Dissolving 3g of ascorbic acid in 50g of acetic acid lowers the freezing point of acetic acid by 1.33degreesC. What is the molecular mass of ascorbic acid?
delta T = Kf*m
Solve for m.
m = mols/kg solvent
solve for mols.
mols = grams/molar mass
Solve for molar mass.
To find the molecular mass of ascorbic acid, we can use the equation for the freezing point depression:
ΔT = Kf × m
Where:
ΔT is the change in freezing point
Kf is the cryoscopic constant (provided for acetic acid)
m is the molality of the solute (ascorbic acid), given by:
m = moles of solute / mass of solvent (in kg)
First, let's find the change in freezing point (ΔT):
ΔT = -1.33 °C
The cryoscopic constant (Kf) for acetic acid can be found in reference material and is generally given as 3.90 °C·kg/mol.
Next, let's calculate the molality (m) using the given information:
mass of ascorbic acid = 3g = 0.003kg
mass of acetic acid = 50g = 0.050kg
moles of ascorbic acid = mass / molecular mass
0.003kg / molecular mass = moles of ascorbic acid
Since we want molality, we divide by the mass of the solvent:
m = (0.003kg / molecular mass) / 0.050kg
Now we can substitute the values into the equation:
-1.33 = (3.90 × (0.003kg / molecular mass)) / 0.050
Simplifying the equation:
-1.33 × 0.050 = 3.90 × (0.003kg / molecular mass)
-0.0665 = 0.0117 / molecular mass
Solving for the molecular mass:
molecular mass = 0.0117 / -0.0665
molecular mass = 176.69 g/mol
Therefore, the molecular mass of ascorbic acid is approximately 176.69 g/mol.