A solution is made by dissolving 0.698 mol of nonelectrolyte solute in 777 g of benzene. Calculate the freezing point and boiling point of the solution
m = mols/kg solvent
Then substitute m into
dT = Kf*m to calculate dT, then subtract from normal freezing point to find new f.p.
Substitute m into
dT = Kb*m and calculate dT, then add to normal boiling point to find new boiling point.
To calculate the freezing point and boiling point of the solution, we need to use the formula for calculating the change in freezing and boiling point due to the presence of a solute.
1. Freezing Point Depression:
The freezing point depression (ΔTf) is given by the formula:
ΔTf = Kf * m
Where:
- ΔTf is the change in freezing point
- Kf is the cryoscopic constant (freezing point depression constant) for the solvent
- m is the molality of the solution
The cryoscopic constant for benzene (C6H6) is 5.12 °C/molal.
First, we need to calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
Given:
moles of solute = 0.698 mol
mass of benzene solvent = 777 g = 0.777 kg
m = 0.698 mol / 0.777 kg = 0.898 mol/kg
Now we can calculate the change in freezing point:
ΔTf = 5.12 °C/molal * 0.898 mol/kg = 4.6 °C
2. Boiling Point Elevation:
The boiling point elevation (ΔTb) is given by the formula:
ΔTb = Kb * m
Where:
- ΔTb is the change in boiling point
- Kb is the ebullioscopic constant (boiling point elevation constant) for the solvent
- m is the molality of the solution
The ebullioscopic constant for benzene is 2.53 °C/molal.
Using the same molality value as calculated before (0.898 mol/kg), we can calculate the change in boiling point:
ΔTb = 2.53 °C/molal * 0.898 mol/kg = 2.27 °C
3. Calculate the new freezing point and boiling point:
The new freezing point of the solution will be the freezing point of the pure solvent (benzene) minus the change in freezing point:
Freezing Point of Solution = Freezing Point of Pure Solvent - ΔTf
Similarly, the new boiling point of the solution will be the boiling point of the pure solvent plus the change in boiling point:
Boiling Point of Solution = Boiling Point of Pure Solvent + ΔTb
The freezing point of pure benzene is 5.5 °C, and the boiling point of pure benzene is 80.1 °C.
Freezing Point of Solution = 5.5 °C - 4.6 °C = 0.9 °C
Boiling Point of Solution = 80.1 °C + 2.27 °C = 82.4 °C
Therefore, the freezing point of the solution is 0.9 °C, and the boiling point of the solution is 82.4 °C.
To calculate the freezing point and boiling point of a solution, you need to use the equation for each property. The freezing point depression equation is given by:
ΔTf = Kf * m
where
ΔTf = the freezing point depression
Kf = the cryoscopic constant (a property of the solvent)
m = molality of the solution
Similarly, the boiling point elevation equation is given by:
ΔTb = Kb * m
where
ΔTb = the boiling point elevation
Kb= the ebullioscopic constant (a property of the solvent)
m = molality of the solution
First, let's calculate the molality of the solution using the given information:
Molality (m) = moles of solute / mass of solvent (in kg)
Given:
Number of moles of solute = 0.698 mol
Mass of solvent = 777 g = 0.777 kg
Molality (m) = 0.698 mol / 0.777 kg = 0.898 mol/kg (rounded to three decimal places)
Now, you need to find the cryoscopic and ebullioscopic constants for benzene. For benzene, the cryoscopic constant (Kf) is 5.12 °C/m and the ebullioscopic constant (Kb) is 2.53 °C/m.
1. Freezing point depression (ΔTf):
Substituting the values into the equation:
ΔTf = 5.12 °C/m * 0.898 mol/kg = 4.604 °C (rounded to three decimal places)
Therefore, the freezing point of the solution is equal to the freezing point of pure benzene minus the freezing point depression:
Freezing point of the solution = 5.500 °C - 4.604 °C = 0.896 °C (rounded to three decimal places)
2. Boiling point elevation (ΔTb):
Substituting the values into the equation:
ΔTb = 2.53 °C/m * 0.898 mol/kg = 2.273 °C (rounded to three decimal places)
Therefore, the boiling point of the solution is equal to the boiling point of pure benzene plus the boiling point elevation:
Boiling point of the solution = 80.1 °C + 2.273 °C = 82.373 °C (rounded to three decimal places)
Hence, the freezing point of the solution is 0.896 °C, and the boiling point of the solution is 82.373 °C.