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The freezing point of a solution of 1.048-g of an unknown non-electrolyte dissolved in 36.21-g of benzene is 1.39°C. Use the freezing point of pure benzene and the freezing point depression constant from part 3.a) to calculate the molecular weight of the unknown.

Fp of depression constant (5.12)

User Dezinezync
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Answer: To calculate the molecular weight of the unknown non-electrolyte, we can use the formula for freezing point depression:

ΔTf = Kf * m

where:

ΔTf = freezing point depression (change in freezing point)

Kf = freezing point depression constant (given as 5.12°C/kg/mol for benzene)

m = molality of the solution (moles of solute per kilogram of solvent)

Step 1: Calculate the molality (m) of the solution.

Molality (m) = moles of solute / mass of solvent (in kg)

Given mass of the unknown non-electrolyte solute = 1.048 g

Given mass of benzene solvent = 36.21 g

Convert the masses to kilograms:

Mass of solute = 1.048 g / 1000 g/kg = 0.001048 kg

Mass of solvent = 36.21 g / 1000 g/kg = 0.03621 kg

Step 2: Calculate the freezing point depression (ΔTf).

ΔTf = freezing point of pure benzene - freezing point of the solution

The freezing point of pure benzene is 5.50°C, and the freezing point of the solution is 1.39°C. Therefore:

ΔTf = 5.50°C - 1.39°C

ΔTf = 4.11°C

Step 3: Calculate the molality (m) of the solution.

m = moles of solute / mass of solvent (in kg)

To find the moles of solute, we need to use the molar mass of the unknown non-electrolyte (Molar mass = m/Moles)

Step 4: Use the formula to find the molar mass of the unknown non-electrolyte:

ΔTf = Kf * (molar mass / molar mass of benzene) * molality

molar mass = ΔTf * molar mass of benzene / (Kf * molality)

molar mass = 4.11°C * 78.11 g/mol (molar mass of benzene) / (5.12°C/kg/mol * 0.001048 kg)

molar mass ≈ 203.45 g/mol

So, the molecular weight of the unknown non-electrolyte is approximately 203.45 g/mol.

User Joum
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