What is the freezing point of a solution made by dissolving 450 g of ethylene glycol (C2H6O2) in 550 g of water? The freezing point of pure water is 0.0ºC and Kf of pure water is -1.86ºC/m.
moles ethylene glycol = grams/molar mass.
Solve for moles.
m = moles solute/kg solvent
Solve for m
delta T = Kf*m
solve for delta T, then for T.
-8.32
To find the freezing point of the solution, we need to use the equation:
ΔT = Kf * m
Where:
ΔT is the change in temperature (freezing point depression)
Kf is the cryoscopic constant (-1.86ºC/m for water)
m is the molality of the solution (moles of solute per kilogram of solvent)
First, let's calculate the molality (m) of the solution:
Step 1: Calculate the number of moles of ethylene glycol (C2H6O2)
moles of ethylene glycol = mass of ethylene glycol / molar mass of ethylene glycol
The molar mass of ethylene glycol (C2H6O2) is:
(2 × (12.01 g/mol)) + (6 × (1.01 g/mol)) + (2 × (16.00 g/mol)) = 62.07 g/mol
moles of ethylene glycol = 450 g / 62.07 g/mol
Step 2: Convert the mass of water to kilograms
mass of water = 550 g = 550 g / 1000 g/kg = 0.55 kg
Step 3: Calculate the molality (m)
m = moles of ethylene glycol / mass of water in kg
m = (450 g / 62.07 g/mol) / 0.55 kg
Now, let's calculate the freezing point depression (ΔT):
ΔT = Kf * m
ΔT = -1.86ºC/m * (moles of ethylene glycol / mass of water in kg)
Finally, let's find the freezing point of the solution:
Freezing point of solution = Freezing point of pure water + ΔT
Note: The freezing point of pure water is 0.0ºC.
Now, you can substitute the values into the equations to find the freezing point of the solution.
To find the freezing point of the solution, we first need to calculate the molality (m) of the solution.
Step 1: Calculate the moles of ethylene glycol (C2H6O2):
First, determine the molar mass of ethylene glycol (C2H6O2):
C = 12.01 g/mol
H = 1.01 g/mol
O = 16.00 g/mol
Molar mass of C2H6O2 = (2 * C) + (6 * H) + (2 * O)
= (2 * 12.01) + (6 * 1.01) + (2 * 16.00)
= 62.07 g/mol
To find the moles of ethylene glycol, divide the mass (in grams) by the molar mass:
Moles of C2H6O2 = Mass of C2H6O2 / Molar mass of C2H6O2
= 450 g / 62.07 g/mol
≈ 7.25 mol
Step 2: Calculate the molality (m) of the solution:
Molality (m) is defined as the moles of solute per kilogram of solvent.
Since we are dissolving ethylene glycol in water, the solvent is water.
Molality (m) = Moles of solute / Mass of solvent (in kg)
= Moles of C2H6O2 / Mass of water (in kg)
= 7.25 mol / (550 g / 1000) kg
≈ 13.18 mol/kg
Step 3: Calculate the change in freezing point (∆Tf):
The change in freezing point is given by the formula:
∆Tf = Kf * m
Where Kf is the cryoscopic constant (-1.86ºC/m) and m is the molality of the solution.
∆Tf = (-1.86ºC/m) * (13.18 mol/kg)
≈ -24.47ºC
Step 4: Calculate the freezing point of the solution:
The freezing point of the solution can be found by subtracting the change in freezing point (∆Tf) from the freezing point of pure water.
Freezing point of solution = Freezing point of pure water - ∆Tf
= 0.0ºC - (-24.47ºC)
= 24.47ºC
Therefore, the freezing point of the solution made by dissolving 450 g of ethylene glycol in 550 g of water is approximately 24.47ºC.