A 0.0230 g sample of an unknown was dissolved in 2.260 g of benzene. The molality of this solution, determined by freezing point depression, was 0.0408 m. What is the molecular weight of the unknow substance?
delta T = Kf*m
Solve for m
m = mols/kg solvent
Solve for mols
mols = grams/molar mass
Solve for molar mass.
To determine the molecular weight of the unknown substance, we need to use the formula for freezing point depression. The formula for freezing point depression is:
ΔTf = Kf * m
Where:
ΔTf is the change in freezing point
Kf is the cryoscopic constant of the solvent (benzene)
m is the molality of the solution
In this case, the change in freezing point (ΔTf) can be determined by subtracting the freezing point of pure benzene from the freezing point of the solution. However, the freezing point of pure benzene is not given in the question, so we can't calculate the actual value of ΔTf.
However, we can still solve the problem using the concept of molality and the freezing point depression equation.
Given:
Mass of the unknown substance (m) = 0.0230 g
Mass of benzene (solvent) = 2.260 g
Molality (m) = 0.0408 m
To find the molecular weight (M) of the unknown substance, we first need to find the moles of the unknown substance and the moles of solvent.
Step 1: Calculate moles of the unknown substance (n_unknown)
Using the formula:
n = mass (m) / molar mass (Molar mass_unknown)
Step 2: Calculate moles of solvent (n_solvent)
Using the formula:
n = mass (m) / molar mass (Molar mass_benzene)
Step 3: Calculate the number of moles of solvent per kilogram of solvent (molality)
Using the formula:
molality (m) = n_solvent / (mass of solvent (kg))
Step 4: Rearrange the equation to find the molar mass of the unknown substance (Molar mass_unknown)
Rearranging the equation:
molar mass_unknown = mass_unknown / n_unknown
Let's calculate each step:
Step 1: Calculate moles of the unknown substance (n_unknown)
n_unknown = m_unknown / Molar mass_unknown
Given: m_unknown = 0.0230 g
n_unknown = 0.0230 g / Molar mass_unknown
Step 2: Calculate moles of solvent (n_solvent)
n_solvent = m_solvent / Molar mass_benzene
Given: m_solvent = 2.260 g
Molar mass_benzene = 78.11 g/mol (This is the molar mass of benzene)
n_solvent = 2.260 g / 78.11 g/mol
Step 3: Calculate the number of moles of solvent per kilogram of solvent (molality)
m = n_solvent / (mass of solvent (kg))
Given: m = 0.0408 m
mass of solvent (kg) = 2.260 g / 1000 g/kg
m = 0.0408 m = n_solvent / 0.00226 kg
n_solvent = m * 0.00226 kg
Step 4: Rearrange the equation to find the molar mass of the unknown substance (Molar mass_unknown)
Molar mass_unknown = m_unknown / n_unknown
Molar mass_unknown = 0.0230 g / n_unknown
Now, you need to substitute n_solvent into the equation for m_unknown.
Finally,
Molar mass_unknown = 0.0230 g / (0.0230 g / Molar mass_unknown)
Simplifying the equation, we find:
Molar mass_unknown = Molar mass_unknown
Therefore, the molecular weight of the unknown substance cannot be determined solely from the given freezing point depression data.