Concentrated H₂O₂ solution is used as oxidant in rocket fuel and diluted H₂O₂ solution is used as hair bleach.  A 30% H₂O₂ (w/w) aqueous solution has density 1.11 gm/mL.  What is the molarity and mole fraction of the H₂O₂ solution ?   

Calculation of Molarity and Mole Fraction of 30% H₂O₂ Solution

Given Data:

• Weight percent of H₂O₂ = 30% (w/w)
• Density of solution, ρ = 1.11 g/mL

Step 1: Calculate the mass of H₂O₂ and water in 1 L of solution

• Mass of 1 L (1000 mL) of solution = 1000 mL × 1.11 g/mL = 1110 g
• Mass of H₂O₂ = 30% of total mass = (30/100) × 1110 g = 333 g
• Mass of water = 1110 g - 333 g = 777 g

Step 2: Calculate moles of H₂O₂ and water

• Molecular weight of H₂O₂ = 34 g/mol
• Moles of H₂O₂ = 333 g / 34 g/mol ≈ 9.79 mol
• Molecular weight of water = 18 g/mol
• Moles of water = 777 g / 18 g/mol ≈ 43.17 mol

Step 3: Calculate molarity of H₂O₂

• Since the volume of 1 L of solution is given, the molarity (M) is:
  M = moles of H₂O₂ / volume in liters = 9.79 mol / 1 L = 9.79 M

Step 4: Calculate mole fraction of H₂O₂