Test
Calcium and Water Hardness
13
INTRODUCTION
Calcium, Ca2+
Calcium, in the form of the Ca2+ ion, is one of the major inorganic cations, or positive ions, in
saltwater and freshwater. It can originate from the dissociation of salts, such as calcium chloride
or calcium sulfate, in water.
CaCl2(s) 
→ Ca2+(aq) + 2 ClÐ(aq)
→ Ca2+(aq) + SO42Ð(aq)
CaSO4(s) 
Most calcium in surface water comes from streams
flowing over limestone, CaCO3, gypsum, CaSO4¥2H2O,
and other calcium-containing rocks and minerals.
Groundwater and underground aquifers leach even higher
concentrations of calcium ions from rocks and soil.
Calcium carbonate is relatively insoluble in water, but
dissolves more readily in water containing significant
levels of dissolved carbon dioxide.1
Sources of Calcium Ions
• Limestone: CaCO3
• Dolomite:
CaCO3ÐMgCO3
• Gypsum:
CaSO4¥2H2O
The concentration of calcium ions (Ca2+) in freshwater is found in a range of 0 to 100 mg/L, and
usually has the highest concentration of any freshwater cation. A level of 50 mg/L is
recommended as the upper limit for drinking water. High levels are not considered a health
concern; however, levels above 50 mg/L can be problematic due to formation of excess calcium
carbonate deposits in plumbing or in decreased cleansing action of soaps. If the calcium-ion
concentration in freshwater drops below 5 mg/L, it can support only sparse plant and animal life,
a condition known as oligotrophic. Typical seawater contains Ca2+ levels of about 400 mg/L.
Calcium Hardness as CaCO3
When water passes through or over mineral deposits such as limestone, the levels of Ca2+, Mg2+ ,
and HCO3Ð ions present in the water greatly increase and
Calcium Hardness as CaCO3
cause the water to be classified as hard water. This term
(mg/L)
results from the fact that calcium or magnesium ions in
water combine with soap molecules, forming a sticky
• Soft:
0-20
scum that interferes with soap action and makes it ÒhardÓ
• Moderately soft:
20-40
to get suds. One of the most obvious signs of water
hardness is a layer of white film left on the surface of
• Moderately hard:
40-80
showers. Since most hard-water ions originate from
• Hard:
80-120
calcium carbonate, levels of water hardness are often
referred to in terms of hardness as CaCO3. For example,
• Very hard:
> 120
if a water sample is found to have a Ca2+ concentration of
30 mg/L, then its calcium hardness as CaCO3 can be calculated using the formula2
(30 mg/L Ca2+) 5 (100 g CaCO3 / 40 g Ca2+) = 75 mg/L calcium hardness as CaCO3
1
2
? ♦ Ca 2+ (aq) + 2HCO3–(aq).
The reaction occurring with limestone is: CaCO3(s) + CO2(aq) + H2O(l) ℜ
This formula takes into account that the molar mass of Ca is 40 g/mol, and of CaCO3 is 100 g/mol.
Water Quality with Computers
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Ca2+
Test 13
Note that 30 mg/L Ca2+ and 75 mg/L calcium hardness as CaCO3 are equivalentÑthey are
simply two different ways of expressing calcium levels. The value of calcium hardness as CaCO 3
can always be obtained by multiplying the Ca2+ concentration by a factor of 100/40, orÊ2.5.
Another common measurement of water hardness is known as total hardness as CaCO3. This
measurement takes into account both Ca2+ and Mg2+ ions. On average, magnesium hardness
represents about 1/3 of total hardness and calcium hardness about 2/3. If you are comparing your
own test results of calcium hardness as CaCO 3 with results in publications that use units of total
hardness as CaCO3, you can estimate total hardness by multiplying the calcium hardness
by 1.5. See Test 14, Total Water Hardness, for further information about this topic.
