Answer to Question #308886 in Chemistry for Junard

Question

What are the mole fractions of hydrochloric acid (HCI) and water in a 20% (w/w) aqeous HCl solution?

Answer 1

Solution:

Suppose we are given 100 g of an aqueous HCl solution

Therefore,

Mass of HCl = Mass of solution × w(HCl) / 100% = (100 g × 20%) / (100%) = 20 g

Mass of H₂O = Mass of solution − Mass of HCl = 100 g − 20 g = 80 g

The molar mass of HCl is 36.458 g/mol

The molar mass of H₂O is 18.015 g/mol

Calculate the moles of each component:

Moles of HCl = (20 g HCl) × (1 mol HCl / 36.458 g HCl) = 0.5486 mol HCl

Moles of H₂O = (80 g H₂O) × (1mol H₂O / 18.015 g H₂O) = 4.4407 mol H₂O

Therefore,

Total moles of solution = Moles of HCl + Moles of H₂O = 0.5486 mol + 4.4407 mol = 4.9893 mol

Calculate the mole fraction (χ) of each component:

χ = Moles of component / Total moles of solution

Therefore,

χ_HCl = Moles of HCl / Total moles of solution = (0.5486 mol) / (4.9893 mol) = 0.1099 = 0.11

χ_HCl = 0.11

χ_H2O = Moles of H₂O / Total moles of solution = (4.4407 mol) / (4.9893 mol) = 0.8900 = 0.89

χ_H2O = 0.89

Answer:

The mole fraction of hydrochloric acid (HCI) is 0.11

The mole fraction of water (H₂O) is 0.89