What is the freezing point of a solution that contains 21.1g of urea, CO(NH2)2, in 305mL water, H2O? Assume a density of water of 1.00 g/mL.

2.59 Degrees

To determine the freezing point of a solution, we need to use the equation:

ΔTf = Kf * m

Where:
ΔTf is the change in freezing point
Kf is the freezing point depression constant (molal freezing point constant) of the solvent
m is the molality of the solute (moles of solute per kilogram of solvent)

First, let's calculate the molality (m) using the given data:

1. Calculate the moles of urea (CO(NH2)2):
Moles of urea = (mass of urea) / (molar mass of urea)

The molar mass of urea (CO(NH2)2) can be calculated as:
molar mass of C = 12.01 g/mol
molar mass of O = 16.00 g/mol
molar mass of N = 14.01 g/mol
molar mass of H = 1.01 g/mol

Molar mass of urea = (12.01 * 1) + (16.00 * 1) + (14.01 * 2) + (1.01 * 4)

Calculate the molar mass of urea and convert grams to moles:
Molar mass of urea = (12.01 * 1) + (16.00 * 1) + (14.01 * 2) + (1.01 * 4)

2. Calculate the moles of water (H2O):
Density of water = 1.00 g/mL
Mass of water = volume of water * density of water

Convert mL to grams:
Mass of water = 305 mL * 1.00 g/mL

Convert grams to moles:
Moles of water = (mass of water) / (molar mass of water)

The molar mass of water (H2O) is 18.02 g/mol.

Now, we can calculate the molality (m):

m = (moles of urea) / (kilograms of water)

1. Convert moles of water to kilograms:
Kilograms of water = (mass of water) / 1000

2. Calculate the molality:
m = (moles of urea) / (kilograms of water)

Once we have the molality (m), we can calculate the change in freezing point (ΔTf).

3. Use the molality (m) and the freezing point depression constant (Kf) to calculate ΔTf:
The freezing point depression constant (Kf) for water is -1.86 °C/molal.

ΔTf = Kf * m

Finally, we can calculate the freezing point of the solution.

4. Calculate the freezing point of the solution:
Freezing point of solution = freezing point of pure solvent + ΔTf

The freezing point of pure water is 0 °C.

Let's calculate the freezing point of the solution step-by-step.

To find the freezing point of the solution, we need to use the concept of freezing point depression. The freezing point of a solution is lower than that of the pure solvent due to the presence of solute particles.

First, we need to calculate the molality (m) of the solution, which is defined as moles of solute per kilogram of solvent.
Given that the mass of urea is 21.1 g and the volume of water is 305 mL (which is equal to 305 grams due to the given density of 1.00 g/mL), we can calculate the moles of urea using its molar mass of 60.06 g/mol.

moles of urea = mass of urea / molar mass of urea
= 21.1 g / 60.06 g/mol
= 0.35 mol

Next, we need to calculate the mass of water in kilograms.

mass of water = volume of water x density of water
= 305 g

Finally, we can calculate the molality of the solution.

molality (m) = moles of solute / mass of solvent (in kg)
= 0.35 mol / (305 g / 1000)
= 1.15 mol/kg

Now we can use the freezing point depression formula to find the freezing point of the solution.
The freezing point depression (∆Tf) is given by:

∆Tf = Kf x m

Where Kf is the molal freezing point depression constant, which is specific to the solvent. For water, its value is 1.86 °C/m. Substitute the value of ∆Tf and solve for the freezing point.

Freezing point = freezing point of the solvent - ∆Tf

The freezing point of pure water is 0 °C, so we can substitute this value into the equation.

Freezing point = 0 °C - ∆Tf
= 0 °C - (1.86 °C/m x 1.15 mol/kg)
= 0 °C - 2.139 °C
≈ -2.14 °C

Therefore, the freezing point of the solution containing 21.1 g of urea in 305 mL of water is approximately -2.14 °C.