After you preform your experiment, you determine that the Kf value for naphthalene is 6.89 °C/m . You are using 10g of naphthalene and added 1.0 g of your unknown. The the freezing point of the solvent decreased by 4.42 °C when the unknown was added. Knowing this information, determine the molar mass of the unknown.
delta T = Kf*molality
You know delta T and Kf, solve for m.
molality = mols/kg solvent. You know m and kg solvent, solve for mols.
Then mols = grams/molar mass
You know mols and grams, solve for molar mass.
To determine the molar mass of the unknown substance, we can use the equation:
ΔTf = Kf * m * i
Where:
ΔTf is the change in freezing point (given as -4.42 °C)
Kf is the cryoscopic constant for the solvent (given as 6.89 °C/m)
m is the molality of the solution
i is the van't Hoff factor, which represents the number of particles formed when the substance dissolves
First, we need to calculate the molality (m). Molality is defined as the moles of solute per kilogram of solvent. In this case, the solvent is naphthalene and we added 1.0 g of the unknown, so the total mass of the solvent-solute mixture is 10g + 1g = 11g.
To calculate the molality (m), we need to convert the mass of the solvent-solute mixture in kilograms:
m = (mass of solute) / (mass of solvent + mass of solute)
= 1g / 11g
Now, let's calculate the van't Hoff factor (i). Since the nature of the unknown substance is not given, we'll assume it is a non-electrolyte, which means it does not dissociate into ions in solution. For non-electrolytes, the van't Hoff factor is 1.
Now, we can substitute the given values and solve for the molality (m):
-4.42 °C = (6.89 °C/m) * (1g / 11g) * 1
Simplifying, we have:
-4.42 = 6.89 / 11
Cross-multiplying, we find:
4.42 * 11 = 6.89
48.62 = 6.89
Finally, to calculate the molar mass of the unknown substance, we can use the equation:
molar mass = (molality * molar mass of the solvent) / change in freezing point
Since the molar mass of the solvent (naphthalene) is 128 g/mol, we have:
molar mass of the unknown = (molality * molar mass of the solvent) / change in freezing point
= (1 * 128 g/mol) / 4.42 °C
Calculating, we find:
molar mass of the unknown = 28.96 g/mol
Therefore, the molar mass of the unknown substance is approximately 28.96 g/mol.
To determine the molar mass of the unknown substance, we can use the formula:
molar mass of unknown = (Kf * mass of solvent) / (freezing point depression)
Given:
Kf (cryoscopic constant for naphthalene) = 6.89 °C/m
mass of naphthalene (solvent) = 10g
mass of unknown = 1.0g
freezing point depression = 4.42 °C
Substituting these values into the formula, we have:
molar mass of unknown = (6.89 °C/m * 10g) / 4.42 °C
Now, let's calculate:
molar mass of unknown = (68.9 g·°C/mol * 10g) / 4.42 °C
molar mass of unknown = 689 g·°C/4.42g-°C
molar mass of unknown ≈ 156.11 g/mol
Therefore, the molar mass of the unknown substance is approximately 156.11 g/mol.