a solution is prepared by dissolving 4.9 g C12H22 O11 (nonelectrolyte) in 175 grams of water. calculate the freezing poitn and osmotic pressure (25C) of this solution.
i got 2.002 atm is that right
I get 2.00 atm also. If you have a density in the problem we can correct for and use M and not m but with no density in what you posted we have no choice but to use m for M.
moles in 4.9g = grams/molar mass = ?
m = molality = mols/kg solvent
delta T = Kf*m. Solve for delta T and subtract from the normal freezing point of H2O (0C) to find the new freezing point.
pi = MRT
M is molarity but in dilute solutions M and m are almost the same. R is 0.08206 and T must be in kelvin; pi comes out in atmospheres.
To calculate the freezing point depression and osmotic pressure of the solution, we need to use the formulas and equations based on colligative properties.
1. Freezing Point Depression:
Freezing point depression is a colligative property that depends on the molality of the solute. The formula to calculate the freezing point depression (ΔTf) is given by:
ΔTf = Kf * m
where:
- ΔTf is the freezing point depression
- Kf is the cryoscopic constant (a characteristic property of the solvent)
- m is the molality of the solute in the solution
For water, the cryoscopic constant (Kf) is 1.86 °C/m.
To find the molality (m), we need to know the moles of the solute and the mass of the solvent.
First, let's calculate the moles of C12H22O11:
Molar mass of C12H22O11 = (12*12) + (22*1) + (11*16) = 342 g/mol
moles = mass / molar mass = 4.9 g / 342 g/mol ≈ 0.0143 mol
Next, we calculate the molality using the formula:
molality (m) = moles of solute / mass of solvent (in kg).
Mass of water = 175 g = 0.175 kg
molality (m) = 0.0143 mol / 0.175 kg ≈ 0.082 mol/kg
Now we can calculate the freezing point depression:
ΔTf = 1.86 °C/m * 0.082 mol/kg = 0.152 °C
So, the freezing point depression (ΔTf) of the solution is approximately 0.152 °C.
2. Osmotic Pressure:
The osmotic pressure (π) of a solution can be calculated using the equation:
π = i * MRT
where:
- π is the osmotic pressure
- i is the van't Hoff factor (number of particles into which the solute dissociates, in case of nonelectrolytes like C12H22O11, i = 1)
- M is the molarity of the solution
- R is the ideal gas constant (0.0821 L.atm/(mol.K))
- T is the temperature in Kelvin
To calculate the molarity (M), we use the formula:
molarity (M) = moles of solute / volume of solution (in L)
Volume of solution = mass of water / density of water = 175 g / 1 g/mL = 175 mL = 0.175 L
Now we can calculate the molarity (M):
M = moles / volume = 0.0143 mol / 0.175 L ≈ 0.082 M
Finally, we can find the osmotic pressure:
π = 1 * 0.082 M * 0.0821 L.atm/(mol.K) * (25 + 273) K
π ≈ 5.5 atm
So, the osmotic pressure (π) of the solution is approximately 5.5 atm.