Worksheet Grade 10 Science

Braemar Wells GAC Treatment for PFAS: Carbon Bed Breakthrough

A grade 10 science worksheet on PFAS removal, carbon contact time, and breakthrough for a fictional district's activated-carbon vessels, with a treatment trade-off.

Grade: Grade 10
Subject: Science
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: None

Standards

HS-ETS1-3 NGSS

Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.

How this material aligns: Items 7 and 8 have students weigh granular activated carbon against ion exchange on prioritized criteria of upfront cost, operating simplicity, and reuse, the trade-off evaluation this standard requires.

All materials for HS-ETS1-3 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Students carry parts per trillion, gallons per minute, and cubic feet through the removal-efficiency, empty-bed-contact-time, and blending calculations in items 1, 5, 6, and 9.

All materials for HSN-Q.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate PFAS removal efficiency and compare an effluent to the federal limit.
Students will calculate empty-bed contact time and explain how flow affects PFAS removal.
Students will weigh granular activated carbon against ion exchange using prioritized criteria.

Vocabulary

PFAS: A large family of human-made chemicals used in things like nonstick pans, waterproof fabric, and firefighting foam. They are called forever chemicals because they take a very long time to break down.
Granular activated carbon: Small black grains of specially treated carbon that grab contaminants as water flows through them. Utilities use big tanks of it to remove PFAS, bad tastes, and odors.

Also: empty-bed contact time, breakthrough, removal efficiency

Teacher overview

PFAS are a family of long-lasting synthetic chemicals now regulated in drinking water, with a federal limit of 4.0 parts per trillion (ppt) for PFOA and for PFOS. Water systems must meet those limits by 2029, and in May 2026 EPA proposed letting eligible systems apply for more time, to 2031. One common way to remove them is to pass the water through vessels of granular activated carbon (GAC), which hold the chemicals on the carbon surface until the carbon is used up and must be replaced. This worksheet uses the fictional Braemar Water District to practice the removal, contact-time, and blending math, and to weigh GAC against another option. Every district value here is invented for this scenario; the 4.0 ppt limit is the real federal value.

Braemar Wells GAC Treatment for PFAS: Carbon Bed Breakthrough — Grade 10 Science

Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional Braemar Water District found PFAS in two wells and installed GAC vessels. Use these scenario values. Removal efficiency (%) = (influent - effluent) / influent x 100. Empty-bed contact time (EBCT) = carbon volume in gallons / flow in gallons per minute, and one cubic foot holds 7.48 gallons.

Federal limit for PFOA: 4.0 ppt
Well A raw PFOA: 20 ppt
Each GAC vessel holds 100 cubic feet of carbon
Design flow through a vessel: 50 gpm

When Well A water (20 ppt) leaves fresh GAC at 2 ppt, calculate the removal efficiency as a percentage.
Does the 2 ppt effluent meet the 4.0 ppt federal limit? By how many ppt does it clear the limit?
After several months, the effluent rises to 3.5 ppt. Is the water still within the 4.0 ppt limit, and what is the remaining margin?
Breakthrough is reached when the effluent climbs to the 4.0 ppt limit and the carbon must be replaced. Explain in your own words what breakthrough means for this vessel.
Calculate the empty-bed contact time in minutes for a vessel holding 100 cubic feet of carbon at the design flow of 50 gpm. (First convert the carbon volume to gallons.)
If the flow rises to 75 gpm, calculate the new empty-bed contact time. Then state whether the shorter contact time would tend to remove more or less PFAS.
The district compares GAC to an ion-exchange system. GAC costs less to install and is simpler to operate, but the carbon must be changed out often, while ion exchange costs more up front but runs longer between change-outs. If the district's top priorities are low upfront cost and simple operation, which option fits better, and why?
Spent GAC can be shipped out, reactivated at high temperature, and reused. Explain how that option affects the cost and environmental sides of the comparison in item 7.
Well A is 20 ppt and Well B is 8 ppt. If the district blends the two wells in equal amounts before treatment, calculate the blended influent concentration.
If GAC removes 90% of the PFAS in the blended water from item 9, calculate the effluent concentration and state whether it meets the 4.0 ppt limit.

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

Answer Key

Answer: 90%. Removal efficiency = (20 - 2) / 20 x 100 = 18 / 20 x 100 = 90%.
Answer: Yes, by 2 ppt. The 2 ppt effluent is below the 4.0 ppt limit, a margin of 4.0 - 2.0 = 2 ppt.
Answer: Yes, with 0.5 ppt of margin. The 3.5 ppt effluent is still under the 4.0 ppt limit: 4.0 - 3.5 = 0.5 ppt remaining.
Answer: Breakthrough means the carbon has taken up about all the PFAS it can hold, so the chemicals begin passing through and the effluent climbs to the 4.0 ppt limit. At that point the spent carbon must be replaced to keep the water compliant.
Answer: About 15 minutes. Carbon volume = 100 cu ft x 7.48 gal/cu ft = 748 gallons. EBCT = 748 gal / 50 gpm = 14.96 minutes, which rounds to about 15 minutes.
Answer: About 10 minutes, and it would remove less PFAS. EBCT = 748 gal / 75 gpm = 9.97 minutes, about 10 minutes. A shorter contact time gives the carbon less time to capture PFAS, so removal drops.
Answer: GAC fits better. It has the lower upfront cost and simpler operation the district prioritized, even though the carbon must be replaced more often. Accept ion exchange only if the student reprioritizes the criteria and defends it.
Answer: Reactivating and reusing the carbon lowers the long-run material cost and reduces waste sent to disposal, which improves both the cost and the environmental side of GAC and makes it more competitive with ion exchange over time.
Answer: 14 ppt. Blending equal amounts averages the two: (20 + 8) / 2 = 14 ppt.
Answer: 1.4 ppt, which meets the limit. Removing 90% leaves 10%: 14 ppt x 0.10 = 1.4 ppt, which is below the 4.0 ppt limit.

Differentiation

Support

Work item 1 with the class using the removal-efficiency formula written out and each value labeled, and provide the cubic-foot-to-gallon conversion (7.48) on a reference card so students can focus on the contact-time steps.

Extension

Ask students to estimate how the empty-bed contact time would change if the district added a second vessel in series at the design flow, and to explain why longer total contact usually delays breakthrough.

ELL supports

Pre-teach "removal efficiency," "contact time," and "breakthrough" with a labeled sketch of water entering and leaving a carbon vessel, in English and, where possible, students' home languages. Provide sentence frames for the trade-off items in 7 and 8.