Worksheet Grade 11 Science

Vardley's Hard Groundwater: Hardness and Alkalinity Worksheet

A grade 11 chemistry worksheet on carbonate hardness and alkalinity, using a fictional town's limestone-aquifer water to compute total hardness and buffering.

Grade: Grade 11
Subject: Science
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

HS-ESS2-5 NGSS

Plan and conduct an investigation of the properties of water and its effects on Earth materials and surface processes.

How this material aligns: Item 6, supported by the hardness calculations in items 1 through 5, connects the water's calcium and magnesium to the dissolving of limestone in the Vardley aquifer, the chemical-weathering and solubility reasoning this standard targets.

All materials for HS-ESS2-5 →

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: Items 1, 2, 3, and 5 carry milligram-per-liter and grains-per-gallon units through a multi-step hardness conversion, the consistent unit reasoning this standard requires.

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 calcium, magnesium, and total hardness from measured ion concentrations.
Students will explain how alkalinity buffers pH and distinguish carbonate from non-carbonate hardness.

Vocabulary

Alkalinity: Alkalinity is water's ability to resist becoming acidic, acting like a buffer that keeps pH from swinging wildly when acids are added. Water with good alkalinity helps protect fish and other aquatic life from sudden pH changes.

Also: hardness, buffering, bicarbonate, carbonate hardness

Teacher overview

The fictional town of Vardley draws its drinking water from a limestone aquifer, so the water arrives at the plant already loaded with dissolved calcium and magnesium. This worksheet has students turn a set of raw laboratory numbers into the values an operator actually reports: calcium hardness, magnesium hardness, total hardness, and how much of that hardness the alkalinity can hold as carbonate. A common student error is treating hardness and alkalinity as the same measurement because both are reported in milligrams per liter as calcium carbonate; the worksheet separates the two ideas directly.

Vardley's Hard Groundwater: Hardness and Alkalinity Worksheet — Grade 11 Science

Name: ____________________________ Date: ______________

Student Worksheet

Use these relationships and the town of Vardley's most recent well sample for every problem.

Calcium hardness (mg/L as CaCO3) = calcium concentration (mg/L) x 2.5
Magnesium hardness (mg/L as CaCO3) = magnesium concentration (mg/L) x 4.1
1 grain per gallon = 17.1 mg/L as CaCO3
Carbonate hardness cannot be larger than the total alkalinity.

Vardley well sample: calcium 72 mg/L, magnesium 24 mg/L, total alkalinity 210 mg/L as CaCO3, pH 7.6.

For this worksheet, classify total hardness using these ranges (mg/L as CaCO3): soft 0 to 60, moderately hard 61 to 120, hard 121 to 180, very hard above 180.

Calculate the calcium hardness of the Vardley sample in mg/L as CaCO3.
Calculate the magnesium hardness of the Vardley sample in mg/L as CaCO3.
Calculate the total hardness by adding your answers to items 1 and 2. Round to the nearest whole number.
Using the ranges above, classify the Vardley water as soft, moderately hard, hard, or very hard.
Convert the total hardness from item 3 into grains per gallon. Round to the nearest tenth.
Explain where the calcium and magnesium in this water came from, using the fact that the aquifer is limestone.
Alkalinity measures how much acid the water can neutralize before its pH drops. Explain in two or three sentences why high alkalinity keeps the plant's finished pH stable when a small amount of acid enters the water.
The pH of the sample is 7.6. In the carbonate system, bicarbonate is the main form of alkalinity between about pH 6.5 and 8.5. State which carbonate species is dominant in this sample and give the reason.
Carbonate hardness equals the total hardness or the alkalinity, whichever is smaller. Calculate the carbonate hardness and the non-carbonate hardness for this sample.
Vardley is considering lime softening to lower the hardness. Explain one benefit and one drawback of softening this water, using your hardness and alkalinity results as support.

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: 180 mg/L as CaCO3.
Calcium hardness = 72 mg/L x 2.5 = 180 mg/L as CaCO3.
Answer: 98.4 mg/L as CaCO3.
Magnesium hardness = 24 mg/L x 4.1 = 98.4 mg/L as CaCO3.
Answer: 278 mg/L as CaCO3.
Total hardness = 180 + 98.4 = 278.4, which rounds to 278 mg/L as CaCO3.
Answer: very hard.
278 mg/L as CaCO3 is above 180, the top of the ranges given, so the water is very hard.
Answer: 16.3 grains per gallon.
278.4 mg/L as CaCO3 divided by 17.1 mg/L per grain = 16.28, which rounds to 16.3 grains per gallon.
Answer: dissolved limestone.
As slightly acidic rainwater and soil water move through the limestone aquifer, they dissolve calcium carbonate and dolomite from the rock. The released calcium and magnesium ions travel with the groundwater, which is why a limestone aquifer produces hard water.
Answer: alkalinity resists pH change.
Alkalinity comes mostly from bicarbonate and carbonate ions, which react with and neutralize added acid. Because the Vardley water carries 210 mg/L as CaCO3 of this acid-neutralizing capacity, a small acid input is consumed by those ions instead of lowering the pH, so the finished pH stays near its starting value.
Answer: bicarbonate.
At pH 7.6, which sits inside the roughly 6.5 to 8.5 range, bicarbonate is the dominant carbonate species. Carbonate becomes important only at higher pH, and dissolved carbon dioxide dominates at lower pH, so this near-neutral sample is mostly bicarbonate.
Answer: 210 mg/L as CaCO3 carbonate, 68 mg/L as CaCO3 non-carbonate.
Carbonate hardness is the smaller of total hardness (278) and alkalinity (210), so carbonate hardness = 210 mg/L as CaCO3. Non-carbonate hardness = 278 - 210 = 68 mg/L as CaCO3.
Answer: softening lowers hardness but adds cost and sludge.
A benefit is that lime softening would cut the very high 278 mg/L as CaCO3 hardness, reducing scale in pipes and water heaters. A drawback is that softening this high-alkalinity water requires large chemical doses and produces a large volume of lime sludge that must be handled, which adds cost. Accept any answer that uses the student's own hardness and alkalinity numbers as support.

Differentiation

Support

Provide the two hardness conversion equations already set up with the sample numbers substituted (72 x 2.5 and 24 x 4.1) so students focus on the arithmetic and the interpretation. Give a labeled number line showing the four hardness ranges for item 4.

Extension

Ask students to calculate how many milligrams per liter of hardness lime softening would need to remove to bring the town of Vardley's water down to a moderately hard target of 120 mg/L as CaCO3, and to explain why the non-carbonate portion is harder to remove than the carbonate portion.

ELL supports

Pre-teach the terms hardness, alkalinity, buffering, and bicarbonate with a simple diagram showing acid being neutralized by bicarbonate ions. Allow items 6, 7, 8, and 10 to be answered with a labeled sketch plus a short phrase rather than full paragraphs.