Pure benzene has a normal freezing point of 5.50 degrees Celsius. A solution containing 11.4 grams of a molecular substance dissolved in 150.0 grams of benzene (Kf=5.12C/m) has a freezing point of 1.20 degrees Celsius. What is the molar mass of the solute?
delta T = Kf*molality.
Solve for molality and substitute in the next equation.
molality = moles/kg solvent. Solve for moles and substitute in the next equation.
moles = grams/molar mass. Solve for molar mass.
To find the molar mass of the solute, we can use the formula:
ΔTf = Kf * m(solute)
where:
ΔTf is the change in freezing point (in Celsius),
Kf is the cryoscopic constant of the solvent (in Celsius per molal),
m(solute) is the molality (in mol/kg) of the solute in the solution.
First, let's calculate the change in freezing point (ΔTf):
ΔTf = normal freezing point - freezing point of the solution
= 5.50°C - 1.20°C
= 4.30°C
Now, we can rearrange the formula to solve for m(solute):
m(solute) = ΔTf / Kf
m(solute) = 4.30°C / 5.12°C/m
= 0.839 mol/kg
Next, we need to calculate the number of moles of the solute in the solution. We can do this by:
moles = mass / molar mass
For the solute, we know the mass (11.4 grams), so we can rewrite the equation as:
moles = 11.4 g / molar mass
To find the molar mass, we need to divide the mass by the number of moles:
molar mass = 11.4 g / moles
Now, substitute the value of moles with the molality (0.839 mol/kg) we calculated earlier:
molar mass = 11.4 g / (0.839 mol/kg)
Finally, convert the kg to g:
molar mass = 11.4 g / (0.839 mol/150.0 g)
Solving this equation will give you the molar mass of the solute.
To find the molar mass of the solute, we can use the formula:
ΔTf = Kf * m
Where:
ΔTf = change in freezing point
Kf = freezing point depression constant (in this case, given as 5.12 °C/m)
m = molality of the solution
First, let's calculate the change in freezing point:
ΔTf = Tf - Tf°
= 1.20 °C - 5.50 °C
= -4.30 °C
Now let's calculate the molality of the solution:
molality (m) = moles of solute / mass of solvent (in kg)
The mass of the solvent (benzene) is:
Mass of benzene = 150.0 grams = 150.0 g / 1000 = 0.150 kg
To find the moles of solute, we need to use the formula:
moles = mass / molar mass
Let's assume the molar mass of the solute is M.
Using the given mass of the solute (11.4 grams):
moles = 11.4 g / M
Now we can substitute these values in the molality equation:
m = (11.4 g / M) / 0.150 kg
Simplifying:
m = 76 g/M
Now we can substitute the values into the freezing point depression equation:
ΔTf = Kf * m
-4.30 °C = 5.12 °C/m * 76 g/M
Now we can solve for the molar mass (M):
M = (5.12 °C/m * 76 g) / (-4.30 °C)
M = - (5.12 °C/m * 76 g) / 4.30 °C
M ≈ 90.8 g/mol
Therefore, the molar mass of the solute is approximately 90.8 g/mol.