10.0 g sample of p-dichlorobenzene, a component of mothballs, is
dissolved in 80.0 g of benzene, C6H6. The freezing-point of the solution is
1.20oC. The freezing point of benzene is 5.48oC. The molal freezing –point
constant, kf, for benzene is 5.12oC/m. Calculate the apparent molar
mass of p-dichlorobenzene.
delta T = i*Kf*m
You know delta T, i = 1 and you know Kf. Solve for m, molality.
Then m = moles/kg solvent.
You know m and kg solvent, solve for moles.
Then moles = grams/molar mass. You know moles and grams, solve for molar mass.
Post your work if you get stuck.
k thanks
Its a practice question for my final exam. No answer is given.
To calculate the apparent molar mass of p-dichlorobenzene, we need to use the freezing point depression equation:
ΔTf = kf * m * i
Where:
ΔTf = change in freezing point (in this case, it is the difference between the freezing point of pure benzene and the freezing point of the solution)
kf = molal freezing-point constant for benzene (given as 5.12oC/m)
m = molality of the solution (mol of solute/kg of solvent)
i = van't Hoff factor (number of particles into which the solute dissociates)
First, let's calculate the molality of the solution:
Molality (m) = moles of solute / kg of solvent
Given:
Mass of p-dichlorobenzene (solute) = 10.0 g
Mass of benzene (solvent) = 80.0 g
To find the moles of solute:
Moles of p-dichlorobenzene = mass / molar mass
The molar mass of p-dichlorobenzene can be determined using the periodic table. The elemental composition is:
Carbon (C) - 6.0 g/mol
Hydrogen (H) - 1.0 g/mol
Chlorine (Cl) - 35.5 g/mol
Molar mass of p-dichlorobenzene = (6 * 12.0) + (4 * 1.0) + (2 * 35.5)
Now we can calculate the moles of p-dichlorobenzene using the given mass:
Moles of p-dichlorobenzene = 10.0 g / molar mass of p-dichlorobenzene
Next, we need to calculate the molality (m) of the solution:
Molality (m) = moles of solute / kg of solvent
Molality (m) = moles of p-dichlorobenzene / (mass of benzene (solvent) / 1000 g/kg)
Now that we have the molality (m), we can use it in the freezing point depression equation to find the apparent molar mass:
ΔTf = kf * m * i
Rearranging the equation:
i = ΔTf / (kf * m)
Given:
ΔTf (change in freezing point) = 5.48oC - 1.20oC
kf = 5.12oC/m (given)
m (molality) = calculated in the previous step
By substituting the values in the equation and solving for i, we can determine the van't Hoff factor.
Finally, the apparent molar mass of p-dichlorobenzene can be calculated using the equation:
Apparent molar mass = (mass of p-dichlorobenzene (solute) / moles of p-dichlorobenzene) / i
By substituting the values in the equation, we can find the apparent molar mass of p-dichlorobenzene.