A stream flows at a rate of \(5.00 \times 10^{4}\) liters per second (L/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 135 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: $$\mathrm{CaO}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(i) $$ What mass of CaO is consumed in an 8.00-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.

Step by step solution

01

a. Total Flow Rate Downstream

To calculate the total flow rate downstream from the first manufacturing plant, we simply need to add the flow rate of the stream and the flow rate of the discharged water from the plant. The formula is: Total Flow Rate = Stream Flow Rate + Plant Discharge Flow Rate So the total flow rate would be: Total Flow Rate = \(5.00 \times 10^{4} \mathrm{L/s} + 3.50 \times 10^{3} \mathrm{L/s}\)

02

b. Concentration of HCl Downstream

To find the concentration of HCl in ppm downstream from the first manufacturing plant, we will use the formula for ppm: ppm = \(\frac{Mass \ of \ Solute}{Mass \ of \ Solution}\) x \(10^{6}\) The mass of HCl from the discharged water is: Mass of HCl = Flow Rate x Concentration x Time We can find the concentration of HCl downstream by dividing the mass of HCl by the total mass of water downstream and then multiplying by \(10^6\).

03

c. Mass of CaO Consumed in an 8.00-hour Workday

To find the mass of CaO consumed, we first need to find the moles of H⁺ ions that need to be neutralized. We can use the formula: Moles of H⁺ ions = Flow Rate x Concentration x Time Then, we can find the moles of CaO needed using the stoichiometric ratio from the balanced equation. After that, we need to find the mass of CaO consumed by multiplying the moles of CaO with the molar mass of CaO and convert the time from hours to seconds.

04

d. Concentration of Ca²⁺ Downstream of the Second Plant

To find the concentration of Ca²⁺ downstream from the second plant, we need to find the mass of Ca²⁺ returned to the stream. This can be done using the following steps: 1. Find the mass of Ca²⁺ initially present in the stream water (using ppm = \(\frac{Mass \ of \ Solute}{Mass \ of \ Solution}\) x \(10^{6}\)). 2. Find the mass of Ca²⁺ added to the stream during the neutralization process. This can be done using the stoichiometric ratio and mass of CaO consumed. 3. Calculate the total mass of Ca²⁺ present after the second plant. 4. Find the concentration of Ca²⁺ in ppm downstream of the second plant by dividing the total mass of Ca²⁺ by the mass of the solution downstream and multiplying by \(10^6\).

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