A solution is prepared by dissolving 0.490 g of an unknown compound in 50.00 mL of water. The freezing point of the solution is –0.201°C. Assuming the compound is a non-electrolyte, what is the molecular mass of the compound? Use 1.00 g/mL as the density of water.
delta T = 0-(-.201) = ?
delta T = Kf*m
You know delta T and Kf, solve for m = molality.
m = mols/kg solvent. You know kg solvent and m, solve for mols.
mols = grams/molar mass. You know grams and mols, solve for molar mass.
90.74
To find the molecular mass of the compound, we will use the formula:
ΔT = Kf * m
Where:
ΔT = the freezing point depression
Kf = the cryoscopic constant
m = molality of the solution
First, let's calculate the molality (m) of the solution using the given data:
Mass of compound = 0.490 g
Density of water = 1.00 g/mL
Volume of water = 50.00 mL = 0.0500 L
Since molality (m) is defined as moles of solute per kilogram of solvent, we need to convert the mass of the solute to moles:
Moles of compound = mass / molar mass
Rearranging the equation, we get:
Molar mass = mass / moles of compound
To find the moles of the compound, we need to calculate the moles of water in the solution:
Moles of water = volume of water * density of water / molar mass of water
The molar mass of water is 18.01528 g/mol.
Now let's determine the moles of water:
Moles of water = 0.0500 L * 1.00 g/mL / 18.01528 g/mol
Moles of water ≈ 0.002772 mol
Since the compound is a non-electrolyte, the moles of solute are equal to the moles of compound. Therefore:
Molar mass = 0.490 g / 0.002772 mol
Molar mass ≈ 176.685 g/mol
Therefore, the molecular mass of the unknown compound is approximately 176.685 g/mol.
To find the molecular mass of the unknown compound, we can use the equation:
ΔT = K_f * m * i
Where:
ΔT is the change in freezing point (in this case, -0.201°C)
K_f is the cryoscopic constant (for water, it is 1.86°C/m)
m is the molality of the solution (in moles of solute per kilogram of solvent)
i is the van't Hoff factor, which represents the number of particles the solute dissociates into (since the compound is assumed to be a non-electrolyte, i = 1)
First, we need to calculate the molality (m) of the solution using the following equation:
m = moles of solute / mass of solvent (in kg)
We know that the mass of the solvent (water) is 50.00 mL or 0.05000 L (since the density of water is 1.00 g/mL). To convert this to kg, we multiply by the density of water (1.00 g/mL):
mass of solvent = 0.05000 L * 1.00 g/mL = 0.05000 kg
Now we need to calculate the moles of solute. The moles of solute can be calculated by dividing the mass of the solute by its molar mass.
moles of solute = mass of solute / molar mass
We are given the mass of solute, which is 0.490 g. Now we need to find the molar mass of the compound.
To find the molar mass, we need to know the empirical formula of the compound or have additional information about the elements present in the compound. Since the given information does not provide this detail, we cannot determine the molar mass of the compound.
Hence, we cannot find the molecular mass of the compound without additional information about its composition.