Anthraquinone contains only carbon, hydrogen, and oxygen and has an empirical formula os C7H2O. The freezing point of camphor is lowered by 22.3 C when 1.32 g anthraquinone is dissolved in 11.4 g camphor. Determine the molecular formula of anthraquinone
of* not os
delta T = Kf*molality
Solve for molality.
molality = mols/kg solvent
You know molality from above and kg solvent is 0.0114; solve for mols.
moles = grams/molar mass
You know mols and grams, solve for molar mass.
To determine the molecular formula of anthraquinone, we need to compare the empirical formula mass with the molar mass of the compound.
1. Calculate the empirical formula mass:
- Carbon (C) atomic mass = 12.01 g/mol
- Hydrogen (H) atomic mass = 1.01 g/mol
- Oxygen (O) atomic mass = 16.00 g/mol
Empirical formula mass = (7 * C) + (2 * H) + (1 * O) = (7 * 12.01) + (2 * 1.01) + (1 * 16.00) = 94.08 g/mol
2. Calculate the molar mass of anthraquinone:
- Mass of anthraquinone = 1.32 g
- Mass of camphor = 11.4 g
The freezing point depression depends on the molality (mol/kg) of the solute:
ΔT = Kf * m,
where ΔT is the freezing point depression, Kf is the cryoscopic constant, and m is the molality of the solute.
Since camphor is the solvent, we can calculate the molality using its molar mass:
- Molar mass of camphor = 152.23 g/mol
- Moles of camphor = mass of camphor / molar mass of camphor = 11.4 g / 152.23 g/mol = 0.0749 mol
Now we can calculate the molality of the solute (anthraquinone):
- Molality = moles of solute / mass of solvent (in kg) = moles of solute / (mass of camphor in g / 1000) = 1.32 g / (11.4 g / 1000) = 115.79 mol/kg
3. Calculate the molality of the empirical formula:
- Moles of empirical formula = mass of empirical formula / empirical formula mass = 94.08 g/mol / 94.08 g/mol = 1 mol
Since 1 mol of the empirical formula (C7H2O) is present, the molecular formula of anthraquinone is also C7H2O.
To determine the molecular formula of anthraquinone, you'll need to know the molar mass of the compound and the empirical formula mass of anthraquinone. The empirical formula mass is the sum of the atomic masses of all the elements in the empirical formula.
1. Calculate the empirical formula mass (EFM) of anthraquinone:
- EFM = (7 x atomic mass of carbon) + (2 x atomic mass of hydrogen) + (atomic mass of oxygen).
- The atomic masses for carbon, hydrogen, and oxygen are 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively.
- Substituting these values, EFM = (7 x 12.01) + (2 x 1.01) + 16.00 = 206.06 g/mol.
2. Determine the molar mass of anthraquinone (MM):
- This can be done by dividing the given mass of anthraquinone by the number of moles present.
- Moles = given mass / molecular mass.
- Given mass = 1.32 g, and using the equation Moles = given mass / molecular mass, we have Moles = 1.32 g / MM.
3. Calculate the freezing point depression (ΔTf):
- ΔTf = Kf x molality.
- Kf is the cryoscopic constant of the solvent, which is camphor. You need to find the value of Kf for camphor.
- Molality is the concentration of a solute in moles divided by the mass of the solvent in kilograms. It is given as 1.32 g / 11.4 g.
4. Rearrange the freezing point depression equation to solve for moles:
- Moles = ΔTf / (Kf x molality).
5. Substitute all the known values into the equation found in Step 4 to solve for the number of moles of anthraquinone.
6. Substitute the value of moles (from Step 2) into the equation from Step 1 to calculate the molecular formula mass (MFM) of anthraquinone.
7. Finally, determine the ratio between the molar mass and the empirical formula mass:
- Ratio = MFM / EFM.
8. Multiply the subscripts in the empirical formula by the ratio obtained in Step 7 to get the molecular formula.
By following these steps, you should be able to determine the molecular formula of anthraquinone.