An ethylene glycol solution contains 23.9 g of ethylene glycol (C2H6O2) in 86.9 mL of water. Compute the freezing point and boiling point of the solution. (Assume a density of 1.00 g/mL for water.)
To calculate the freezing point and boiling point of the solution, we need to use the concept of colligative properties. Colligative properties depend on the amount of solute particles, rather than the specific identity of the solute.
First, we can calculate the molality (mol/kg) of the ethylene glycol in the solution. To do this, we need to find the moles of ethylene glycol and the mass of water in kg.
1. Moles of ethylene glycol (C2H6O2):
- Mass of ethylene glycol = 23.9 g
- Molar mass of ethylene glycol (C2H6O2) = 2(12.01) + 6(1.01) + 2(16) = 62.07 g/mol
- Moles of ethylene glycol = mass / molar mass = 23.9 g / 62.07 g/mol = 0.385 mol
2. Mass of water in kg:
- Volume of water = 86.9 mL
- Density of water = 1.00 g/mL
- Mass of water = volume * density = 86.9 g
To convert grams to kilograms:
- Mass of water in kg = 86.9 g / 1000 = 0.0869 kg
Next, we need to calculate the freezing point depression and the boiling point elevation of the solution using the following equations:
Freezing point depression (ΔTf):
ΔTf = Kf * molality
Boiling point elevation (ΔTb):
ΔTb = Kb * molality
Kf is the cryoscopic constant for water and it is equal to -1.86 °C/m.
Kb is the ebullioscopic constant for water and it is equal to 0.512 °C/m.
Now, let's calculate the freezing point (Tf) and boiling point (Tb) of the solution.
1. Freezing point:
- ΔTf = Kf * molality = -1.86 °C/m * 0.385 mol/kg = -0.7151 °C
- Tf (freezing point of pure water) = 0 °C
Therefore, the freezing point of the solution is Tf = 0 °C - 0.7151 °C = -0.7151 °C.
2. Boiling point:
- ΔTb = Kb * molality = 0.512 °C/m * 0.385 mol/kg = 0.19712 °C
- Tb (boiling point of pure water) = 100 °C
Therefore, the boiling point of the solution is Tb = 100 °C + 0.19712 °C = 100.19712 °C.
So, the freezing point of the solution is approximately -0.7151 °C, and the boiling point is approximately 100.19712 °C.