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Worksheet Grade 8 Science

Sabino Mesa's Reverse Osmosis Plant: Modeling Salt Removal

A grade 8 science worksheet where students model how a reverse osmosis membrane separates water from dissolved salt and calculate salt rejection.

Objectives

  1. Students will model why a reverse osmosis membrane passes water molecules but holds back dissolved salt ions.
  2. Students will calculate salt rejection and recovery percentages from feed and permeate concentrations.
  3. Students will write dissolved-solids concentrations in scientific notation and compare their magnitudes.

Vocabulary

Reverse osmosis
Reverse osmosis cleans water by pushing it through a membrane with holes so tiny that salt and most other dissolved things cannot fit through. It can even turn seawater into fresh water.
Total dissolved solids (TDS)
Total dissolved solids is a measure of everything dissolved in water that you cannot see or filter out, like minerals and salts. Water with very high TDS can taste salty or bitter, even though it might look perfectly clear.

Also: membrane, permeate, salt rejection

Teacher overview

The fictional desert town of Sabino Mesa has no nearby river or lake, so it draws salty groundwater and treats it with reverse osmosis. In reverse osmosis, a pump pushes water against a thin membrane that lets water molecules slip through while holding back most of the dissolved salt. This worksheet has students model that separation at the particle level and then use the plant's numbers to calculate how much salt the membrane removes. A common misconception is that a membrane strains out salt the way a coffee filter strains grounds; in reverse osmosis the openings are so small that size and charge decide which particles pass, not a visible mesh.

Sabino Mesa's Reverse Osmosis Plant: Modeling Salt Removal — Grade 8 Science
Name: ____________________________ Date: ______________

Student Worksheet

Use the following information about the fictional town of Sabino Mesa for every item.

Sabino Mesa's reverse osmosis (RO) plant draws brackish groundwater with a total dissolved solids (TDS) level of 3,000 mg/L. Most of those dissolved solids are sodium ions and chloride ions from salt. The pump forces this feed water against the RO membrane. Water molecules pass through and become treated water, called permeate, with a TDS of 90 mg/L. For every 100 gallons of feed water, the plant recovers 45 gallons of permeate; the other 55 gallons leave the membrane as concentrate, a salty stream that carries away the rejected solids. In fresh water and mildly salty water like this feed, 1 mg/L is about equal to 1 part per million (ppm). In much saltier water, such as seawater, above about 7,000 mg/L, the two units differ enough that a correction is needed.

  1. A water molecule is written H2O. How many hydrogen atoms and how many oxygen atoms does one water molecule contain?
  2. The membrane lets water molecules through but blocks dissolved sodium and chloride ions. Using the idea of particle size, explain in one or two sentences why the salt ions are held back while the smaller water molecules pass.
  3. Salt rejection is found with this formula: rejection (%) = (feed TDS − permeate TDS) ÷ feed TDS × 100. Using the feed TDS of 3,000 mg/L and the permeate TDS of 90 mg/L, calculate the salt rejection percentage.
  4. How many mg/L of dissolved solids did the membrane remove from each liter of feed water?
  5. Write the feed TDS of 3,000 mg/L in scientific notation.
  6. Write the permeate TDS of 90 mg/L in scientific notation.
  7. Using your two scientific-notation answers, about how many times more dissolved solids are in the feed water than in the permeate?
  8. For every 100 gallons of feed water, the plant recovers 45 gallons of permeate. What percent of the feed water becomes treated permeate? (This percentage is called the recovery.)
  9. Of every 100 gallons of feed water, how many gallons leave as concentrate, and what happens to the salt that the membrane removed?
  10. The permeate has a TDS of 90 mg/L. Because 1 mg/L is about equal to 1 ppm in fresh water, write the permeate concentration in parts per million.
  11. Sabino Mesa's operators check the permeate TDS every shift. Explain what a sudden rise in permeate TDS might tell them about the condition of the membrane.

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: Two hydrogen atoms and one oxygen atom.
    The formula H2O shows two hydrogen atoms bonded to one oxygen atom in each water molecule.
  2. Answer: The salt ions are larger and charged, so the membrane blocks them.
    Dissolved sodium and chloride ions, along with the water shells around them, are wider than the tiny gaps that water molecules fit through, so they cannot pass while water molecules can.
  3. Answer: 97%.
    Rejection = (3,000 − 90) ÷ 3,000 × 100 = 2,910 ÷ 3,000 × 100 = 0.97 × 100 = 97 percent.
  4. Answer: 2,910 mg/L.
    The membrane lowered the TDS from 3,000 mg/L to 90 mg/L, a removal of 3,000 − 90 = 2,910 mg/L.
  5. Answer: 3 × 10^3 mg/L.
    3,000 = 3 × 1,000 = 3 × 10^3.
  6. Answer: 9 × 10^1 mg/L.
    90 = 9 × 10 = 9 × 10^1.
  7. Answer: About 33 times.
    Divide the two values: (3 × 10^3) ÷ (9 × 10^1) = 3,000 ÷ 90 ≈ 33.3, so the feed water holds roughly 33 times as much dissolved solids as the permeate.
  8. Answer: 45%.
    Recovery = 45 gallons of permeate ÷ 100 gallons of feed × 100 = 45 percent.
  9. Answer: 55 gallons.
    Since 45 of every 100 gallons become permeate, 100 − 45 = 55 gallons leave as concentrate, and the removed salt leaves with that concentrate stream.
  10. Answer: 90 ppm.
    Because 1 mg/L is about equal to 1 ppm in fresh water, a permeate TDS of 90 mg/L is about 90 ppm.
  11. Answer: The membrane may be torn, worn, or fouled.
    A sudden jump in permeate TDS means more salt is getting through than usual, which signals that the membrane has developed a leak or damage and needs inspection or replacement.

Differentiation

Support (below grade level)

Provide a labeled diagram showing feed water, the membrane, permeate, and concentrate as four separate arrows, and work through the salt-rejection formula once with a different example: suppose a feed of 2,000 mg/L and a permeate of 100 mg/L before students try items 3 and 4 on their own. Allow a calculator for every step.

Extension (above grade level)

Ask students to find what the permeate TDS would be if the membrane's salt rejection dropped from 97 percent to 90 percent while the feed stayed at 3,000 mg/L, and to explain whether that treated water still improved on the feed.

ELL supports

Pre-teach "membrane," "dissolved," "permeate," and "concentrate" with a simple picture card for each term next to a short definition. Allow students to answer items 1, 2, and 11 with a labeled sketch or short phrases instead of full sentences.

Extensions

Have students calculate, using only the numbers on this worksheet, how many gallons of concentrate Sabino Mesa produces for every 45 gallons of drinking water it delivers, then discuss where a desert town might safely send that salty concentrate stream.