When 42.5 g of benzamide (C7H7NO) are dissolved in 500 g of a certain mystery liquid X, the freezing point of the solution is 6.40 °C less than the freezi point of pure X. Calculate the mass of iron(III) nitrate (Fe(NO3)3 that must be dissolved in the same mass of X to produce the same depression in freezing point.

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