Step-by-step explanation:
To solve the problem, we can use the freezing point depression equation:
ΔT = Kf · molality
where ΔT is the change in freezing point, Kf is the freezing point depression constant, and molality is the concentration of the solution in moles of solute per kilogram of solvent.
In this case, we're looking for the freezing point of a solution of C5H4 in benzene, given that the freezing point of pure benzene is 5.50 °C, and the freezing point depression constant is 5.12 °C/m.
First, let's calculate the molality of the solution:
molality = moles of solute / kilograms of solvent
To find the moles of solute, we need to know the molar mass of C5H4. By looking it up in a periodic table, we find:
Molar mass of C5H4 = 64.09 g/mol
The problem doesn't tell us how much solute was added, but it does give us the concentration of the solution as 0.41 m (which means 0.41 moles of C5H4 per kilogram of benzene). Therefore:
molality = 0.41 moles / 0.998 kg ≈ 0.411 mol/kg
Now we can calculate the freezing point depression:
ΔT = Kf · molality
ΔT = 5.12 °C/m · 0.411 mol/kg ≈ 2.10 °C
The freezing point depression tells us how much the freezing point of the solution is lowered compared to the freezing point of pure benzene. Therefore, the freezing point of the solution is:
Freezing point = 5.50 °C - 2.10 °C = 3.40 °C
Therefore, the freezing point of the 0.41 m solution of C5H4 in benzene is 3.40 °C.