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?
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To calculate the volume of ethylene glycol (C2H6O2) needed to produce an antifreeze solution with a specific freezing point, we need to use the freezing point depression equation:
ΔT = Kf * molality
Where:
ΔT = change in freezing point
Kf = cryoscopic constant (for water, Kf = 1.86 °C/m)
molality = moles of solute / kilograms of solvent
In this case, the freezing point depression (ΔT) is given as -30.0 °C. We need to find the molality and the moles of solute to determine the volume of ethylene glycol needed.
First, let's find the moles of solute:
Molar mass of ethylene glycol (C2H6O2):
C = 2 * atomic mass of carbon = 2 * 12.01 g/mol = 24.02 g/mol
H = 6 * atomic mass of hydrogen = 6 * 1.01 g/mol = 6.06 g/mol
O = 2 * atomic mass of oxygen = 2 * 16.00 g/mol = 32.00 g/mol
Total molar mass = 24.02 + 6.06 + 32.00 = 62.08 g/mol
To convert the given 13.7 L of water to kilograms, we need to use the density of water, which is approximately 1 g/cm³ or 1000 kg/m³:
Mass of water = Volume * Density = 13.7 L * 1000 g/L = 13700 g = 13.7 kg
Now, calculate the molality of the solute:
molality = moles of solute / kilograms of solvent
Rearranging the equation, we get:
moles of solute = molality * kilograms of solvent
Since ethylene glycol is a nonelectrolyte, it doesn't dissociate in water. Therefore, we can assume that the molality is equal to the moles of ethylene glycol per kilogram of water.
Now, let's substitute the values into the equation:
molality = moles of ethylene glycol / 13.7 kg
Next, rearrange the equation to solve for moles of solute:
moles of ethylene glycol = molality * kilograms of water
Finally, calculate the volume of ethylene glycol:
volume of ethylene glycol = (moles of ethylene glycol * molar mass of ethylene glycol) / density of ethylene glycol
To determine the density of ethylene glycol, we need the given temperature, as the density of ethylene glycol varies with temperature.
After finding the density, substitute the values into the equation to get the volume of ethylene glycol required.
Note: This calculation assumes ideal behavior and neglects any potential interactions between the solute and solvent.