To solve this problem, first, we need to calculate the freezing point depression caused by the organic compound in the cyclohexane solution. We can then use this information to calculate the molecular weight, and finally, determine the molecular formula of the compound.
Step 1: Calculate the freezing point depression (ΔTf):
ΔTf = Kf * molality
Where Kf is the freezing point depression constant for cyclohexane (20.0 °C kg/mol), and molality (m) is the concentration of the solute in the solution.
First, we find the moles of the organic compound:
1. Calculate the molar mass of the organic compound using the percentages given.
- For carbon (C): 70.58 g C / 12.01 g/mol = 5.878 mol C
- For hydrogen (H): 5.9 g H / 1.01 g/mol = 5.842 mol H
- For oxygen (O): 23.50 g O / 16.00 g/mol = 1.469 mol O
2. Divide the moles of each element by the smallest number of moles to find the simplest whole number ratio.
- C: 5.878 / 1.469 ≈ 4
- H: 5.842 / 1.469 ≈ 4
- O: 1.469 / 1.469 = 1
The empirical formula is C4H4O.
Step 2: Calculate the molar mass of the empirical formula:
Molar mass = (4 * 12.01) + (4 * 1.01) + 16.00 = 64.08 g/mol
Step 3: Calculate the van 't Hoff factor (i):
The organic compound is molecular, therefore the van 't Hoff factor (i) is approximately 1.
Step 4: Use the formula to calculate the molality (m) using the given data points:
ΔTf = Kf * i * m
ΔTf = 6.59 °C - 3.82 °C = 2.77 °C
m = ΔTf / (Kf * i) = 2.77 °C / (20.0 °C kg/mol * 1) = 0.1385 mol/kg
Finally, use the calculated molality to determine the molecular weight:
Molar mass = mass / moles
Moles = molality * kg solvent = 0.1385 mol/kg * 0.6227 kg = 0.08626 mol
Molar mass = 11.3 g / 0.08626 mol = 130.93 g/mol
The molecular formula weight (130.93 g/mol) is close to a molecular weight of C8H8O2 (which equals 128.16 g/mol). Hence, the molecular formula of the organic compound is C8H8O2.
