The molal freezing point constant(Kf) for acetic acid is 3.90 C/m. When 31.5 grams of unknown solute is dissolved in 650 grams of acid the freezing point is lowered by 0.79 what is the molar mass
We must assume this is a non-volatile, non-ionizable solute.
delta T = Kf*m
Substitute and solve for m
m = mols/kg solvent
Substitute and solve for mols.
Then mols = grams/molar mass. You know grams and mols; solve for molar mass.
To find the molar mass of the unknown solute, you can use the formula:
Molar mass (g/mol) = (Freezing point depression (°C) / Freezing point constant (°C/m)) / Molality (mol/kg)
Given data:
Freezing point depression (ΔTf) = 0.79 °C
Freezing point constant (Kf) = 3.90 °C/m
First, we need to find the molality (mol/kg) of the solution. Molality is defined as moles of solute per kilogram of solvent. We can calculate it using the following formula:
Molality (mol/kg) = moles of solute / mass of solvent (in kg)
Given data:
Mass of solute = 31.5 g
Mass of solvent = 650 g
First, we need to convert the masses from grams to kilograms:
Mass of solute (kg) = 31.5 g / 1000 g/kg = 0.0315 kg
Mass of solvent (kg) = 650 g / 1000 g/kg = 0.65 kg
Now, we can calculate the molality:
Molality (mol/kg) = moles of solute / mass of solvent (in kg)
Molality (mol/kg) = moles of solute / 0.65 kg
Next, we need to find the moles of solute in the solution. We can use the molar mass of the solute and the given mass to calculate it:
Moles of solute = mass of solute / molar mass
Now, rearranging the formula, we can express the molar mass as:
Molar mass = mass of solute / moles of solute
Substituting the given values, we get:
Molar mass = 31.5 g / (moles of solute / 0.65 kg)
To find the moles of solute, we multiply the molality by the mass of solvent:
Moles of solute = molality * mass of solvent (in kg)
Let's substitute this back into the formula for molar mass:
Molar mass = 31.5 g / ((molality * mass of solvent) / 0.65 kg)
Now, we can calculate the molar mass using the given data:
Molar mass = 31.5 g / ((0.79 °C / 3.90 °C/m) / 0.65 kg)
Simplifying:
Molar mass = 31.5 g / (0.79/3.90) / 0.65
Molar mass ≈ 148.51 g/mol
Therefore, the molar mass of the unknown solute is approximately 148.51 g/mol.