What is the freezing point of a solution of 1.17g of 1-naphthol, C10H8O, dissolved in 2.00ml of benzene at 20 degrees C? The density of benzene at 20 degrees C is 876g/ml. Kf for benzene is 5.12 degrees C/m, and benzene's normal freezing point is 5.53 degrees C.
moles = grams/molar mass
Solve for moles.
molality = moles/kg solvent
Solve for molality.
delta T = kf*m
Solve for delta T and convert to freezing point.
You will need to use density to convert from volume to grams or kg.
To find the freezing point of the solution, we can use the equation:
ΔTf = Kf * m
Where:
ΔTf = change in freezing point
Kf = freezing point depression constant
m = molality of the solution
First, let's calculate the molality of the solution.
Step 1: Calculate the moles of 1-naphthol
Given that the mass of 1-naphthol is 1.17g and the molar mass is 144.17 g/mol, we can use the formula:
moles = mass / molar mass
moles = 1.17g / 144.17 g/mol
moles ≈ 0.0081 mol
Step 2: Calculate the mass of benzene
Given that the volume of benzene is 2.00ml and the density of benzene is 876 g/ml, we can use the formula:
mass = volume * density
mass = 2.00ml * 876 g/ml
mass ≈ 1752 g
Step 3: Calculate the molality (m)
Molality is defined as the moles of solute per kilogram of solvent. We need to convert the mass of benzene from grams to kilograms:
m = moles / mass of solvent in kg
m = 0.0081 mol / 1.752 kg
m ≈ 0.0046 mol/kg
Step 4: Calculate the freezing point depression (ΔTf)
Now that we have the molality, we can calculate the freezing point depression using the equation:
ΔTf = Kf * m
Given that Kf for benzene is 5.12 degrees C/m:
ΔTf = 5.12 degrees C/m * 0.0046 mol/kg
ΔTf ≈ 0.0235 degrees C
Step 5: Calculate the freezing point of the solution
The freezing point of the solution is the normal freezing point of benzene minus the freezing point depression:
Freezing point = Normal freezing point - ΔTf
Freezing point = 5.53 degrees C - 0.0235 degrees C
Freezing point ≈ 5.51 degrees C
Therefore, the freezing point of the solution is approximately 5.51 degrees C.
To determine the freezing point of the solution, you can use the equation:
ΔT = Kf * m
Where:
ΔT is the change in freezing point
Kf is the cryoscopic constant of benzene
m is the molality of the solution
First, let's calculate the molality of the solution using the given information:
Step 1: Calculate the moles of 1-naphthol
To find the moles, we divide the given mass by the molar mass of 1-naphthol.
Molar Mass of 1-naphthol (C10H8O):
M(C) = 12.01 g/mol
M(H) = 1.01 g/mol
M(O) = 16.00 g/mol
Molar Mass of C10H8O:
12.01 * 10 + 1.01 * 8 + 16.00 = 144.18 g/mol
Moles of 1-naphthol = Mass / Molar Mass
Moles of 1-naphthol = 1.17 g / 144.18 g/mol
Step 2: Calculate the molality
Molality (m) = Moles of solute / Mass of solvent (in kg)
The mass of the benzene is the product of its density and volume:
Mass of benzene = Density * Volume
Mass of benzene = 876 g/ml * 2.00 ml
Convert the mass of benzene to kg:
Mass of benzene = (876 g/ml * 2.00 ml) / 1000
Molality (m) = (Moles of 1-naphthol) / (Mass of benzene in kg)
Now that we have obtained the molality, we can calculate the change in freezing point (ΔT):
ΔT = Kf * m
Finally, we can calculate the freezing point of the solution:
Freezing Point = Normal Freezing Point of Benzene - ΔT
Substitute the values of Normal Freezing Point of Benzene and ΔT to find the freezing point of the solution.