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------------------------------------------------ A solution containing 10.0 g of an unknown liquid and 100.0 g of water has a freezing point of -3.55 °C. Given [tex]$K_f = 1.86\,°C/m$[/tex] for water, the molar mass of the unknown liquid is:

A. 62.1 g/mol
B. 98.2 g/mol
C. 52.6 g/mol
D. 69.0 g/mol

Answer :

Final answer:

To find the molar mass of the unknown liquid, use the formula: Molar mass = (mass of solute)/(moles of solute).

Calculate the moles of water and the moles of the unknown liquid.

Then, determine the molality of the solution and use the freezing point depression formula to solve for the molar mass of the unknown liquid.

Explanation:

To find the molar mass of the unknown liquid, we can use the formula:

Molar mass (g/mol) = (mass of solute)/(moles of solute)

First, we need to calculate the moles of solute:

Calculate the moles of water, using its formula weight:

    1. Formula weight of water = 2(1.008 g/mol) + 16.00 g/mol = 18.016 g/mol
    2. Moles of water = mass of water/molar mass of water = 100 g/18.016 g/mol = 5.550 mol
  2. Calculate the moles of the unknown liquid, using its formula weight:
    1. Moles of the unknown liquid = mass of unknown liquid/molar mass of the unknown liquid
    2. Moles of the unknown liquid = 10.0 g/molar mass of the unknown liqui

Next, we can determine the molecular formula of the unknown liquid:

  1. Calculate the molality of the solution:
    1. Molality (m) = moles of solute/mass of solvent (in kg)
    2. Given that the mass of water is 100.0 g and the density of water at 25°C is approximately 1 g/mL, the mass of water in kg is:
    3. Mass of water (kg) = 100.0 g/1000 g/kg = 0.100 kg
    4. Molality (m) = (moles of the unknown liquid + moles of water)/0.100 kg = (10.0 g/molar mass of the unknown liquid + 5.550 mol)/0.100 kg
  2. Use the freezing point depression formula to solve for the molar mass of the unknown liquid:
    1. ∆T = Kf * m
    2. Given that the freezing point depression (∆T) is -3.55°C and the cryoscopic constant (Kf) is 1.86°C/m, we can solve for the molar mass:
    3. -3.55°C = 1.86°C/m * [(10.0 g/molar mass of the unknown liquid + 5.550 mol)/0.100 kg]

By solving this equation, we can find the molar mass of the unknown liquid.

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