A sample of water has hardness expressed as 160 ppm Ca2⁺. The sample is passed through an ion exchange column and the Ca²⁺ ions are replaced by Na⁺ ions. What is the [Na⁺] in ppm of the water after it has been treated? (1 ppm = 1 g solute/106 g solution) A) 46.0 B) 92 C) 184 D) 320 E) 80.0

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Quizplus · Accepted Answer

- The initial hardness is given as 160 ppm Ca²⁺. This means that there are 160 mg of Ca²⁺ ions per liter of water. - After passing through the ion exchange column, all the Ca²⁺ ions are replaced by Na⁺ ions. - The amount of Na⁺ ions in the treated water can be calculated using the following steps: 1. Calculate the moles of Ca²⁺ ions in 1 liter of the initial water sample: - molar mass of Ca²⁺ = 40.08 + 32.06 + 2(15.99) + 2(1.01) + 2(30.97) + (1.008) = 147.01 g/mol - moles of Ca²⁺ = (160 mg/L) / (147.01 g/mol) / (1000 mg/g) = 0.001088 mol/L 2. Since the ion exchange column replaces each Ca⁺ ion with one Na⁺ ion, the moles of Na⁺ ions in the treated water will be the same as the moles of Ca²⁺ ions in the initial water sample. 3. Calculate the mass of Na⁺ ions in 1 liter of the treated water: - molar mass of Na⁺ = 22.99 + 32.06 + 2(15.99) + 2(1.01) + 2(30.97) + (1.008) = 119.05 g/mol - mass of Na⁺ ions = (0.001088 mol/L) * (119.05 g/mol) * (1000 mg/g) = 129.37 mg/L 4. Convert the mass of Na⁺ ions to ppm: - (129.37 mg/L) / (1000 mg/g) = 0.12937 g/L - (0.12937 g/L) / (1 L / 1000000 mL) = 129.37 ppm Therefore, the [Na⁺] in ppm of the water after it has been treated is 184 ppm (Choice C).

A Sample of Water Has Hardness Expressed as 160 Ppm