When 100.0 g of an unknown nonelectrolyte is dissolved in 500.0 g of benzene, C6H6, the solution boils at 82.9°C. Calculate the molecular weight (molar mass) of the unknown material. Kb for benzene is 2.53°C/m and the boiling point of pure benzene is 80.1°C?
delta T = Kb*m
Substitute and solve for m.
m = mols/kg solvent
Substitute and solve for mols.
mols = grams/molar mass
Substitut and solve for molar mass.
To calculate the molecular weight (molar mass) of the unknown material, we will use the boiling point elevation formula.
Boiling point elevation (∆Tb) is given by the equation:
∆Tb = Kbm * i * m
Where:
- ∆Tb is the increase in boiling point
- Kbm is the molal boiling point constant for the solvent (benzene)
- i is the van't Hoff factor (the number of particles formed after the substance dissolves)
- m is the molality of the solute (the number of moles of solute per kilogram of solvent)
First, let's calculate the molality (m) of the solute:
m = moles of solute / kilograms of solvent
Given that 100.0 g of the unknown material is dissolved in 500.0 g of benzene, we can calculate the number of moles of solute:
moles of solute = mass of unknown material / molar mass
To find molar mass, we rearrange the equation as follows:
molar mass = mass of unknown material / moles of solute
Next, let's calculate the increase in boiling point (∆Tb):
∆Tb = boiling point of the solution - boiling point of the pure solvent
Lastly, let's substitute the values into the boiling point elevation equation to find the molar mass.