The freezing point of a cyclohexane sample is 6.20*C. A soltuion is prepared by dissolving 0.4660g of an unknown solute in 36.0g cyclohexane. The freezing point of the solution if 4.11*C. Calculate the molar mass of the unknown solute. Kf for cyclohexane is 20.0*Ckg/mole.
To solve this problem, we can use the formula for freezing point depression:
ΔT = Kf * m
where:
ΔT is the change in freezing point
Kf is the cryoscopic constant
m is the molality of the solution
First, calculate the change in freezing point (∆T) using the freezing point of the pure solvent (6.20°C) and the freezing point of the solution (4.11°C):
ΔT = 6.20°C - 4.11°C
ΔT = 2.09°C
Next, calculate the molality (m) of the solution:
m = moles of solute / mass of solvent (in kg)
To find the moles of solute, we need to convert the given mass of the unknown solute (0.4660g) to moles. To do this, we divide the mass by the molar mass (M) of the unknown solute:
moles of solute = mass of solute / molar mass
Now, rearrange the formula to solve for the molar mass:
molar mass = mass of solute / moles of solute
Now let's calculate the moles of solute:
moles of solute = 0.4660g / molar mass
Substituting this into the molality formula:
m = (0.4660g / molar mass) / (36.0g / 1000g/kg)
Simplify the equation further:
m = (0.4660g / molar mass) / 0.0360 kg
Solve for m:
m = 12.94 / molar mass
Now, substitute the values in the freezing point depression formula:
2.09°C = (20.0°C·kg/mole) * (12.94 / molar mass)
Simplify the equation:
2.09°C = (20.0°C·kg/mole) * (12.94 / molar mass)
2.09°C = 258.8 / molar mass
Now solve for the molar mass:
molar mass = 258.8 / 2.09°C
molar mass = 124.00 g/mol
Therefore, the molar mass of the unknown solute is 124.00 g/mol.
To find the molar mass of the unknown solute, we can use the freezing point depression equation:
ΔT = Kf * m
Where:
ΔT is the change in freezing point (ΔT = Tf - Tf°)
Kf is the freezing point depression constant for cyclohexane (20.0 °Ckg/mole)
m is the molality of the solution (moles of solute per kg of solvent)
First, let's calculate the change in freezing point (ΔT):
ΔT = Tf - Tf°
= 4.11 °C - 6.20 °C
= -2.09 °C
Next, we need to calculate the molality of the solution (m):
m = (moles of solute) / (mass of solvent in kg)
The mass of solvent (cyclohexane) is given as 36.0 g, which is equal to 0.036 kg.
Now, we can calculate the moles of solute:
moles of solute = (mass of solute) / (molar mass of solute)
The mass of solute is given as 0.4660 g.
Now, we can rearrange the equation for molality to solve for the molar mass of the solute:
m = (moles of solute) / (mass of solvent in kg)
m = (0.4660 g / molar mass) / 0.036 kg
In the molality formula, the moles of solute cancel out:
0.036 kg * m = 0.4660 g / molar mass
Simplifying the equation:
m = (0.4660 g / molar mass) / 0.036 kg
m = 12.94 g / (molar mass * 0.036 kg)
Cross-multiplying and rearranging the equation:
molar mass * 0.036 kg = 12.94 g
molar mass = 12.94 g / 0.036 kg
Calculating the molar mass:
molar mass = 359.44 g/mol
Therefore, the molar mass of the unknown solute is 359.44 g/mol.
delta T = Kf*molality
Solve for molality.
molality = moles/kg solvent
Solve for moles.
moles = grams/molar mass
Solve for molar mass.