What is the freezing point of a solution of sucrose (table sugar), a nonelectrolyte, that contains 60.0 g of C12H22O11 dissolved in 413 g of water?

mols C12H22O11 = grams/molar mass

Then m = mols/kg solvent
Then delta T = Kf*m. You know m and Kf, solve for dT, then subtract from 0C to find the new freezing point.

To determine the freezing point of a solution, we need to use the concept of freezing point depression, which states that the presence of a solute in a solvent lowers the freezing point of the solution compared to the pure solvent.

First, we need to calculate the molality (m) of the sucrose solution. Molality is defined as the moles of solute per kilogram of solvent. The formula to calculate molality is:

m = (moles of solute) / (mass of solvent in kg)

1. Determine the moles of sucrose (C12H22O11):
The molar mass of sucrose (C12H22O11) is calculated by adding up the atomic masses of all the atoms in the compound.
C = 12.01 g/mol x 12
H = 1.01 g/mol x 22
O = 16.00 g/mol x 11

Molar mass of C12H22O11 = 342.34 g/mol

To calculate the moles of sucrose:
moles of sucrose = (mass of sucrose) / (molar mass of sucrose)
moles of sucrose = 60.0 g / 342.34 g/mol

2. Determine the mass of the solvent (water) in kg:
mass of solvent = 413 g of water
mass of solvent in kg = 413 g / 1000 = 0.413 kg

3. Calculate the molality (m):
m = (moles of solute) / (mass of solvent in kg)
m = (moles of sucrose) / (mass of solvent in kg)

Now that we have the molality (m) of the solution, we can use the freezing point depression constant (Kf) to calculate the change in freezing point (∆Tf). The value of Kf for water is 1.86 °C/m.

4. Calculate the change in freezing point (∆Tf):
∆Tf = Kf × m

Finally, to determine the freezing point of the solution, we need to subtract the calculated change in freezing point (∆Tf) from the normal freezing point of water, which is 0 °C.

5. Calculate the freezing point of the solution:
Freezing point of the solution = 0 °C - ∆Tf

By following these steps, you can find the freezing point of the sucrose solution containing 60.0 g of C12H22O11 dissolved in 413 g of water.