What will be the freezing point of a solution made by dissolving 5.25 g of naphthalene (C10H8) in 100.0 g benzene (C6H6?). The normal freezing point of benzene is 5.5°C and K f (benzene) is 5.12°C / m.
3.4
mols naphthalene = grams/molar mass = ?
molality = m = mols naphthalene/kg solvent
Then delta T = Kf*m and solve for delta T. Subtract from the normal freezing point to arrive at the new freezing point.
To calculate the freezing point of the solution, we can use the formula:
ΔT = K_f * m
Where:
ΔT is the change in freezing point
K_f is the molal freezing point depression constant
m is the molality of the solution
First, let's calculate the molality of the solution:
Molar mass of naphthalene (C10H8) = (12.01 * 10) + (1.01 * 8) = 128.18 g/mol
Moles of naphthalene = mass / molar mass = 5.25 g / 128.18 g/mol = 0.041 mol
Moles of benzene (C6H6) = mass / molar mass = 100.0 g / 78.11 g/mol = 1.28 mol
Molality (m) = moles of solute / mass of solvent (in kg)
= moles of naphthalene / (mass of benzene in g / 1000)
= 0.041 mol / (100.0 g / 1000)
= 0.41 mol/kg
Now, we can calculate the change in freezing point (ΔT):
ΔT = K_f * m
= 5.12°C / m * 0.41 mol/kg
= 2.0992°C
Finally, we can determine the freezing point of the solution:
Freezing point = normal freezing point of benzene - ΔT
= 5.5°C - 2.0992°C
= 3.4008°C
Therefore, the freezing point of the solution will be approximately 3.4008°C.
To find the freezing point of the solution, we can use the equation:
ΔT = Kf * m
Where:
- ΔT is the change in freezing point
- Kf is the freezing point depression constant (Cryoscopic constant) for the solvent
- m is the molality of the solution
To find the molality of the solution, we first need to calculate the number of moles of naphthalene and benzene.
1. Calculate the number of moles of naphthalene (C10H8):
- The molar mass of naphthalene (C10H8) = (12.01 g/mol * 10) + (1.01 g/mol * 8) = 128.18 g/mol
- Number of moles of naphthalene = mass / molar mass = 5.25 g / 128.18 g/mol
2. Calculate the number of moles of benzene (C6H6):
- The molar mass of benzene (C6H6) = (12.01 g/mol * 6) + (1.01 g/mol * 6) = 78.11 g/mol
- Number of moles of benzene = mass / molar mass = 100.0 g / 78.11 g/mol
3. Calculate the molality of the solution:
- Molality (m) = moles of solute / mass of solvent (in kg)
- Convert the mass of benzene to kg by dividing it by 1000: 100.0 g / 1000 = 0.1 kg
- Molality (m) = moles of naphthalene / mass of benzene (in kg)
Now that we have the molality, we can calculate the freezing point depression:
ΔT = Kf * m
Substitute the values:
ΔT = 5.12 °C/m * (moles of naphthalene / 0.1 kg)
Finally, we can find the freezing point of the solution by subtracting the freezing point depression from the normal freezing point of benzene:
Freezing point of the solution = Normal freezing point of benzene - ΔT
Substitute the values to find the freezing point of the solution.