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Worksheet Grade 10 Math

Nettlebrook Reservoir: Chlorine Dosing and pH Compliance Worksheet

A grade 10 worksheet on chlorine dosing with the pounds formula and pH compliance checks against real EPA drinking-water standards for a fictional treatment plant.

Objectives

  1. Students will use the pounds formula to calculate pounds of chlorine needed per day from a dosage and a flow rate.
  2. Students will calculate chlorine demand from dosage and residual readings.
  3. Students will compare pH and chlorine readings against real EPA drinking-water standards.

Vocabulary

Key words: chlorine demand, residual, pounds formula, MRDL, secondary standard

Teacher overview

Nettlebrook Reservoir Water Treatment Plant (a fictional facility used for this worksheet) disinfects its water with chlorine and monitors pH before the water leaves the plant. Operators use the pounds formula, Loading (lbs/day) = Concentration (mg/L) × Flow (MGD) × 8.34, to calculate how much chlorine to feed each day, and they compare their readings against two real EPA standards: the maximum residual disinfectant level (MRDL) for chlorine and the secondary standard for pH. A common misconception is assuming a higher dosage is always safer; operators instead aim for the lowest dosage that still disinfects effectively, since chlorine byproducts increase as dosage rises.

Nettlebrook Reservoir: Chlorine Dosing and pH Compliance Worksheet — Grade 10 Math
Name: ____________________________ Date: ______________

Student Worksheet

Nettlebrook Reservoir (a fictional facility used for this worksheet) treats water at a flow of 1.8 MGD with a chlorine dosage of 2.5 mg/L. A downstream sample shows a residual of 1.1 mg/L. The MRDL for chlorine is 4.0 mg/L, and the secondary standard for pH is 6.5 to 8.5.

  1. Using the pounds formula, calculate how many pounds of chlorine the plant needs per day at its current flow and dosage.
  2. Calculate the chlorine demand, defined as dosage minus residual.
  3. Compare the measured residual (1.1 mg/L) to the MRDL of 4.0 mg/L. By how many mg/L is the residual under the MRDL?
  4. A pH reading in the treated water leaving the plant is 7.8. Is this within the 6.5-8.5 secondary standard? By how much could the pH rise before exceeding the upper limit?
  5. A second sample shows a pH of 8.9. Is this within the secondary standard? In one sentence, explain why exceeding this range matters even though it is an aesthetic, not a health-based, standard.
  6. The plant's flow increases to 2.4 MGD, with the dosage held at 2.5 mg/L. Recalculate the pounds of chlorine needed per day.
  7. How many more pounds of chlorine per day does the plant need at the higher flow (item 6) compared to its original flow (item 1)?
  8. In one or two sentences, explain why a plant might deliberately keep its chlorine residual well below the 4.0 mg/L MRDL rather than letting it run close to the limit.
  9. Chlorine costs a hypothetical $1.35 per pound. What is the plant's daily chemical cost at its original flow and dosage (item 1's pounds per day)?
  10. Using your answers to items 1 and 6, explain in one sentence how flow rate affects the pounds of chlorine required each day, referencing the pounds formula directly.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: 37.5 lb/day.
    2.5 mg/L × 1.8 MGD × 8.34 = 37.53, which rounds to 37.5 lb/day.

  2. Answer: 1.4 mg/L.
    2.5 mg/L − 1.1 mg/L = 1.4 mg/L.

  3. Answer: 2.9 mg/L.
    4.0 mg/L − 1.1 mg/L = 2.9 mg/L under the MRDL.

  4. Answer: 0.7.
    8.5 − 7.8 = 0.7. The pH is within the standard, with 0.7 of room before reaching the upper limit of 8.5.

  5. Answer: No, it is not within the standard.
    8.9 exceeds the 8.5 upper limit by 0.4. Even though pH is an aesthetic standard, water above 8.5 can taste like soda, feel slippery, and leave scale deposits in pipes and fixtures, and chlorine disinfects less effectively at high pH.

  6. Answer: 50.0 lb/day.
    2.5 mg/L × 2.4 MGD × 8.34 = 50.04, which rounds to 50.0 lb/day.

  7. Answer: 12.5 lb/day.
    50.04 − 37.53 = 12.51, which rounds to about 12.5 more pounds per day.

  8. Answer: A residual near 4.0 mg/L leaves little margin for error.
    Flow and demand change during the day, so if demand drops, the residual can rise past the MRDL; a lower target residual protects against that.

  9. Answer: $50.67.
    37.53 lb/day × $1.35/lb = $50.6655, which rounds to $50.67 per day.

  10. Answer: More flow requires more chlorine at the same dosage.
    Comparing items 1 and 6 shows that raising flow from 1.8 to 2.4 MGD, with dosage unchanged, raised the daily chlorine requirement from 37.5 to 50.0 pounds, because the pounds formula multiplies dosage directly by flow.

Differentiation

Support (below grade level)

Provide the pounds formula and the chlorine demand formula as a printed reference card, and work item 1 together as a class, showing each factor (dosage, flow, and the constant 8.34) labeled before students continue independently.

Extension (above grade level)

Ask students to find the maximum dosage, in mg/L, that the fictional Nettlebrook Reservoir could use at its original 1.8 MGD flow that keeps the residual at least 1.0 mg/L under the 4.0 mg/L MRDL, assuming demand stays at 1.4 mg/L, and to check their answer using the pounds formula.

ELL supports

Pre-teach "dosage," "residual," and "demand" with a simple diagram showing chlorine added at the plant (dosage), some of it reacting with the water (demand), and the amount left over when it reaches a customer (residual). Provide the pounds formula in both symbol form and a plain-language sentence form.

Extensions

Have students look up a real municipal water quality report from their own community's water utility (most utilities publish one online each year) and compare its reported chlorine residual and pH values to the ranges used in this worksheet, discussing any values that fall outside the ranges shown here.