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Worksheet Grade 10 Science

Elderbrook Water Hardness: From Limestone to Lime Softening

A grade 10 chemistry worksheet on water hardness, converting between mg/L and grains per gallon and finding softening removal for a fictional utility.

Objectives

  1. Students will convert water hardness between mg/L as calcium carbonate and grains per gallon.
  2. Students will calculate how much hardness a softening process removes and express it as a percentage.

Vocabulary

Key words: hardness, calcium carbonate, grains per gallon, lime softening, polar solvent

Teacher overview

Elderbrook is a fictional utility whose source water seeps through the Graystone limestone before reaching its wells. Along the way the water dissolves calcium and magnesium, which makes it hard. This worksheet has students measure that hardness in two common units, classify the water, and calculate how much hardness a lime-softening plant removes. A common error to watch for is treating grains per gallon and mg/L as if they were the same number, when one grain per gallon equals about 17.1 mg/L.

Elderbrook Water Hardness: From Limestone to Lime Softening — Grade 10 Science
Name: ____________________________ Date: ______________

Student Worksheet

Elderbrook is a fictional utility, and all values below describe its Graystone source water. Use these given numbers and conversions:

  • Raw (untreated) total hardness: 256 mg/L as calcium carbonate.
  • Of that total, calcium hardness is 180 mg/L as calcium carbonate.
  • Conversion: 1 grain per gallon = 17.1 mg/L as calcium carbonate.
  • Classification (as calcium carbonate): soft is under 60 mg/L, moderately hard is 60 to 120, hard is 120 to 180, and very hard is over 180.
  • After lime softening, the finished water leaves the plant at 85 mg/L as calcium carbonate.
  1. Water is a polar molecule, so its slightly charged ends pull on the ions locked in limestone. Using that idea, explain why water moving through the Graystone limestone becomes hard.
  2. Convert the raw hardness of 256 mg/L to grains per gallon. (Divide the mg/L value by 17.1.)
  3. Use the classification scale to describe the raw water. Is it soft, moderately hard, hard, or very hard?
  4. Magnesium hardness is the total hardness minus the calcium hardness. Calculate Elderbrook's magnesium hardness in mg/L as calcium carbonate.
  5. How much total hardness, in mg/L, does the lime-softening plant remove between the raw water and the finished water?
  6. Express the amount removed in item 5 as a percentage of the raw hardness. Round to the nearest whole percent.
  7. Convert the finished hardness of 85 mg/L to grains per gallon.
  8. A home softener in Elderbrook regenerates after it removes 30,000 grains of hardness. If every gallon of raw water carries 15 grains, how many gallons pass through before the softener must regenerate?
  9. Utilities spend money to soften very hard water rather than sending it straight to customers. Give one practical reason a utility would choose to soften hard water before delivery.

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: Water's polar ends attract the charged calcium and magnesium ions in the limestone and pull them into solution. Because the mineral is slightly soluble, water flowing through Graystone steadily picks up those ions and becomes hard. Carbon dioxide dissolved in the water forms weak carbonic acid, which greatly increases how much limestone the water can dissolve.
  2. Answer: about 15 gpg. 256 mg/L divided by 17.1 mg/L per grain = 14.97, which rounds to about 15 grains per gallon.
  3. Answer: Very hard. At 256 mg/L the water is above the 180 mg/L cutoff, so it falls in the very hard category.
  4. Answer: 76 mg/L. Magnesium hardness = 256 mg/L total minus 180 mg/L calcium = 76 mg/L as calcium carbonate.
  5. Answer: 171 mg/L. Removed hardness = 256 mg/L raw minus 85 mg/L finished = 171 mg/L.
  6. Answer: 67%. 171 divided by 256, times 100 = 66.8 percent, which rounds to 67 percent.
  7. Answer: about 5 gpg. 85 mg/L divided by 17.1 mg/L per grain = 4.97, which rounds to about 5 grains per gallon.
  8. Answer: 2,000 gallons. 30,000 grains divided by 15 grains per gallon = 2,000 gallons before regeneration.
  9. Answer: Accept any sound reason, such as preventing scale that clogs pipes and water heaters, reducing the soap and detergent customers need, or protecting appliances from mineral buildup.

Differentiation

Support

Provide a worked conversion example (a different mid-range hardness value converted to grains per gallon) before students try items 2 and 7, and give the classification scale on a printed reference strip so students can match values without recalling the cutoffs.

Extension

Ask students to calculate the blended hardness if Elderbrook mixed equal volumes of its raw Graystone water with a softer well at 40 mg/L as calcium carbonate, then decide whether that blend alone would reach the 85 mg/L the plant now delivers without any lime softening.

ELL supports

Pair "hardness," "grains per gallon," and "calcium carbonate" with a simple visual of water passing through rock and picking up small mineral particles. Provide the conversion as a labeled arrow rule ("mg/L divided by 17.1 gives grains per gallon") and allow item 1 to be answered with a labeled sketch plus a short phrase.