A sample of water has hardness expressed as 160 ppm Ca²⁺(aq).The sample is passed through an ion exchange column and the Ca²⁺(aq)ions are replaced by Na⁺(aq)ions.What is the [Na⁺] in ppm of the water after it has been treated? (1 ppm = 1 g solute/10⁶ g solution)

Question

Quizplus · Accepted Answer

The hardness of the water is due to calcium ions, which have a molar mass of approximately 40.08 g/mol. When these ions are replaced by sodium ions (with a molar mass of approximately 22.99 g/mol) through an ion exchange process, the mass of ions in the water changes according to the ratio of their molar masses. The calculation for the concentration of sodium ions in ppm after treatment is based on the stoichiometry of the ion exchange reaction and the molar masses of calcium and sodium. Given that 1 ppm = 1 mg/L, and considering the molar mass ratio, the concentration of sodium ions will be higher than that of calcium ions because sodium has a lower molar mass. The correct calculation involves determining the equivalent mass of sodium ions that would replace the calcium ions, keeping the charge balance and mass action in consideration. Since the molar mass of sodium is less than half of calcium's, replacing each calcium ion (approximately 40 g/mol) with two sodium ions (approximately 23 g/mol each) would approximately double the mass of ions in solution, leading to an answer of 184 ppm.

A Sample of Water Has Hardness Expressed as 160 Ppm