Phosphorus is essential for plant growth, but an excess of phosphorus can be catastrophic in aqueous ecosystems. Too much phosphorus can cause algae to grow at an explosive rate and this robs the rest of the ecosystem of oxygen. Effluent from sewage treatment plants must be treated before it can be released into lakes or streams because the effluent contains significant amounts of H₂PO₄^- and HPO₄^2-. (Detergents are a major contributor to phosphorus levels in domestic sewage because many detergents contain Na₂HPO₄.) A simple way to remove H₂PO₄^- and HPO₄^2- from the effluent is to treat it with lime, CaO, which produces Ca²⁺ and OH^- ions in water. The OH^- ions convert H₂PO₄^- and HPO₄^2- ions into PO₄^3- ions and, finally, Ca²⁺, OH^-, and PO₄^3- ions combine to form a precipitate of Ca₅(PO₄)₃OH(s).

(a) Write balanced chemical equations for the four reactions described above.

(b) How many kilograms of lime are required to remove the phosphorus from a 1.00 x 10⁴ L holding tank filled with contaminated water, if the water contains 10.0 mg of phosphorus per liter?