If 1373 g of a substance is dissolved in 2315 g of cyclohexane solvent, the boiling point of the solution is 87.69 oC. Calculate the apparent molar mass (g/mol) of substance.
delta T = Kb*molality
Calculate molality, then
molality = moles/kg solvent
Calculate moles, then
moles = g/molar mass,
calculate molar mass.
Post your work if you get stuck.
You will need to look up the boiling point of cyclohexane if it isn't given in the problem.
To calculate the apparent molar mass of the substance, you can use the Colligative Property equation:
ΔT = K_b * m
Where:
ΔT = the boiling point elevation of the solution
K_b = the molal boiling point constant of the solvent
m = molality of the solution (moles of solute per kilogram of solvent)
First, we need to calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
Given:
Mass of solvent (cyclohexane) = 2315 g = 2.315 kg
Molar mass of substance = ?
Mass of substance = 1373 g
Number of moles of substance = mass / molar mass
Now we need to calculate the molality (m):
m = moles of solute / mass of solvent (in kg)
Number of moles of solute = mass of substance / molar mass
m = (mass of substance / molar mass) / mass of solvent
Now, let's plug the values into the equation:
m = (1373 g / molar mass) / 2.315 kg
Now, we can calculate the apparent molar mass using the boiling point elevation equation:
ΔT = K_b * m
Given:
Boiling point elevation (ΔT) = 87.69 °C
Rearranging the equation and solving for the apparent molar mass:
molar mass = (ΔT / (K_b * m)) * mass of solvent
Now, plug in the known values:
molar mass = (87.69 °C / (K_b * ((1373 g / molar mass) / 2.315 kg))) * 2.315 kg
Simplifying the equation may require rearranging it multiple times and solving it iteratively. In this case, you could estimate the molar mass to initiate the iteration process.
Keep repeating these calculations until the molar mass converges to a consistent value.