Sodium hydroxide is a common ingredient in drain cleaners such as Drano. The mole fraction of sodium hydroxide in a saturated aqueous solution is 0.310. What is the molality of the solution? (a) 12.4 m

(b) 0.690 m

(c) 25.0 m

(d) 1.24 m

(e) 0.310 m

The correct answer to this question is (c) 25.0 m

Explanation:

To solve this we list out the variables thus

mole fraction of sodium hydroxide = 0.310

Mole fraction = number of moles of a component : total number of moles in the solution

Mole fraction = 0.310

In a saturaturated aqueous solution we have NaOH and water

∴ Number of moles of water molecules per unit = 1 - 0.310 = 0.690

However 0.690 moles of H₂O weighs = 0.690 mole * 18.01528 g/mol = 12.43 g = 0.01243 kg of H₂O

But the molality = number of moles per Kilogram of H₂O

therefore molality of NaOH in the sample of solution =

(0.310 mol of NaOH) : (0.01243 kg of H₂O)

= 24.93 mol/kg or ≅ 25.0 m