The procedure described in this experiment was used to determine the molar mass of unknown liquid (non-electrolyte). The solution was made by mixing 0.961 g of the unknown with 100.0 g of water. The freezing point depression of the solution was −3.7°C. Calculate the molar mass of the unknown. Assume that the molal freezing point depression constant of water is 1.86°C·kg/mol and that the freezing point of water is 0.00°C.

To determine the molar mass of the unknown liquid using the freezing point depression method, we'll use the following formula:

ΔT = K_f * m * i

Where:
ΔT = change in freezing point (in °C)
K_f = molal freezing point depression constant of water (in °C·kg/mol)
m = molality of the solution (in mol/kg)
i = van't Hoff factor (for a non-electrolyte, i = 1)

First, we need to calculate the molality of the solution. The molality (m) is defined as the moles of solute per kilogram of solvent. In our case, the solvent is water.

moles of unknown = mass of unknown / molar mass of unknown

Given:
mass of unknown = 0.961 g

To calculate the moles of the unknown, we need the molar mass of the unknown liquid. However, since we are trying to determine the molar mass, we have a bit of a conundrum. We can estimate a rough molar mass and iterate until we find a value that matches the experimental data.

Let's assume a molar mass of 50 g/mol.

moles of unknown = 0.961 g / (50 g/mol) = 0.01922 mol

Next, we need to calculate the molality (m):

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

Given:
mass of solvent (water) = 100.0 g = 0.1000 kg

molality (m) = 0.01922 mol / 0.1000 kg = 0.1922 mol/kg

Now, we can calculate the change in freezing point (ΔT) using the formula:

ΔT = K_f * m * i

Given:
K_f = 1.86 °C·kg/mol
i = 1 (for a non-electrolyte)

ΔT = 1.86 °C·kg/mol * 0.1922 mol/kg * 1 = 0.3571 °C

The change in freezing point (ΔT) is given as -3.7 °C in the question. We take the absolute value in this case (-3.7 °C becomes 3.7 °C).

Now we can substitute the values into the formula and solve for the molar mass of the unknown:

3.7 °C = 1.86 °C·kg/mol * 0.1922 mol/kg * 1 * (molar mass of unknown) / 0.1000 kg

Simplifying the equation:

3.7 °C * 0.1000 kg / (1.86 °C·kg/mol * 0.1922 mol/kg) = molar mass of unknown

Solving the equation:

Molar mass of unknown = 19.92 g/mol

Therefore, the molar mass of the unknown liquid (non-electrolyte) is approximately 19.92 g/mol.