Find the molecular mass of a solute by freezing point depression. Solvent: para-dichlorobenzene Freezing point of pure solvent: 53.02C Mass of unknown substance: 2.04g Freezingpointdepressin constant:7.1c/m Mass of para-dichlo...: 24.80g Freexing point solution: 50.78 C Can you explain how you got it, Please and thank you
delta T = Kf*molality.
Calculate molality.
molality = moles/kg solvent.
Calculate moles.
moles = grams/molar mass.
Calculate molar mass.
260.73 g/mol
Temp of solvent - Temp of solution = constant x molality
solve for molality.
molality = mol of solute/kg of solvent
molality = change in Temp/constant
molality = (53.02-50.78)/7.1 = 0.3155 mol/kg
Convert to mol/g, so divide by 1000g.
molality = 3.155e-4 mol/g
multiply molality by grams of solvent to get moles of solute.
3.155e-4 mol/g x 24.8 g = 0.007824 mol
Now you have moles of solute. Solve for molecular mass by diving the grams of the solute by the calculated moles of solute.
Molecular mass of solute = 2.04 g/0.007824 mol = 260.73 mol/g of solute.
To find the molecular mass of a solute using freezing point depression, you need to use the formula:
ΔT = Kf * m * i
where:
ΔT is the change in freezing point
Kf is the freezing point depression constant
m is the molality (moles of solute per kilogram of solvent)
i is the van't Hoff factor
In this case, the freezing point depression constant for para-dichlorobenzene is given as 7.1°C/m.
First, calculate the change in freezing point (ΔT):
ΔT = Freezing point of pure solvent - Freezing point of solution
= 53.02°C - 50.78°C
= 2.24°C
Next, calculate the molality (m):
m = (mass of solute / molecular mass of solute) / (mass of solvent / molar mass of solvent)
= (2.04 g / molecular mass of solute) / (24.80 g / 147.045 g/mol)
= (2.04 g / molecular mass of solute) / 0.16767 mol
Now, substitute the given values into the formula to solve for the molecular mass (molecular weight):
ΔT = Kf * m * i
2.24°C = 7.1°C/m * [(2.04 g / molecular mass of solute) / 0.16767 mol] * i
Simplifying the equation:
2.24°C * 0.16767 mol = 7.1°C/m * 2.04 g / molecular mass of solute * i
0.3750016 = (14.484 * i) / molecular mass of solute
To solve for the molecular mass of solute, rearrange the equation:
molecular mass of solute = (14.484 * i) / 0.3750016
Now, use the value of the van't Hoff factor (i). For a non-ionic solute, i equals 1.
molecular mass of solute = (14.484 * 1) / 0.3750016
molecular mass of solute ≈ 38.622 g/mol
Therefore, the molecular mass (or molecular weight) of the solute is approximately 38.622 g/mol.
To find the molecular mass of a solute using freezing point depression, you can use the equation:
∆T = Kf * m
where ∆T is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution (moles of solute per kilogram of solvent).
In this case, the freezing point depression (∆T) is the difference between the freezing point of the pure solvent (53.02°C) and the freezing point of the solution (50.78°C). Therefore, ∆T = 53.02°C - 50.78°C = 2.24°C.
The molality of the solution (m) can be calculated using the formula:
m = (moles of solute) / (mass of solvent in kg)
First, we need to find the moles of solute. To do this, we need the molecular mass of the solute.
Given that the mass of the solute is 2.04g and the mass of the solvent (para-dichlorobenzene) is 24.80g, we can calculate the moles of solute as follows:
moles of solute = (mass of solute) / (molar mass of solute)
Next, we need to find the mass of the solvent in kg. To convert grams to kilograms, divide the mass of the solvent by 1000:
mass of solvent in kg = (mass of solvent) / 1000
Now, we can calculate the molality (m) using the formula mentioned earlier:
m = (moles of solute) / (mass of solvent in kg)
Finally, we can substitute the values into the freezing point depression equation to solve for the molecular mass of the solute:
2.24°C = 7.1°C/m * m
Solving for m:
m = 2.24°C / 7.1°C/m
m ≈ 0.316 m
Now, rearrange the molality equation to solve for the moles of solute:
moles of solute = m * (mass of solvent in kg)
moles of solute ≈ 0.316 m * 0.0248 kg
moles of solute ≈ 0.00783 mol
Finally, rearrange the moles of solute equation to solve for the molecular mass of the solute:
molar mass of solute = (mass of solute) / (moles of solute)
molar mass of solute = 2.04 g / 0.00783 mol
molar mass of solute ≈ 260.88 g/mol
Therefore, the molecular mass of the solute is approximately 260.88 g/mol.