Question

Zeolite A, Na₁₂[(AlO₂)₁₂(SiO₂)₁₂] · 27H₂O, is used to soften water by replacing Ca²⁺ and Mg²⁺ with Na⁺. Hard water from a certain source is 4.20 × 10⁻³M Ca²⁺ and

8.20 × 10⁻⁴M Mg²⁺, and a pipe delivers 2.20 × 10⁴ L of this hard water per day. What mass (in kg) of zeolite A is needed (in kg) to soften a day's supply of the water? (Assume zeolite A loses its capacity to exchange ions when 85.0% mol of its Na⁺ has been lost.)

(Enter your answer in scientific notation.)

Answer 1

Per day supply of hard water = 22000L

Concentration of Ca2+ = 0.00420mol /L

Total mole of Ca2+ = 22000 × 0.00420= 92.4mol

Molar mass of Ca2+ = 40.08g/mol

Mass of Ca2+ in hard water = 92.4×40.08g = 3703.4g

Concentration of Mg2+ = 0.000820mol/L

Total mol of Mg2+ = 0.000820 × 22000=18.04

Molar mass of Mg2+ = 24.31g/mol

Mass of Mg2+ in Hard water = 24.31g × 18.04 = 438.6g

Molar mass of Zeolite A = 2190g/mol

No of mole of Ca2+ removed by 1 mole of Zeolite A = 6

Mass of Ca2+ removed by 2190g of Zeolite A = 240.48g

Mass of Zeolite A required to remove 3703.4g of Ca2+ = 33.73kg

If consider Zeolite efficiency is 85%

Mass of Zeolite A to remove Ca2+ = 39.68kg

No of mole of Mg2+ removed by 1 mole of ZeoliteA = 6

Mass of Mg2+ removed by 2190g of ZeoliteA = 145.86g

Mass of Zeolite required to remove 438.6g of Mg2+= 6.59kg

Considering the 85% as the efficient of Zeolite A

Mass of Zeolite A required to remove Mg2+ = 7.75kg

Total mass of Zeolite A required = 39.68kg + 7.75kg = 47.43kg