Question

A 20% (by mass) solution of cane sugar in water has a freezing point of 271 K. Calculate the freezing point of a 5% glucose solution in water if the freezing point of pure water is 273.15 K.

a. 273.15 K
b. 272.5 K
c. 271 K
d. 270.5 K

Answer 1

To calculate the freezing point of a solution, divide the moles of solute by the mass of the solvent and use the freezing point depression equation, ΔT = Kf * m. The freezing point depression constant for water is 1.86 °C/m.

Step-by-step explanation:

To calculate the freezing point of a solution, you use the equation ΔT = Kf * m, where ΔT is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solute. In this case, the molality of the solution can be calculated by dividing the moles of solute by the mass of the solvent (water). Firstly, calculate the moles of sucrose using its molar mass and mass. Then, divide the moles by the kilograms of water to get the molality. Finally, use the equation to calculate the freezing point depression and subtract it from the freezing point of pure water to get the freezing point of the solution.

The freezing point depression constant for water, also known as Kf, is 1.86 °C/m. The molar mass of sucrose (C12H22O11) is 342.3 g/mol.

1. Calculate the moles of sucrose by dividing the mass of sucrose by its molar mass.
2. Convert the mass of water to kilograms by dividing by 1000.
3. Calculate the molality of the solution by dividing the moles of sucrose by the kilograms of water.
4. Calculate the freezing point depression by multiplying the molality by Kf.
5. Subtract the freezing point depression from the freezing point of pure water to get the freezing point of the solution.

Using these steps, you can calculate the freezing point of the 115.0 g sucrose solution in 350.0 g of water.