The solubility of Na₃AsO₄(H₂O)₁₂ is 38.9g per 100g H₂O. What is the mass percentage of Na₃AsO₄ in the saturated solution? (As = 75, Na = 23, O = 16…

Explanation

The solubility tells us that 38.9g of Na₃AsO₄(H₂O)₁₂ dissolves in 100g of water. But the question asks for the mass percentage of Na₃AsO₄ (without the water of crystallization) in the saturated solution.

First, find the molar mass of Na₃AsO₄(H₂O)₁₂:
Na₃ = 3 × 23 = 69
As = 75
O₄ = 4 × 16 = 64
12H₂O = 12 × 18 = 216
Total = 69 + 75 + 64 + 216 = 424

Next, find the molar mass of Na₃AsO₄ (anhydrous part only):
Na₃AsO₄ = 69 + 75 + 64 = 208

Now find the fraction of Na₃AsO₄ in the hydrated salt:
Fraction = 208 ÷ 424 = 0.4906

The mass of actual Na₃AsO₄ in 38.9g of the hydrated salt:
Mass of Na₃AsO₄ = 0.4906 × 38.9 = 19.08g

The total mass of the saturated solution is the mass of dissolved salt plus the mass of water:
Total solution mass = 38.9 + 100 = 138.9g

Finally, calculate the mass percentage:
Mass % = (19.08 ÷ 138.9) × 100 = 13.74% ≈ 13.75%

The mass percentage of Na₃AsO₄ in the saturated solution is 13.75%.