What mass of ethylene glycol C2H6O2, the main component of antifreeze, must be added to 10.0 L water to produce a solution for use in a car's radiator that freezes at -23.3 degrees Celsius? Assume the density for water is exactly 1 g/mL
Use the freezing point depression
-23.3=molessolute/10kgwater * -.52
calculate the moles of solute (tehylene glycol) and convert that to mass.
A small correction here to correct a typo. The -.52 should be -1.86.
To solve this problem, we need to determine the mass of ethylene glycol required to freeze the solution at the given temperature.
The freezing point depression equation can be used:
ΔT = Kf * m
where:
ΔT is the change in freezing point
Kf is the molal freezing point depression constant
m is the molality of the solution
First, we need to calculate the change in freezing point (ΔT). The freezing point of pure water is 0 degrees Celsius, and we want the solution to freeze at -23.3 degrees Celsius. Therefore,
ΔT = (0 - (-23.3)) = 23.3 degrees Celsius
Next, we need to calculate the molality (m) of the solution. Molality is the number of moles of solute per kilogram of solvent.
Since the density of water is 1 g/mL, the mass of 10.0 L (10,000 mL) of water is 10,000 grams.
To calculate the molality, we need to convert grams of ethylene glycol to moles. The molar mass of ethylene glycol (C2H6O2) can be found by adding the atomic masses of each element:
C: 12.01 g/mol
H: 1.01 g/mol (there are 6 hydrogen atoms)
O: 16.00 g/mol (there are 2 oxygen atoms)
Molar mass of ethylene glycol = (2 * 12.01) + (6 * 1.01) + (2 * 16.00) = 62.07 g/mol
Next, we convert the mass of water to kilograms:
mass of water = 10,000 grams = 10 kilograms
Now we can calculate the molality:
molality (m) = moles of ethylene glycol / mass of water in kg
We still need to find the moles of ethylene glycol. We can use the molality formula:
m = moles of solute / mass of solvent in kg
Rearranging the formula, we get:
moles of solute = m * mass of solvent in kg
Plugging in the values, we get:
moles of solute = m * 10 kg
Finally, we can calculate the mass of ethylene glycol:
mass of ethylene glycol = moles of ethylene glycol * molar mass of ethylene glycol
Substituting the values, we get:
mass of ethylene glycol = (m * 10 kg) * (62.07 g/mol)
Using this equation, you can calculate the mass of ethylene glycol required to produce a solution that freezes at -23.3 degrees Celsius.