In the lime soda process once used in large scale munici-pal water softening, calcium hydroxide prepared from lime and sodium carbonate are added to precipitate Ca2+ as CaCO3(s) and Mg2+ as Mg(OH)2(s): Ca2+(aq) + CO32-(aq) → CaCO3(s) Mg2+(aq) + 2 OH-(aq) → MgOH2(aq) How many moles of Ca(OH)2 and Na2CO3 should be added to soften (remove the Ca2+ and Mg2+) 1200 L of water in which [Ca2+] = 5.0x10-4 M and [Mg2+] = 7.0x10-4 M?

Verified step by step guidance

1. Calculate the total moles of Ca2+ in the water by multiplying the concentration of Ca2+ by the volume of water. Use the formula: Moles of Ca2+ = [Ca2+] × Volume of water (in liters).
2. Calculate the total moles of Mg2+ in the water by multiplying the concentration of Mg2+ by the volume of water. Use the formula: Moles of Mg2+ = [Mg2+] × Volume of water (in liters).
3. Determine the moles of Ca(OH)2 needed by recognizing that the stoichiometry of the reaction between Ca2+ and OH- from Ca(OH)2 is 1:2. Therefore, the moles of Ca(OH)2 required will be equal to the moles of Ca2+.
4. Determine the moles of Na2CO3 needed by recognizing that the stoichiometry of the reaction between Ca2+ and CO32- is 1:1. Therefore, the moles of Na2CO3 required will be equal to the moles of Ca2+.
5. Calculate the moles of NaOH needed for precipitating Mg2+ as Mg(OH)2 by recognizing that the stoichiometry of the reaction between Mg2+ and OH- is 1:2. Therefore, the moles of NaOH required will be twice the moles of Mg2+.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equations. It allows us to determine the amount of substances needed or produced in a reaction. In this context, understanding the stoichiometric relationships between calcium hydroxide, sodium carbonate, and the ions in water is essential for calculating the required moles to achieve water softening.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is crucial for determining how much of a substance is present in a given volume of solution. In this question, the molarity of calcium and magnesium ions in the water is provided, which is necessary for calculating the total moles of these ions that need to be removed through precipitation.

Precipitation Reactions

Precipitation reactions occur when two soluble reactants form an insoluble product, or precipitate, that separates from the solution. In the lime soda process, calcium and magnesium ions react with carbonate and hydroxide ions to form solid calcium carbonate and magnesium hydroxide. Understanding these reactions is key to determining how to effectively remove these ions from water to achieve softening.