Calculate the molar mass of an unknown molecular compound mixed with solid camphor C10H16O, heated and then cooled giving the following data. show all steps in calculation.
mass of unknown: 0.195 g
Tf(camphor)= 179.8 degree C
Kf(camphor)=-40.0 degree C/m
mass of camphor-25.03g
Tf(solution)=176.7 degree C
delta T = Kf*m
delta T = 179.8-176.7 = ?
Kf = from your table.
Solve for molality.
Then m = mols/kg solvent
m from above.
kg solvent = 0.02503 kg
Solve for mols.
Then mols = grams/molar mass
mols from above.
mass unknown = 0.195g
Solve for molar mass.
To calculate the molar mass of the unknown molecular compound, we will use the concept of freezing-point depression. The molar mass can be determined based on the change in freezing point caused by the presence of the unknown compound in the camphor solution.
Step 1: Calculate the change in the freezing point (ΔTf):
ΔTf = Tf(solution) - Tf(camphor)
= 176.7 °C - 179.8 °C
= -3.1 °C
Step 2: Calculate the molality (m) of the solution:
Given that Kf(camphor) = -40.0 °C/m, we can use the formula:
ΔTf = Kf × m
Substituting the values:
-3.1 °C = -40.0 °C/m × m
Solving for m:
m = ΔTf / Kf
= -3.1 °C / -40.0 °C/m
= 0.0775 m
Step 3: Calculate the moles of the unknown compound:
The molality (m) is defined as moles of solute per kilogram of solvent.
Since 1 kg of solvent contains 25.03 g of camphor, we can calculate the moles of camphor:
moles of camphor = mass of camphor / molar mass of camphor
= 25.03 g / molar mass of camphor
But the molar mass of camphor is already known, which is 152.23 g/mol.
moles of camphor = 25.03 g / 152.23 g/mol
= 0.164 mol
Since the unknown compound is mixed with camphor, we assume that the change in freezing point is solely due to the presence of the unknown compound. Therefore, the moles of the unknown compound can be expressed as:
moles of unknown compound = m × moles of camphor
= 0.0775 mol/kg × 0.164 mol
= 0.0127 mol
Step 4: Calculate the molar mass of the unknown compound:
The molar mass (M) is defined as the mass per mole of a substance.
Molar mass of the unknown compound = mass of unknown compound / moles of unknown compound
= 0.195 g / 0.0127 mol
= 15.35 g/mol
Therefore, the molar mass of the unknown compound is approximately 15.35 g/mol.