A plant manufacturing nails and screws uses a large pool (volume = 10,000 L) to collect and treat its residual waste water before discharging it in a nearby stream.  The manufacturing process makes use of a strong acid (HCl) and a weaker one (phosphoric acid, H₃PO₄; pK_a1 = 2.148, pK_a2 = 7.20, pK_a3 = 12.15), before discharging them in the pool for treatment (neutralization).  Once the pool is filled to its maximum capacity, a technician measures the chlorine and phosphorus concentrations in the waste water to be 0.5 M and 1.0 M, respectively.  Assume (i) that chlorine and phosphorus come only from HCl and phosphoric acid, respectively, and (ii) that no H⁺ was consumed (or neutralized) in the manufacturing process.

(a)   Knowing that the technician has to bring the pH of the waste water back to a minimum of 7.2 before discharging it in the stream, what is the minimum amount (in kg) of NaOH_(s) (40 g/mol) that he has to add to the pool before discharging the waste water in the stream?

(b)   What will be the pH of the waste water following the addition of 200 kg of NaOH?

(c)    What will then be the number of moles of each phosphorus species (H₃PO₄, H₂PO₄^–, HPO₄^2- and PO₄^3-) in the pool after the addition of NaOH?

(d)   What will be the pH of the waste water if the technician adds 10.0 kg of NaOH in excess to what is needed to bring the pH to 7.2?