Can anyone direct me on how to solve this problem? All of the variables are makin my head spin--not sure how to organize them. If you can give equations to use that would help.Thnx!
1 L of an impure water solution has a freezing point of -11 °C. Which of the following is the
best estimate of the vapor pressure of the solution at 25 °C? Assume the vapor pressure of pure
water at 25oC = 23.76 atm, kF = 2 (K kg)/mol, and that water is 55 mol/L. Assume the density of
water is 1 g/mL.
delta T = Kf*molality
11 = Kf*m
Calculate m
molality = moles/kg solvent.
I think we must assume 1 kg solvent although that won't be exactly right.
Calculate (estimate) # moles.
#moles + 55.5 for H2O = total moles.
Calculate mole fraction water,
Then vapor pressure H2O = mole fraction water x 23.76 BUT I don't think that is atm (It must be torr or mm Hg). This would be an estimate at best. Check my thinking.
To solve this problem, we can use the equation for freezing point depression:
ΔTf = i * Kf * molality
where ΔTf is the change in freezing point, i is the van't Hoff factor, Kf is the cryoscopic constant, and molality is the concentration of solute in mol/kg of solvent.
First, let's calculate the molality of the solution:
1 L of water weighs 1000 g (since the density of water is 1 g/mL).
The number of moles of solute (water) in 1 L is given as 55 mol/L.
So, the molality (m) of the solution is:
m = (55 mol/L) / (1000 g/L)
m = 0.055 mol/g
Now, let's calculate the change in freezing point (ΔTf) of the solution:
Given that the freezing point of the solution is -11 °C, and the freezing point of pure water is 0 °C, the change in freezing point is:
ΔTf = -11 °C - 0 °C
ΔTf = -11 °C
Given that Kf = 2 (K kg)/mol, we can now calculate the vapor pressure of the solution at 25 °C using the equation for ΔTf:
ΔTf = i * Kf * m
Since we want to solve for the vapor pressure at 25 °C, we don't need to consider the temperature in the equation. Rearranging the equation, we get:
i * Kf * m = ΔTf
Now, we can substitute the known values:
i * 2 * 0.055 = -11
Solving for i (the van't Hoff factor):
i = -11 / (2 * 0.055)
i ≈ -100
However, the van't Hoff factor (i) should be a positive whole number, so we take the absolute value of -100, and round it to the nearest whole number, giving us an estimated van't Hoff factor of 100.
Finally, using the relationship between vapor pressure and the van't Hoff factor: p = i * p°, where p° is the vapor pressure of pure water at the given temperature (25 °C = 298 K), and plugging in the known values:
p = 100 * 23.76 atm
p ≈ 2376 atm
So, the best estimate of the vapor pressure of the solution at 25 °C is approximately 2376 atm.