A stream flows at a rate of \(5.00 \times 10^{4}\) liters per second \((\mathrm{L} / \mathrm{s})\) upstream of a manufacturing plant. The plant discharges \(3.50 \times\) \(10^{3} \mathrm{~L} / \mathrm{s}\) of water that contains \(65.0 \mathrm{ppm} \mathrm{HCl}\) into the stream. (See Exercise 113 for definitions.) a. Calculate the stream's total flow rate downstream from this plant. b. Calculate the concentration of \(\mathrm{HCl}\) in ppm downstream from this plant. c. Further downstream, another manufacturing plant diverts \(1.80 \times 10^{4} \mathrm{~L} / \mathrm{s}\) of water from the stream for its own use. This plant must first neutralize the acid and does so by adding lime: $$ \mathrm{CaO}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$ What mass of \(\mathrm{CaO}\) is consumed in an \(8.00-\mathrm{h}\) work day by this plant? d. The original stream water contained \(10.2 \mathrm{ppm} \mathrm{Ca}^{2+}\). Although no calcium was in the waste water from the first plant, the waste water of the second plant contains \(\mathrm{Ca}^{2+}\) from the neutralization process. If \(90.0 \%\) of the water used by the second plant is returned to the stream, calculate the concentration of \(\mathrm{Ca}^{2+}\) in ppm downstream of the second plant.

To calculate the total flow rate downstream, we add the stream's initial flow rate to the flow rate of the water discharged by the first plant: Total flow rate downstream = Initial flow rate + Discharged flow rate Total flow rate downstream = \(5.00 \times 10^4 L/s + 3.50 \times 10^3 L/s\) Total flow rate downstream = \(5.35 \times 10^4 L/s\)

First, we'll find the mass of HCl added by the first plant: Mass of HCl = Discharged flow rate * HCl concentration Mass of HCl = \(3.50 \times 10^3 L/s * 65.0 ppm\) Note: 1 ppm = \(1 \times 10^{-6} g/L\) Mass of HCl = \(3.50 \times 10^3 L/s * 65.0 * 10^{-6} g/L\) Mass of HCl = \(2.275 \times 10^{-1} g/s\) Next, we'll calculate the concentration of HCl downstream: HCl concentration downstream = Mass of HCl / Total flow rate downstream HCl concentration downstream = \(\frac{2.275 \times 10^{-1} g/s}{5.35 \times 10^4 L/s} \) HCl concentration downstream = \(4.25 \times 10^{-6} g/L = 4.25 ppm\)

The second plant takes \(1.80 \times 10^4 L/s\) of water at a concentration of 4.25 ppm of HCl. To neutralize it, we need to use the stoichiometry of the reaction: 1 mol CaO neutralizes 2 mol HCl: \(CaO + 2H^{+} \rightarrow Ca^{2+} + H_2O\) First, we calculate the moles of HCl to be neutralized: Moles of HCl = Flow rate * Time * HCl concentration_downstream / molar_mass_HCl Moles of HCl = \(\frac{1.80 \times 10^4 L/s * 8.00 h * 60 min/h * 60 s/min * 4.25 \times 10^{-6} g/L}{36.46 g/mol}\) Moles of HCl = \(8409.85 mol\) Next, we calculate the moles of CaO needed to neutralize it: Moles of CaO = Moles of HCl / 2 = \(4204.93 mol\) Now, we calculate the mass of CaO needed: Mass of CaO = Moles of CaO * molar_mass_CaO Mass of CaO = \(4204.93 mol * 56.08 g/mol\) Mass of CaO = \(235984.61 g\)

The original stream water contained 10.2 ppm Ca^2+. Additionally, the waste water from the second plant contains Ca^2+ from the neutralization reaction (converting CaO to Ca^2+). The mass of Ca^2+ added by the waste water is the same as the mass of CaO used in the neutralization, so: Mass of Ca^2+ added = Mass of CaO used = \(235984.61 g\) Now, we need to determine how much water is returned to the stream after being used by the second plant: Water returned = Water used by the second plant * 0.90 Water returned = \(1.80 \times 10^4 L/s * 0.90\) Water returned = \(1.62 \times 10^4 L/s\) Now, we can find the total flow rate after the second plant: Total flow rate downstream_second_plant = Total flow rate downstream_first_plant - Water used by the second plant + Water returned Total flow rate downstream_second_plant = \(5.35 \times 10^4 L/s - 1.80 \times 10^4 L/s + 1.62 \times 10^4 L/s\) Total flow rate downstream_second_plant = \(5.17 \times 10^4 L/s\) Finally, we can calculate the Ca^2+ concentration downstream: Ca^2+ concentration downstream = (Initial Concentration * Initial Flow Rate + Ca^2+ mass added) / Total Flow Rate downstream_second_plant Ca^2+ concentration downstream = \(\frac{10.2 \times 10^{-6} g/L * 5.00 \times 10^4 L/s + 235984.61}{5.17 \times 10^4 L/s}\) Ca^2+ concentration downstream = \(15.47 \times 10^{-6} g/L = 15.47 ppm\)