When 0.500 g of an unknown compound was dissolved in 15.0 g benzene, the freezing point depression was determined to be 0320C. The molar mass of the unknown compound is ?? g/mol.
(The freezing point depression constant for benzene is 5.12C kgmol.
I really don't know where to begin. Can someone provide with some kind of equation so I can solve this?
*CORRECTION 0320C is supposed to be 0.320C
Certainly! To solve this problem, we will use the equation for freezing point depression:
ΔTf = Kf * m * i
where:
ΔTf is the freezing point depression in degrees Celsius,
Kf is the freezing point depression constant for benzene (given as 5.12 °C kg/mol),
m is the molality (moles of solute per kilogram of solvent),
i is the van't Hoff factor (a measure of the number of particles into which a solute dissociates in a solution).
In this case, we need to find the molar mass of the unknown compound, so we can start by calculating the molality using the given information.
Step 1: Calculate the number of moles of solute
Given that the mass of the unknown compound is 0.500 g, we can calculate the number of moles using the molar mass (M) of the unknown compound. The formula is:
moles = mass / molar mass
We are trying to find the molar mass, so we'll rearrange the equation:
molar mass = mass / moles
Step 2: Calculate the molality (m)
Molality is defined as the moles of solute per kilogram of solvent. We need to convert the mass of benzene (15.0 g) to kilograms by dividing by 1000:
mass of benzene (kg) = mass of benzene (g) / 1000
Step 3: Calculate the freezing point depression (ΔTf)
We know that the freezing point depression (ΔTf) is given as 0.32 °C.
Step 4: Calculate the van't Hoff factor (i)
The van't Hoff factor depends on the nature of the solute. For most compounds, it is 1. However, if the compound dissociates into ions in solution (such as in the case of an ionic compound), the van't Hoff factor can be greater than 1.
Step 5: Rearrange the freezing point depression equation to solve for the molar mass
We'll rearrange the equation to solve for the molar mass:
molar mass = ΔTf / (Kf * m * i)
Now, you can plug in the known values into this equation to find the molar mass of the unknown compound.