Expected Levels
The concentration of calcium ions (Ca2+) in freshwater is found in a range of 4 to 100 mg/L
(10 Ð250 mg/L of calcium hardness as CaCO3). Seawater contains calcium levels of 400
mg/LÊCa2+ (1000 mg/L of calcium hardness as CaCO3).
Table 1: Calcium, Calcium Hardness, and Total Hardness in Selected Sites
Site (fall season)
Merrimack River, Lowell, NH
Calcium
(mg/L Ca2+)
Ca hardness
Total hardness
(mg/L as CaCO3) (mg/L as CaCO3)
6.3
15.8
20.8
Mississippi River, Memphis, TN
48.0
120.0
178.3
Rio Grande River, El Paso, TX
84.0
210.0
297.5
Ohio River, Grand Chain, OH
24.0
60.0
86.3
6.4
16.0
25.2
Missouri River, Garrison Dam, ND
53.0
132.5
215.8
Sacramento River, Keswick, CA
11.0
27.5
46.3
Hudson River, Poughkeepsie, NY
26.0
65.0
84.6
Platte River, Louisville, NE
72.0
180.0
250.8
Colorado River, Andrade, CA
76.0
190.0
294.2
Willamette River, Portland, OR
Summary of Method
A Vernier Calcium Ion-Selective Electrode (ISE) is used to measure the calcium ion
concentration in the water, in mg/L as Ca 2+ , either on site or after returning to the lab. This value
is then multiplied by a factor of 2.5 to obtain a value for calcium hardness as CaCO3, in mg/L.
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Water Quality with Computers
Ca2+
Calcium and Water Hardness
CALCIUM ION-SELECTIVE ELECTRODE
Materials Checklist
___ laptop computer (Power Mac or Windows)
___ Vernier computer interface, battery-powered
___ Logger Pro
___ Vernier ISE Amplifier
___ Calcium Ion-Selective Electrode
___ Low Standard (10 mg/L Ca2+)
___ High Standard (1000 mg/L Ca2+)
___ wash bottle with distilled water
___ tissues
___ small paper or plastic cup (optional)
Advanced Preparation
The Vernier Calcium Ion-Selective Electrode (ISE) must be soaked in the
Calcium High Standard solution (included with the ISE) for approximately 30
minutes. Important: Make sure the ISE is not resting on the bottom, and that the
small white reference contacts are immersed. Make sure no air bubbles are
trapped below the ISE.
If the ISE needs to be transported to the field during the soaking process, use the
ISE soaking bottle included with the ISE. Remove the cap from the ISE soaking
bottle and fill the bottle 3/4 full with High Standard. Slide the cap onto the
electrode, insert it into the bottle, and tighten. Important: Do not leave the ISE
soaking for more than 24Êhours. Long-term storage should be in a dry
environment.
ISE soaking
for travel
Collection and Storage of Samples
1. This test can be conducted on site or in the lab. A 100-mL water sample is required.
2. It is important to obtain the water sample from below the surface of the water and as far away
from shore as is safe. If suitable areas of the stream appear to be unreachable, samplers
consisting of a rod and container can be constructed for collection. Refer to page Intro-4 of
the Introduction of this book for more details.
Testing Procedure
1. Position the computer safely away from the water. Keep water away from the computer at all
times.
2. Prepare the computer for data collection by opening ÒTest 13 Calcium and HardnessÓ from
the Water Quality with Computers experiment files of Logger Pro. On the Graph window, the
vertical axis has calcium concentration scaled from 0 to 100 mg/L Ca2+. The horizontal axis
has time scaled from 0 to 10 seconds. There is also a Meter window which displays live
calcium concentration readings.
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Ca2+
Test 13
3. Prepare the Calcium Ion-Selective Electrode (ISE) for data collection.
a. The ISE should be soaking in the High Standard. Make sure that it is not resting on the
bottom of the container, and that the small white reference contacts are immersed.
b. Plug the ISE Amplifier into the Port 1 or Channel 1 of the Vernier computer interface.
Connect the Calcium ISE to the ISE Amplifier.
