A 0.750 g sample of an unknown substance is dissolved in 20.0 g of benzene, C6H6. The freezing point of the solution is 4.53 oC. Calculate the molar mass of the substance. The normal freezing point for benzene is 5.53 oC and Kf is 5.12 oC/m.

See below.

0.732 g/mol

To calculate the molar mass of the substance, we need to use the equation for freezing point depression. The formula for freezing point depression is:

ΔTf = Kf × m

where:
ΔTf is the change in freezing point,
Kf is the freezing point depression constant for the solvent (benzene in this case), and
m is the molality of the solution.

First, we need to calculate the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. To do this, we'll need to convert the given quantities into the appropriate units:

Mass of substance (unknown) = 0.750 g
Mass of solvent (benzene) = 20.0 g
Freezing point depression constant (Kf) = 5.12 oC/m

Now, let's calculate the molality (m):
molality (m) = moles of substance / mass of solvent (in kg)

To convert the mass of substance to moles, we need to divide it by the molar mass of the substance.

Next, let's calculate the change in freezing point (ΔTf):
ΔTf = normal freezing point of solvent - freezing point of the solution

Finally, we can rearrange the freezing point depression equation to solve for the molar mass (M) of the substance:
M = (ΔTf / (Kf × m)) × (mass of solvent / moles of substance)

Let's plug in the values and calculate the molar mass.