Calculate the normal freezing point of an aqueous solution containing 30% w/w ethylene glycol. Thanks
30% w/w means 30 g ethylene glycol/100 g soln or 30 g ethyl glycol/(30g eth + 70g H2O).
Convert 30 g ethylene glycol to moles. moles = grams/molar mass
Calculate molality of the solution. That will be molality = moles/kg soln.
Then delta T = Kf*m
Solve for delta T and subtract from 0 C.
To calculate the normal freezing point of a solution, you can use the equation:
ΔTf = Kf * molality
Where:
ΔTf is the change in freezing temperature,
Kf is the cryoscopic constant, and
molality is the molal concentration of the solute.
The molal concentration (molality) is the number of moles of solute per kilogram of solvent. In this case, the solute is ethylene glycol, and the solvent is water.
1. Calculate the molecular weight of ethylene glycol (C2H6O2).
- Carbon (C) has an atomic mass of 12.01 g/mol.
- Hydrogen (H) has an atomic mass of 1.01 g/mol.
- Oxygen (O) has an atomic mass of 16.00 g/mol.
So the molecular weight of ethylene glycol is:
(2 * 12.01) + (6 * 1.01) + (2 * 16.00) = 62.07 g/mol
2. Calculate the mass of ethylene glycol in the solution.
If the solution contains 30% w/w ethylene glycol, it means 30 g of ethylene glycol is present in 100 g of the solution (since the unit "w/w" refers to weight/weight).
So, the mass of ethylene glycol in the solution is:
(30 g / 100 g) * 1000 g = 300 g
3. Calculate the number of moles of ethylene glycol.
Divide the mass (in grams) of ethylene glycol by its molar mass.
Moles of ethylene glycol = Mass of ethylene glycol / Molecular weight of ethylene glycol
Moles of ethylene glycol = 300 g / 62.07 g/mol
4. Calculate the molality of the solution.
Molality = Moles of solute / Mass of solvent (in kg)
Since we are dealing with an aqueous solution, the solvent is water.
We need to calculate the mass of water in the solution by subtracting the mass of ethylene glycol from the total mass of the solution.
Mass of water = Total mass of solution - Mass of ethylene glycol
Mass of water = 1000 g - 300 g = 700 g
Molality = Moles of ethylene glycol / Mass of water (in kg)
Molality = (300 g / 62.07 g/mol) / (700 g / 1000 g/kg)
5. Determine the cryoscopic constant (Kf) for water.
The cryoscopic constant for water is approximately 1.86 °C/m. This value represents the change in freezing temperature per molal concentration of solute in kg of solvent.
6. Calculate the change in freezing temperature (ΔTf).
ΔTf = Kf * Molality
ΔTf = 1.86 °C/m * Molality
This value represents the amount by which the freezing point of the solution differs from the normal freezing point of pure water.
7. Calculate the normal freezing point of the solution.
The normal freezing point of water is 0 °C. Subtract the value of ΔTf from 0 °C to obtain the normal freezing point of the solution.
Normal Freezing Point = 0 °C - ΔTf
By following these steps and plugging in the appropriate values, you can calculate the normal freezing point of the aqueous solution containing 30% w/w ethylene glycol.