A solution is made by dissolving 0.624 mol of nonelectrolyte solute in 795 g of benzene. Calculate the freezing point and boiling point of the solution.
Tf=_ˆC
Tb=_ˆC
To calculate the freezing point and boiling point of a solution, we need to use two formulas: the freezing point depression equation and the boiling point elevation equation.
1. Freezing Point Depression Equation:
The freezing point depression is given by the equation:
ΔTf = Kf * m * i
Where:
ΔTf is the freezing point depression
Kf is the cryoscopic constant (freezing point depression constant) of the solvent
m is the molality of the solution
i is the van't Hoff factor (1 for nonelectrolytes)
2. Boiling Point Elevation Equation:
The boiling point elevation is given by the equation:
ΔTb = Kb * m * i
Where:
ΔTb is the boiling point elevation
Kb is the ebullioscopic constant (boiling point elevation constant) of the solvent
m is the molality of the solution
i is the van't Hoff factor (1 for nonelectrolytes)
Now, let's calculate the freezing point (Tf) and boiling point (Tb) of the solution step by step:
Step 1: Convert the mass of benzene to moles.
Since the molar mass of benzene (C6H6) is 78.11 g/mol, we can calculate moles:
Moles of benzene = Mass of benzene / Molar mass of benzene
Moles of benzene = 795 g / 78.11 g/mol = 10.18 mol
Step 2: Calculate the molality (m) of the solution.
Molality is defined as moles of solute per kilogram of solvent.
Molality (m) = Moles of solute / Mass of solvent (kg)
Molality (m) = 0.624 mol / 0.795 kg = 0.785 m
Step 3: Calculate the freezing point depression (ΔTf).
Using the freezing point depression equation, we can calculate ΔTf:
ΔTf = Kf * m * i
Since benzene is the solvent and it is a nonelectrolyte, the van't Hoff factor (i) is 1.
Now, we need to find the Kf (freezing point depression constant) value for benzene.
For benzene, Kf = 5.12 ˚C/m (given constant)
ΔTf = 5.12 ˚C/m * 0.785 m * 1 = 4.02 ˚C
So, the freezing point (Tf) of the solution is 4.02 ˚C lower than the freezing point of pure benzene.
Step 4: Calculate the boiling point elevation (ΔTb).
Using the boiling point elevation equation, we can calculate ΔTb:
ΔTb = Kb * m * i
Since benzene is the solvent and it is a nonelectrolyte, the van't Hoff factor (i) is 1.
Now, we need to find the Kb (boiling point elevation constant) value for benzene.
For benzene, Kb = 2.53 ˚C/m (given constant)
ΔTb = 2.53 ˚C/m * 0.785 m * 1 = 1.98 ˚C
So, the boiling point (Tb) of the solution is 1.98 ˚C higher than the boiling point of pure benzene.
Therefore, the freezing point (Tf) of the solution is 4.02 ˚C and the boiling point (Tb) of the solution is 1.98 ˚C.