Question

An aqueous solution of sodium chloride is marked 10% on the bottle the density of the solution is 1.07 what is the molality and molarity also calculate the mole fraction of each component in the solution

Answer 1

Molarity = % (w/W) of solute × density of solution × 10/Molecular weight of solute
Given, % (w/W) of solute = 10 %
density of solution = 1.07 g/ml
Molecular weight of NaCl = 23 + 35.5 = 58.5 g/ml
Now, molarity = 10 × 1.07 × 10/58.5
= 107/58.5 M
= 1.82 M

Now, use formula,
1/m = d/M - Ms/1000
Where m is molality, M is molarity , d is density and Ms is molar mass of solute.
∴ 1/m = 1.07/1.82 - 58.5/1000
= 0.581 - 0.0585
= 0.523
m = 1/0.523 = 1.91

mol fraction of solute is x
Then, molality = x × 1000/(1 - x)× M'
Where M' is molar mass of solvent
M = 18 g/mol
Now, 1.91 = x × 1000/(1 - x) 18
18 × 1.91 (1 - x) = 1000x
x ≈ 0.033
Hence, mole fraction of solute is 0.033