A 0.750 g sample of an unknown substance is dissolved in 20.0 g of benzene, C6H6. The freezing point of the solution is 4.53 oC. Calculate the molar mass of the substance. The normal freezing point for benzene is 5.53 oC and Kf is 5.12 oC/m.
To solve this problem, we can use the equation for freezing point depression:
ΔT = Kf * m
Where:
ΔT = change in freezing point (normal freezing point - observed freezing point)
Kf = cryoscopic constant for benzene (5.12 oC/m)
m = molality of the solution
Step 1: Calculate the change in freezing point (ΔT)
ΔT = normal freezing point - observed freezing point
= 5.53 oC - 4.53 oC
= 1.00 oC
Step 2: Calculate the molality (m) of the solution
Molality (m) is defined as the moles of solute per kilogram of solvent.
Mass of benzene = 20.0 g
Moles of benzene = mass / molar mass (molar mass of benzene = 78.11 g/mol)
= 20.0 g / 78.11 g/mol
= 0.256 mol
Mass of solute = 0.750 g
Moles of solute = mass / molar mass of solute (let's call it 'X')
= 0.750 g / X g/mol
= 0.750 / X mol
Molality (m) = moles of solute / mass of solvent (in kg)
= 0.750 g / (0.020 kg)
= 37.50 mol/kg
Step 3: Calculate the molar mass of the substance (X)
ΔT = Kf * m
1.00 oC = 5.12 oC/m * 37.50 mol/kg
Rearranging the equation:
X = (ΔT / (Kf * m))
Substitute the given values into the equation:
X = (1.00 oC) / (5.12 oC/m * 37.50 mol/kg)
X = 0.532 mol/kg
The molar mass of the substance is 0.532 g/mol.
To calculate the molar mass of the unknown substance, we need to use the freezing point depression equation:
ΔT = Kf * m
Where ΔT is the freezing point depression, Kf is the molal freezing point depression constant, and m is the molality of the solution.
First, let's calculate the molality of the solution using the given information:
Molality (m) = moles of solute / mass of solvent in kg
We are given that a 0.750 g sample of the unknown substance is dissolved in 20.0 g of benzene. To calculate the molality, we need to convert the masses to kg:
mass of solute = 0.750 g = 0.750 * 10^-3 kg
mass of solvent = 20.0 g = 20.0 * 10^-3 kg
Now we can calculate the molality:
molality (m) = (0.750 * 10^-3 kg) / (20.0 * 10^-3 kg) = 0.0375 mol/kg
Next, we can calculate the freezing point depression (ΔT) using the given information:
ΔT = 5.53 oC - 4.53 oC = 1.00 oC
Now we can use the freezing point depression equation to find the molar mass:
ΔT = Kf * m
1.00 oC = (5.12 oC/m) * (0.0375 mol/kg)
Rearranging the equation to solve for the molar mass (M):
M = (1.00 oC) / [(5.12 oC/m) * (0.0375 mol/kg)]
M = 42.7 g/mol
Therefore, the molar mass of the unknown substance is approximately 42.7 g/mol.
delta T = Kf*m
Calculate m
m = mols/kg solvent.
calculate moles.
moles = grams/molar mass
calculate molar mass.