kg
m = 3.8 mol/kg
Now, we can calculate the change in freezing point:
ΔT = Kf * m
ΔT = 1.86 °C/m * 3.8 m
ΔT = 7.068 °C
Since the freezing point of pure water is 0 °C, the freezing point of the solution will be:
Freezing point = 0 °C - ΔT
Freezing point = 0 °C - 7.068 °C
Freezing point = -7.068 °C
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