Calculate the new freezing point of a solution from 227 g of FeCl3 dissolved in 999g of water

Question

227 g of FeCl

999 g of water

Answer 1

The freezing point depression of a solution is calculated as ΔT_f = K_f x m x i where ΔT_f is the change in freezing point, K_f is the molal freezing point depression constant (1.86^OC/m for water), m is the molality, and i is the van’t Hoff factor which describes the number of ions a solute breaks up into. In this case, i = 4 because FeCl₃ dissociates as Fe³⁺ and 3 Cl^-.

We can first calculate the molality, which is defined as moles of solute per kilogram of solvent.

227 g FeCl₃ x (1 mol FeCl₃/162.2 g FeCl₃) = 1.40... mol FeCl₃

Molality = Moles of Solute/Kilograms of Solvent

Molality = 1.40... mol/0.999 kg

Molality = 1.40... m

ΔT_f = K_f x m x i

ΔT_f = (1.86^OC/m)(1.40... m)(4)

ΔT_f = 10.4...^OC

This indicates the freezing point of the solution is 10.4...^OC lower than the freezing point of pure water. Since water has a freezing point of 0^OC, the freezing point of the solution is -10.4^OC