Answer :
Let's go through the steps to find the polyphosphate dose in pounds per million gallons (lb/Mgal).
1. Understand Concentration and Volume:
- The concentration of the polyphosphate solution is 1 milligram per milliliter (mg/mL).
- Volume of the stock solution added is 7 milliliters (mL).
2. Calculate the Mass of Polyphosphate Added:
- Since the concentration is 1 mg/mL, the mass of polyphosphate in 7 mL is:
[tex]\[
\text{Mass in mg} = 1 \, \text{mg/mL} \times 7 \, \text{mL} = 7 \, \text{mg}
\][/tex]
3. Convert the Mass from Milligrams to Pounds:
- Knowing that 1 mg = 2.20462 × 10^-6 pounds, the mass in pounds is:
[tex]\[
\text{Mass in pounds} = 7 \, \text{mg} \times 2.20462 \times 10^{-6} \, \text{lb/mg} \approx 1.54323 \times 10^{-5} \, \text{lb}
\][/tex]
4. Convert the Volume of the Sample from Liters to Million Gallons:
- The sample volume is 1 liter, which is equivalent to 1000 milliliters (mL).
- Convert this volume to million gallons, knowing that 1 mL = 2.64172 × 10^-7 million gallons:
[tex]\[
\text{Volume in Mgal} = 1000 \, \text{mL} \times 2.64172 \times 10^{-7} \, \text{Mgal/mL} = 0.000264172 \, \text{Mgal}
\][/tex]
5. Calculate the Dose in Pounds per Million Gallons:
- Using the mass in pounds and the volume in million gallons, the dose is:
[tex]\[
\text{Dose in lb/Mgal} = \frac{1.54323 \times 10^{-5} \, \text{lb}}{0.000264172 \, \text{Mgal}} \approx 0.0584 \, \text{lb/Mgal}
\][/tex]
So, the best answer for the polyphosphate dose is approximately 58 lb/Mgal.
1. Understand Concentration and Volume:
- The concentration of the polyphosphate solution is 1 milligram per milliliter (mg/mL).
- Volume of the stock solution added is 7 milliliters (mL).
2. Calculate the Mass of Polyphosphate Added:
- Since the concentration is 1 mg/mL, the mass of polyphosphate in 7 mL is:
[tex]\[
\text{Mass in mg} = 1 \, \text{mg/mL} \times 7 \, \text{mL} = 7 \, \text{mg}
\][/tex]
3. Convert the Mass from Milligrams to Pounds:
- Knowing that 1 mg = 2.20462 × 10^-6 pounds, the mass in pounds is:
[tex]\[
\text{Mass in pounds} = 7 \, \text{mg} \times 2.20462 \times 10^{-6} \, \text{lb/mg} \approx 1.54323 \times 10^{-5} \, \text{lb}
\][/tex]
4. Convert the Volume of the Sample from Liters to Million Gallons:
- The sample volume is 1 liter, which is equivalent to 1000 milliliters (mL).
- Convert this volume to million gallons, knowing that 1 mL = 2.64172 × 10^-7 million gallons:
[tex]\[
\text{Volume in Mgal} = 1000 \, \text{mL} \times 2.64172 \times 10^{-7} \, \text{Mgal/mL} = 0.000264172 \, \text{Mgal}
\][/tex]
5. Calculate the Dose in Pounds per Million Gallons:
- Using the mass in pounds and the volume in million gallons, the dose is:
[tex]\[
\text{Dose in lb/Mgal} = \frac{1.54323 \times 10^{-5} \, \text{lb}}{0.000264172 \, \text{Mgal}} \approx 0.0584 \, \text{lb/Mgal}
\][/tex]
So, the best answer for the polyphosphate dose is approximately 58 lb/Mgal.
