When 0.354 g of an unknown nonelectrolyte compound was dissolved in 12.5 g of benzene a solution was formed that froze at 4.46 degrees C. Calculate the molar mass of the unknown compound. The freezing point of benzene if 5.48 degrees C, and the Kf of benzene is 5.12 degrees C/Molal
delta T = Kf*m
Substitute and solve for m.
m = mols kg solvent
substitute and solve for mols
mols = grams/molar mass
Substitute and solve for molar mass
To calculate the molar mass of the unknown compound, we need to use the concept of freezing point depression.
Freezing point depression is a colligative property, which means it depends on the concentration of solute particles, but not their identity. It can be calculated using the equation:
∆Tf = Kf × m
where:
∆Tf is the freezing point depression (the difference between the freezing point of the pure solvent and the freezing point of the solution),
Kf is the freezing point depression constant (a property of the solvent), and
m is the molality of the solution (the amount of solute in moles divided by the mass of the solvent in kg).
In this case, we are given:
Mass of solute (unknown compound) = 0.354 g
Mass of solvent (benzene) = 12.5 g
Freezing point of solution = 4.46°C
Freezing point of pure benzene = 5.48°C
Kf of benzene = 5.12°C/molal
First, we need to calculate the molality of the solution.
To do this, we divide the moles of solute by the mass of the solvent in kg.
Moles of solute = mass of solute / molar mass of solute
Since we do not know the molar mass of the unknown compound, we'll denote it as "X" for now.
Moles of solute = 0.354 g / X g/mol.
Next, we need to convert the mass of the solvent to kg:
Mass of solvent = 12.5 g / 1000 = 0.0125 kg.
Now, we can calculate the molality:
m = Moles of solute / Mass of solvent in kg
m = (0.354 g / X g/mol) / 0.0125 kg
Substituting the given values, we have:
∆Tf = (5.12°C/molal) × [(0.354 g / X g/mol) / 0.0125 kg]
∆Tf = 4.46 - 5.48 = -1.02°C
Now, we can rearrange the equation to solve for the molar mass, X:
X = (0.354 g / (∆Tf * 0.0125 kg / (5.12°C/molal))
Substituting the given values:
X = (0.354 g / (-1.02°C * 0.0125 kg / (5.12°C/molal))
Calculating this expression will give us the molar mass of the unknown compound.