what mass of ethylene glycol, 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 degree C? Assume the density for water is exactly 1 g/ml.
To calculate the mass of ethylene glycol needed to produce an antifreeze solution, we need to consider the freezing point depression. The freezing point depression is a colligative property, which depends on the number of solute particles in relation to the solvent.
The formula to calculate freezing point depression (ΔTf) is:
ΔTf = Kf * m
Where:
ΔTf is the freezing point depression,
Kf is the cryoscopic constant for the solvent (water in this case),
m is the molality of the solution (the amount of solute in moles per kilogram of solvent).
First, let's calculate the freezing point depression (ΔTf):
ΔTf = (-23.3 °C) - (0 °C) = -23.3 °C
Next, we need the cryoscopic constant for water, which is 1.86 °C/m.
Now, let's calculate the molality (m):
m = moles of solute / mass of water (in kg)
Since the density of water is 1 g/mL and we have 10.0 L of water, the mass of water is 10.0 kg.
The molality formula can be rearranged to find the moles of solute:
moles of solute = m * mass of water (in kg)
Substituting the values:
moles of solute = (ΔTf / Kf) * mass of water (in kg)
To convert the volume of water to mass, we use the density of water:
mass of water = 10.0 kg
Finally, we can solve for the moles of solute:
moles of solute = (ΔTf / Kf) * mass of water (in kg)
Now we need to calculate the mass of ethylene glycol:
mass of ethylene glycol = moles of solute * molar mass of ethylene glycol
The molar mass of ethylene glycol (C2H6O2) is approximately 62.07 g/mol.
Therefore, substitute the values and solve for the mass of ethylene glycol to find the answer.