What volume of ethylene glycol (C2H6O2), a nonelectrolyte, must be added to 13.7 L of water to produce an antifreeze solution with a freezing point of -30.0¡ÆC? (The density of ethylene glycol is 1.11 g/cm3, and the density of water is 1.00 g/cm3.)
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delta T = Kb*molality
You know delta T. I assume you know Kb. Calculate molality.
Then molality = moles/molar mass
You know molality and molar mass of the glycol, calculate moles.
Then moles = grams/molar mass.
You know moles and molar mass, calculate grams.
Knowing mass and density, you can determine the volume.
mass = volume x density.
To solve this problem, we need to use the concept of molality and the colligative properties of solutions. First, let's understand the steps involved in solving this problem:
1. Calculate the molality (m) of the solution.
2. Determine the molal freezing-point constant (Kf) for water.
3. Calculate the change in freezing point (ΔTf) using the formula: ΔTf = Kf * m.
4. Determine the freezing point depression, ΔTf = T(initial) - T(final).
5. Calculate the mass of ethylene glycol required using its density, mass = volume * density.
6. Finally, convert the mass of ethylene glycol to volume using its density, volume = mass / density.
Now let's go through each step in detail:
1. Calculate molality (m):
Molality is defined as moles of solute per kilogram of solvent. In this case, the solvent is water.
To find the molality (m), we need to calculate the number of moles of ethylene glycol and the mass of water:
Moles of ethylene glycol = mass of ethylene glycol / molar mass
Given that the density of ethylene glycol is 1.11 g/cm^3, we can convert this to kilograms by dividing by 1000:
Density of ethylene glycol = 1.11 g/cm^3 = 1.11 kg/L
The molar mass of ethylene glycol (C2H6O2) can be calculated as:
Molar mass = (2 * atomic mass of C) + (6 * atomic mass of H) + (2 * atomic mass of O)
Look up the atomic masses of carbon (C), hydrogen (H), and oxygen (O) in the periodic table and substitute them into the equation.
Note: The atomic mass of an element can be found on the periodic table.
2. Determine the molal freezing-point constant (Kf) for water:
The molal freezing-point constant (Kf) is a constant specific to the solvent. For water, Kf = 1.86 °C/m.
3. Calculate the change in freezing point (ΔTf):
ΔTf = Kf * m
This formula will give you the change in freezing point caused by the addition of the solute.
4. Determine the freezing point depression, ΔTf:
ΔTf = T(initial) - T(final)
Here, T(initial) is the freezing point of pure water (0 °C) and T(final) is the desired freezing point (-30 °C).
5. Calculate the mass of ethylene glycol required:
mass = volume * density
We are given the volume of water (13.7 L) and the density of water (1.00 g/cm^3). Using the given density, convert the volume of water to mass.
6. Finally, calculate the volume of ethylene glycol required:
volume = mass / density
Substitute the calculated mass of ethylene glycol and its given density into the formula to find the volume of ethylene glycol required.
By following these steps, you will be able to calculate the volume of ethylene glycol required to produce the desired antifreeze solution with a freezing point of -30.0 °C.