Calculate the mass of NaCl that was dissolved

Question

A certain liquid X has a normal freezing point of 1.30°C and a freezing point depression constant K_f = 5 .16·°C·kgmol^-1. A solution is prepared by dissolving some sodium chloride (NaCl) in 550.g of X. This solution freezes at −3.3°C. Calculate the mass of NaCl that was dissolved. Round your answer to 2 significant digits.

Answer 1

The freezing point depression is given by

∆T = imK

∆T = change in freezing point = 1.30º - 3.3º = 2º

i = van't Hoff factor = 2 for NaCl (1Na + 1Cl = 2 particles)

m = molality = moles NaCl / kg solvent = ?

K = freezing constant for liquid X = 5.16 º/m

Solve for m:

2 = (2)(m)(5.16)

m = 2 / (2)(5.16) = 0.194 molal

This means there are 0.0.194 moles NaCl / kg solvent X

We have only 550 g solvent X, or 0.550 kg solvent X

Therefore the moles of NaCl dissolved = 0.0.194 mols / Kg x 0.550 kg = 0.107 moles NaCl

Mass NaCl dissolved = 0.107 mols NaCl x 58.44 g / mol = 6.23 g NaCl dissolved