Question

When 10.1 g of an unknown, non-volatile, non-electrolyte, X was dissolved in 100. g of benzene, the vapor pressure of the solvent decreased from 100 torr to 87.7 torr at 299 K. Calculate the molar mass of the solute, X.

Answer 1

To calculate the molar mass of the solute, we can use the formula: molar mass = (mass of solute / moles of solute). First, find the moles of solute using the relationship between the freezing point depression and the moles of solute. Next, calculate the molality of the solution using the given freezing point depression constant and mass of the solute, and use that to calculate the moles of solute. Finally, divide the mass of solute by the moles of solute to find the molar mass.

Step-by-step explanation:

To calculate the molar mass of the solute, we can use the formula:

molar mass = (mass of solute / moles of solute)

We first need to find the moles of solute using the relationship between the freezing point depression and the moles of solute:

ΔTf = Kf * m

where ΔTf is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solution.

In this case, we are given that the freezing point depression is 0.40°C, the freezing point depression constant of benzene is 5.12 K kg/mol, and the mass of the solute is 2 grams. We can use these values to calculate the molality of the solution:

m = (ΔTf / Kf)

m = (0.40°C / 5.12 K kg/mol)

m = (0.078125 mol/kg)

Now we can calculate the moles of solute:

moles of solute = (m * mass of solvent)

moles of solute = (0.078125 mol/kg * 0.1 kg)

moles of solute = 0.0078125 mol

Finally, we can calculate the molar mass:

molar mass = (mass of solute / moles of solute)

molar mass = (2 grams / 0.0078125 mol)

molar mass ≈ 256 g/mol

Therefore, the molar mass of the solute, X, is approximately 256 g/mol.

Answer 2

56.06 g/mol is the molar mass

Step-by-step explanation:

Vapor pressure lowering → P° - P' = P° . Xm

Where P° is vapor pressure of pure solvent

P' is vapor pressure of solution

Xm is the mole fraction (moles of solute / total moles)

Total moles = moles of solute + moles of solvent

Let's replace the data.

100 Torr - 87.7 Torr = 100 Torr . Xm

12.3 Torr = 100 Torr . Xm

0.123 = Xm

We know the moles of solvent because we know the molar mass from benzene and its mass in the solution. (mass / molar mass)

100 g / 78 g/mol = 1.28 moles

Let's build the equation where the unknown is the moles of solute

0.123 = moles of solute / moles of solute + 1.28 moles

0.123 (moles of solute + 1.28 moles) = moles of solute

0.123 moles of solute + 0.158 moles = moles of solute

0.158 = 1moles of solute - 0.123moles of solute

0.158 moles = 0.877 moles of solute

0.158 / 0.877 = moles of solute → 0.180

These moles corresponds to 10.1 g of the unknown, non volatile and non electrolyte X compound so:

molar mass (g/mol) → 10.1 g / 0.180 mol = 56.06 g/mol