City X imposes a penalty for discharged waste water when a BOD5 value exceeds 300 mg/L. The penalty is calculated at a rate of $0.25/lb of oxygen for the excess portion.
Waste water (a flow rate of 1,000,000 gal/year) from Factory Y has a BOD5 value of 500 mg/L. How much penalty does Factory Y have to pay per year?

To calculate the penalty that Factory Y has to pay per year for the excess BOD5 (Biochemical Oxygen Demand over 5 days) in its wastewater, we'll follow these steps:

### Step 1: Calculate the excess BOD5 concentration
The permissible BOD5 concentration is 300 mg/L. Factory Y has a BOD5 concentration of 500 mg/L. The excess BOD5 concentration is:

\[
\text{Excess BOD5} = 500 \, \text{mg/L} - 300 \, \text{mg/L} = 200 \, \text{mg/L}
\]

### Step 2: Convert the excess BOD5 concentration to pounds of oxygen
First, convert the flow rate from gallons to liters (since BOD5 is measured in mg/L):

\[
1 \, \text{gallon} = 3.78541 \, \text{liters}
\]

\[
1,000,000 \, \text{gallons/year} \times 3.78541 \, \text{liters/gallon} = 3,785,410 \, \text{liters/year}
\]

Now, calculate the total amount of excess BOD5 in milligrams:

\[
\text{Total excess BOD5} = 200 \, \text{mg/L} \times 3,785,410 \, \text{liters/year} = 757,082,000 \, \text{mg/year}
\]

Convert milligrams to pounds (since 1 pound = 453,592.37 mg):

\[
\text{Total excess BOD5 in pounds} = \frac{757,082,000 \, \text{mg/year}}{453,592.37 \, \text{mg/pound}} \approx 1,669 \, \text{pounds/year}
\]

### Step 3: Calculate the penalty
The penalty is $0.25 per pound of excess oxygen:

\[
\text{Penalty} = 1,669 \, \text{pounds/year} \times 0.25 \, \text{\$/pound} = 417.25 \, \text{\$/year}
\]

### Final Answer:
Factory Y has to pay a penalty of **$417.25 per year**.

---

Would you like more details or have any other questions? Here are some related questions to consider:

1. How would the penalty change if the BOD5 value increased to 600 mg/L?
2. What is the significance of BOD5 in wastewater management?
3. How does the penalty change if the flow rate of wastewater increases?
4. What measures can Factory Y take to reduce its BOD5 levels?
5. How does temperature affect the BOD5 value in wastewater?

**Tip:** When dealing with unit conversions, always keep track of the units throughout the calculation to avoid errors.

City X imposes a penalty for discharged waste water when a BOD5 value exceeds 300 mg/L. The penalty is calculated at a rate of $0.25/lb of oxygen for the excess portion. Waste water (a flow rate of 1,000,000 gal/year) from Factory Y has a BOD5 value of 500 mg/L. How much penalty does Factory Y have to pay per year?

Learn how to calculate the penalty for Factory Y's excess BOD5 in wastewater. This problem involves unit conversion, proportional reasoning, and penalty calculation. Suitable for students in Grades 10-12.

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