Calculate the expected freezing point of a solution of 0.579 g pelargonic acid in 4.225 g of lauric acid, if the melting point of pure lauric acid was measured to be 43.20*C. (MM pelargonic acid = 158.2 g/mol; MM laruic acid = 200.32 g/mol). Kf for lauric acid is 3.90*C/Mc; unit answers are in *C
I have tried solving for Mc, which = 11.076923 mole/kg (Mc)
and tried getting just moles for lauric acid by multiplying 11.07692 mol/kg x 1kg/1000g x 4.225g = 0.0468 moles
I am unsure where to go from here. Please help.
I think you're on the wrong track.
Kf has the units of *C/molal
pel = pelargonic acid
lau = lauric acid
mols pel = grams/molar mass = ?
m = molality pel = mols/kg lau = ?
dT = Kf*m. You know Kf and m, solve for dT. Subtract dT from 43.2 to arrive at the new freezing point.
To calculate the expected freezing point of a solution, you can use the equation:
ΔT = Kf * m
where ΔT is the freezing point depression, Kf is the cryoscopic constant, and m is the molality of the solution.
First, let's calculate the molality (m) of the solution. Molality is defined as the number of moles of solute (pelargonic acid) per kilogram of solvent (lauric acid).
Given:
Mass of pelargonic acid (solute) = 0.579 g
Molar mass of pelargonic acid = 158.2 g/mol
Mass of lauric acid (solvent) = 4.225 g
Molar mass of lauric acid = 200.32 g/mol
To calculate the number of moles of pelargonic acid, use the formula:
moles = mass / molar mass
moles of pelargonic acid = 0.579 g / 158.2 g/mol = 0.00366 mol
To calculate the molality of the solution, use the formula:
molality (m) = moles of solute / mass of solvent (in kg)
mass of solvent = 4.225 g / 1000 (convert to kg) = 0.004225 kg
molality (m) = 0.00366 mol / 0.004225 kg = 0.8679 mol/kg
Now that we have the molality (m), we can calculate the freezing point depression (ΔT).
Given:
Cryoscopic constant (Kf) for lauric acid = 3.90°C/molal
ΔT = Kf * m
ΔT = 3.90°C/molal * 0.8679 mol/kg = 3.3858°C
Finally, to calculate the expected freezing point of the solution, subtract the freezing point depression (ΔT) from the melting point of pure lauric acid.
Expected freezing point = Melting point of pure lauric acid - ΔT
Expected freezing point = 43.20°C - 3.3858°C = 39.8142°C
Therefore, the expected freezing point of the solution is approximately 39.8142°C.