NaOH aqueous solution is labelled as 10% (w/v). Density of the solution is 1.02 g/ml. Then the mole fraction of the solute in the solution is
 

Given:

• 10% w/v means 10 g of NaOH is present in 100 mL of solution.
• Density of the solution (ρ): 1.02 g/mL.

Step 1: Calculate the mass of the solution

Mass of solution = Volume × Density

Mass of solution = 100 mL × 1.02 g/mL = 102 g.

Step 2: Calculate the mass of the solvent (water)

Mass of solvent = Mass of solution - Mass of solute (NaOH)

Mass of solvent = 102 g - 10 g = 92 g.

Step 3: Convert the masses to moles

(a) Moles of NaOH:

Moles of NaOH = Mass of NaOH / Molar mass of NaOH

Molar mass of NaOH = 40 g/mol.

Moles of NaOH = 10 g / 40 g/mol = 0.25 mol.

(b) Moles of water:

Moles of water = Mass of water / Molar mass of water

Molar mass of water = 18 g/mol.

Moles of water = 92 g / 18 g/mol = 5.11 mol.

Step 4: Calculate the mole fraction of NaOH

Mole fraction of NaOH (χ_NaOH) = Moles of NaOH / (Moles of NaOH + Moles of water)

χ_NaOH = 0.25 / (0.25 + 5.11)

χ_NaOH = 0.25 / 5.36 = 0.0466.

Final Answer:

The mole fraction of NaOH in the solution is approximately 0.0466.