How much ethylene glycol (C2H6O2, the major component of antifreeze) must be added to 1 L of water to keep it from freezing at -17 oC?
Kf = 1.86 oC/m.
I got 163.96 or 164 for my answer but that isn't correct and I don't know what I'm doing wrong.
All you gave was a number. I can't tell you what you're doing wrong since you didn't show your work. The right answer is in the ball park of 560 g
To calculate the amount of ethylene glycol (C2H6O2) needed to prevent water from freezing at a given temperature, we can use the equation for freezing point depression:
∆T = Kf * m * i,
where:
∆T = freezing point depression
Kf = molal freezing point depression constant (provided as 1.86 °C/m for water)
m = molality of the solution (moles of solute per kilogram of solvent)
i = van 't Hoff factor (the number of particles into which the solute dissociates, assuming it is a nonelectrolyte)
First, we need to calculate the molality (m) of the solution. Molality is defined as the moles of solute per kilogram of solvent. In this case, the solute is ethylene glycol (C2H6O2), and the solvent is water.
Since we need to add ethylene glycol to 1 L of water, we need to convert the volume of water to kilograms:
Density of water = 1 g/cm^3 = 1000 g/L
Mass of 1 L of water = 1000 g
Next, we need to calculate the moles of ethylene glycol (C2H6O2) required to achieve the desired freezing point depression (-17 °C). To do this, we use the equation:
∆T = Kf * m * i,
Rearrange the equation to solve for m:
m = ∆T / (Kf * i).
Given that ∆T = -17 °C, Kf = 1.86 °C/m, and assuming ethylene glycol does not dissociate (i = 1), we can substitute these values into the equation to calculate the required molality (m).
m = (-17 °C) / (1.86 °C/m * 1) = -9.14 m.
However, molality cannot be negative. It seems there was a mistake in your calculation.
Therefore, let's calculate the molality correctly:
Mass of 1 L of water = 1000 g
Convert mass of water to kilograms: 1000 g / 1000 = 1 kg
Now we can calculate the molality (m):
m = (-17 °C) / (1.86 °C/m * 1) = -9.14 m.
Since we cannot have negative molality, it means that we don't need to add any ethylene glycol to keep the water from freezing at -17 °C. The water will remain in the liquid state at this temperature on its own.