The molar mass of a non-dissociated, non-volatile compound is to be determined by dissolving 5.00 g of the compound into 50.0 g of benzene. The freezing point of benzene was lowered by 2.5 degrees C. The freezing point depression constant (Kf) for benzene is 5.0 degree C/molal. What is the molar mass of this compound?

delta T = Kf m
delta T is given as 2.5o C
Kf = 5.0 C/molal
solve for m = molality.

Then m = # mols/kg solvent and mols = grams/molar mass.

Post your work if you get stuck.

To determine the molar mass of the compound, we can use the equation:

delta T = Kf * m

where:
delta T is the change in freezing point of the solvent (benzene)
Kf is the freezing point depression constant for benzene (5.0 °C/molal)
m is the molality of the solution (mol solute/kg solvent)

Given:
delta T = 2.5 °C
Kf = 5.0 °C/molal

We need to solve for m, which is the molality of the solution. The formula for molality is:

m = mol solute / kg solvent

In this case, we are given the mass of the compound (5.00 g) and the mass of the solvent (50.0 g). To find the molality, we need to convert these masses to moles.

First, we find the moles of compound by dividing the mass of the compound by its molar mass. Let's call the molar mass of the compound M:

moles of compound = 5.00 g / M

Next, we find the moles of solvent by dividing the mass of the solvent by its molar mass. The molar mass of benzene is approximately 78.11 g/mol, so:

moles of solvent = 50.0 g / 78.11 g/mol

Now, we can calculate the molality by dividing the moles of compound by the mass of the solvent in kilograms:

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

Given that mass of the solvent is 50.0 g and there are 1000 g in a kg:

m = (moles of compound / moles of solvent) / (50.0 g / 1000 g/kg)

Simplifying the equation:

m = (moles of compound / moles of solvent) * (1000 g/kg / 50.0 g)

Now substitute the value of m into the original equation:

2.5 °C = 5.0 °C/molal * [(moles of compound / moles of solvent) * (1000 g/kg / 50.0 g)]

Now solve for the moles of compound:

moles of compound = (2.5 °C * moles of solvent) / (5.0 °C/molal * 1000 g/kg / 50.0 g)

After finding the moles of compound, we can calculate its molar mass by dividing the mass of the compound (5.00 g) by the moles of compound:

Molar mass = 5.00 g / moles of compound

By following these steps, you should be able to determine the molar mass of the compound.