assuming complete dissociation of the solute, how many grams of KNO3 must be added to 275 mL of water to produce a solution that freezes at -14.5 C? The freezing point for pure water is 0.0 C and is equal to 1.86 C/m .
delta T = i*Kf*m
where i = 2, solve for m.
m = moles/kg solvent
Solve for moles.
moles = g/molar mass
solve for grams.
To calculate the number of grams of KNO3 that must be added to the water, we need to use the formula for the freezing point depression. The formula is:
ΔT = Kf * m * i
Where:
- ΔT is the change in temperature (in this case, the freezing point depression),
- Kf is the cryoscopic constant (which is given as 1.86 °C/m),
- m is the molality of the solution (which is calculated as moles of solute per kilogram of solvent), and
- i is the van't Hoff factor, which represents the number of particles formed when the solute dissolves (since KNO3 fully dissociates in water, i = 3 in this case).
First, we need to calculate the molality (m) of the solution. Molality is the moles of solute divided by the mass of the solvent in kilograms. In this case, the solvent is water.
Given that you have 275 mL of water, we need to convert it to kilograms:
275 mL = 275 grams (since the density of water is close to 1 g/mL) = 0.275 kg
Now, we can calculate the molality (m) by dividing the moles of solute by the mass of the solvent:
m = moles of solute / mass of solvent
Since we don't know the moles of KNO3 yet, let's assume we have x grams of KNO3.
The molecular weight of KNO3 is:
K: 39.10 g/mol
N: 14.01 g/mol
O: 16.00 g/mol (x3)
Adding them up gives:
39.10 + 14.01 + (16.00 * 3) = 101.10 g/mol
Now we can calculate the moles of KNO3:
moles of KNO3 = x grams / 101.10 g/mol
Substituting these values into the molality equation:
ΔT = Kf * (x / (0.275 kg + x * 0.10110 kg/mol)) * 3
Since we want the solution to freeze at -14.5 °C, the change in temperature (ΔT) is equal to the freezing point of pure water (0.0 °C) minus the desired freezing point (-14.5 °C):
ΔT = 0.0 °C - (-14.5 °C) = 14.5 °C
Now, we can substitute all the known values into the formula and solve for x:
14.5 °C = 1.86 °C/m * (x / (0.275 kg + x * 0.10110 kg/mol)) * 3
Solving this equation will give us the value of x, which represents the number of grams of KNO3 that must be added to the water to produce a solution with the desired freezing point depression.