How much ethylene glycol (C2H6O2, the major component of antifreeze) must be added to 1 L of water to keep from it freezing at -15 °F?
Change -15F to degrees C. That's approximately -26
Then delta T = Kf*m
approx 26 = 1.86*m
solve for molality.
m = mols/kg solvent = mols/1kg
You have m and kg, solve for mols.
Then mol = g/molar mass. You have molar mass and mols, solve for g
14 mols/kg
To determine the amount of ethylene glycol (C2H6O2) needed to prevent water from freezing at -15 °F, we can use the concept of freezing point depression.
The freezing point depression can be calculated using the formula:
ΔTf = Kf * m
where:
ΔTf is the freezing point depression,
Kf is the cryoscopic constant (which is specific to the solvent),
m is the molality of the solution (moles of solute per kilogram of solvent).
First, let's convert the temperature from Fahrenheit to Celsius, as the formula uses Celsius.
-15 °F = -26.11 °C
Next, we need to find the cryoscopic constant (Kf) for water. The Kf value for water is 1.86 °C/m.
Now, let's calculate the molality (m) of the solution. Since we are adding ethylene glycol to 1 L of water, we need to consider the density of ethylene glycol to convert volume to mass.
The density of ethylene glycol is approximately 1.11 g/mL. Therefore, 1 L of ethylene glycol weighs 1110 g. We can convert this to kilograms by dividing by 1000.
Mass of ethylene glycol = 1110 g = 1.11 kg
Since we are adding 1 L of ethylene glycol to 1 L of water, we have a total of 2 L of solution.
Mass of water = volume of water * density of water
Mass of water = 1 L * 1000 g/L = 1000 g = 1 kg
Now, we can calculate the molality:
m = moles of solute / mass of solvent (in kg)
To find the moles of solute, we need to calculate the molar mass of ethylene glycol:
C2H6O2:
2 * atomic mass of carbon (12 g/mol) = 24 g/mol
6 * atomic mass of hydrogen (1 g/mol) = 6 g/mol
2 * atomic mass of oxygen (16 g/mol) = 32 g/mol
Total molar mass = 24 + 6 + 32 = 62 g/mol
Moles of ethylene glycol = mass of ethylene glycol / molar mass of ethylene glycol
Moles of ethylene glycol = 1.11 kg / 62 g/mol
Now, we can calculate the freezing point depression (ΔTf):
ΔTf = Kf * m
= 1.86 °C/m * (moles of ethylene glycol / mass of water)
Finally, we can solve for the amount of ethylene glycol needed to prevent freezing at -15 °F:
ΔTf = -26.11 °C
moles of ethylene glycol = (ΔTf * mass of water) / (Kf * 1.86 °C/m)
The result will give you the number of moles of ethylene glycol required to prevent the water from freezing at -15 °F.