Answer:
21.3g of Fe(NO₃)₃ are required to produce the same depression in freezing point of solution.
Explanation:
Freezing point depression is a colligative property which indicates, in determined mixture, the freezing point of solution is lower that the freezing point of the solvent, according the amount of solute.
Formula is: ΔT = Kf . m . i
Kf is the cryoscopic constant, which is particular for each solvent. We do not have that data, so we need to find it out in order to solve the question:
ΔT = Freezing point of pure solvent - Freezing point of solution.
This data is known → 6.40°C
m, means molality, moles of solute in 1kg of solvent. Let's get the moles of benzamide: 42.5 g . 1mol / 121g = 0.351 moles
m = 0.351 mol / 0.5kg = 0.702 m
As benzamide is an organic compound i, = 1. i are the number of ions dissolved in solution. Let's find out Kf:
6.40°C = Kf . 0.702 m . 1
6.40°C /0.702m = 9.11 °C/m.
Let's go to the next question.
ΔT is the same → 6.40°C
But this is, an inorganic salt, a ionic salt: Fe(NO₃)₃ → 1Fe³⁺ + 3NO₃⁻
For this case, we have 1 mol of Iron(III) and 3 nitrates, so i = 4
Let's replace data: 6.40°C = 9.11 °C/m . m . 4
6.40°C / (9.11 m/°C . 4) = 0.176 m
This data represents that, in 1 kg of solvent we have 0.176 moles of nitrate.
Mass of solvent X required in this case is 0.500 kg, so, the moles that are contained are: 0.500 kg . 0.176 mol/kg = 0.088 mol
Let's determine the mass of salt: 0.088 mol . 241.85g /1mol = 21.3 g
