Calculate the freezing point depression of an aqueous solution prepared by mixing 22.0 g C6H12O6, with 600 ml of water
moles C6H12O6 = grams/molar mass
Solve for moles.
m = mols/kg solvent
Solve for m
delta T = Kf*m
Solve for delta T.
To calculate the freezing point depression of the aqueous solution, we need to know the molality of the solute and the cryoscopic constant of water.
Step 1: Calculate the number of moles of solute.
To find the number of moles of C6H12O6 (solute), divide the given mass by its molar mass. The molar mass of C6H12O6 is the sum of the atomic masses of its constituent elements:
C = 12.01 g/mol, H = 1.01 g/mol, and O = 16.00 g/mol.
Thus, the molar mass of C6H12O6 = 6 * 12.01 + 12 * 1.01 + 6 * 16.00 = 180.18 g/mol.
Number of moles = Mass / Molar mass
Number of moles = 22.0 g / 180.18 g/mol
Step 2: Determine the molality of the solution.
Molality is defined as the number of moles of solute per kilogram of solvent. To calculate the molality, we need to know the mass of the solvent (water) in kilograms.
Given that the volume of water is 600 ml, which is equivalent to 600 grams (since the density of water is approximately 1 g/ml), we can convert grams to kilograms by dividing by 1000.
Mass of water = 600 g = 600 / 1000 kg
Molality (m) = Number of moles of solute / Mass of solvent in kg
Step 3: Find the freezing point depression constant (cryoscopic constant) of water.
The cryoscopic constant (Kf) is a constant specific to the solvent (water) and is equal to 1.86 °C/m.
Step 4: Calculate the freezing point depression.
The freezing point depression (∆Tf) is given by the formula:
∆Tf = Kf * m
Substituting the values we obtained into the formula, we have:
∆Tf = 1.86 °C/m * molality
Now we can add the calculational steps together:
Number of moles = 22.0 g / 180.18 g/mol
Mass of water = 600 g = 600 / 1000 kg
Molality (m) = Number of moles of solute / Mass of solvent in kg
∆Tf = 1.86 °C/m * molality
By following these steps, you can calculate the freezing point depression of the aqueous solution prepared by mixing 22.0 g of C6H12O6 with 600 ml of water.