what is the freezing point of a solution that contains 20.2g of urea CO(NH2)2 in 295mL water? Assume a density of water of 1.00g/mL
mols urea = grams/molar mass = ?
m urea = mols urea/kg solvent (kg solvent = 0.295)
delta T = Kf*m. Solve for delta T
Then subtract delta T from the initial freezing point.
To find the freezing point of a solution, we can use the formula for freezing point depression:
ΔT = Kf * m
where:
ΔT is the change in freezing point
Kf is the freezing point depression constant for water, which is -1.86 °C/m
m is the molality of the solution
First, let's calculate the molality of the solution:
Molality (m) is the moles of solute per kilogram of solvent.
To find the moles of urea (CO(NH2)2), we can use its molar mass:
Molar mass of CO(NH2)2 =
(12.01 g/mol * 1) + (14.01 g/mol * 1) + (1.01 g/mol * 2) + (14.01 g/mol * 2) = 60.06 g/mol
Now we can calculate the number of moles of urea:
moles of urea = mass / molar mass
= 20.2 g / 60.06 g/mol
= 0.3366 mol
Next, let's calculate the mass of water in the solution:
mass of water = volume of water * density of water
= 295 mL * 1.00 g/mL
= 295 g
We need to convert the mass of water to kilograms:
mass of water (kg) = 295 g / 1000
= 0.295 kg
Now we can calculate the molality of the solution:
molality (m) = moles of solute / mass of solvent (in kg)
= 0.3366 mol / 0.295 kg
= 1.141 m
Finally, we can calculate the change in freezing point:
ΔT = Kf * m
= -1.86 °C/m * 1.141 m
≈ -2.12 °C
Therefore, the freezing point of the solution that contains 20.2 g of urea CO(NH2)2 in 295 mL of water is lowered by approximately 2.12 °C.
To determine the freezing point of a solution, you need to use a concept called freezing point depression. The freezing point of a pure solvent is typically higher than that of a solution. When a solute is added to a solvent, it disrupts the formation of the solvent's crystal lattice, which lowers the freezing point.
To calculate the freezing point depression, you need to use the formula:
ΔT = Kf * m
Where:
ΔT is the freezing point depression
Kf is the freezing point depression constant (specific to the solvent)
m is the molality of the solution
To find the molality of the solution, you can use the formula:
m = moles of solute / mass of solvent (in kg)
1. Determine the moles of urea (CO(NH2)2):
To find the moles of urea, divide the given mass of urea by its molar mass. The molar mass of CO(NH2)2 is calculated as follows:
C: 12.01 g/mol (carbon)
O: 16.00 g/mol (oxygen)
N: 14.01 g/mol (nitrogen)
H: 1.01 g/mol (hydrogen)
Molar mass of CO(NH2)2 = (12.01 * 1) + (16.00 * 1) + (14.01 * 2) + (1.01 * 4) = 60.06 g/mol
moles of urea = mass of urea / molar mass of urea
2. Determine the mass of the water (solvent):
The volume of water is given as 295 mL, and the density of water is given as 1.00 g/mL. Therefore, the mass of water can be calculated as follows:
mass of water = volume of water * density of water
3. Calculate the molality of the solution:
molality (m) = moles of urea / mass of water (in kg)
4. Calculate the freezing point depression:
ΔT = Kf * m
Finally, to find the freezing point of the solution, subtract the freezing point depression from the freezing point of the pure solvent (water):
Freezing point of the solution = Freezing point of pure solvent - ΔT
Note: The value of Kf depends on the solvent. In this case, we assume you are using water, and the Kf value for water is 1.86 °C/m.