4. You are now ready to prepare the computer and Calcium ISE for calibration.
First Calibration Point
a. Choose Calibrate from the Experiment menu and then click
b. Type Ò1000Ó (the concentration in mg/LÊCa2+ ) in the edit box.
c. When the displayed voltage reading for Input 1 stabilizes, click
.
Keep
.
Second Calibration Point
d. Rinse the ISE thoroughly with distilled water and gently blot it dry with a tissue. Be very
gentle when blotting the membrane. Important: Failure to carefully rinse and dry the ISE
will contaminate the standard.
e. Place the tip of the ISE into the Low Standard (10 mg/L Ca2+). Be sure that the ISE is not
resting on the bottom of the bottle and that the small white reference contacts are
immersed. Make sure no air bubbles are trapped below the ISE.
f. After briefly swirling the solution, hold the ISE still and wait approximately 30 seconds
for the voltage reading displayed on the computer screen to stabilize.
g. Enter Ò10Ó (the concentration in mg/LÊCa2+ ) in the edit box.
h. When the displayed voltage reading for Input 1 stabilizes, click Keep , then click OK .
5. You are now ready to collect calcium concentration data.
a. Rinse the ISE with distilled water and gently blot it dry.
b. Place the tip of the probe into the stream at Site 1, or into a cup with sample water from
the stream. Make sure the ISE is not resting on the bottom and that the small white
reference contacts are immersed. Make sure that no air bubbles are trapped below the ISE.
c. After briefly swirling the solution, hold the ISE still and wait approximately 30 seconds.
d. If the calcium concentration value appears stable, simply record it on the Data &
Calculations sheet and proceed to Step 7.
6. If the calcium concentration value displayed in the Meter window is fluctuating, determine
the mean (or average) value. To do this:
a. Click Collect to begin a 10-second sampling run. Important: Leave the probe tip
submerged for the 10 seconds that data is being collected.
b. Click on the Statistics button,Ê , to display the statistics box on the graph.
c. Record the mean calcium concentration value on the Data & Calculations sheet.
7. Return to Step 5 to obtain a second reading.
8. Convert the calcium concentration (mg/L Ca2+ ) to units of calcium hardness (mg/L as
CaCO3). The calculation takes into account the difference in the molar masses of calcium
(40Êg/mol Ca2+) and calcium carbonate (100 g/mol CaCO3). To convert to units of calcium
hardness, perform the following calculation:
calcium hardness as CaCO3 = (mg/L Ca2+ ) 5 (100 g CaCO3 / 40 g Ca2+)
= (mg/L Ca2+ ) 5 2.5
Record this value on the Data & Calculations sheet (round to the nearest 0.01 mg/L).
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Water Quality with Computers
Ca2+
Calcium and Water Hardness
DATA & CALCULATIONS
Calcium and Calcium Hardness
Stream or lake: ___________________________
Time of day: __________________________
Site name: ______________________________
Student name: ________________________
Site number: ____________________________
Student name: ________________________
Date: __________________________________
Student name: ________________________
Reading
A
B
Calcium
(mg/L Ca2+)
Calcium hardness
(mg/L CaCO3)
1
2
Average
Column Procedure:
A. Record the calcium concentration (mg/L Ca2+) from the computer.
B. Multiply calcium concentration (mg/L Ca2+) by 2.5 to obtain calcium hardness (as CaCO3).
Field Observations (e.g., weather, geography, vegetation along stream) _________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Test Completed: ________________ Date: ______
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Ca2+
Test 13
ADDITIONAL INFORMATION
Tips for Instructors
1. The range of the Calcium Ion-Selective Electrode is 0.20 to 40,000 mg/L Ca2+. As stated in
the introduction, most values you measure from streams and lakes will be in the range of 4 to
100 mg/LÑthe lower end of the useful range of the sensor. Calcium hardness is found in the
range of 10 to 250 mg/L as CaCO3.
2. Two standard solutions are included with the Calcium ISEÑa High Standard that is
1000Êmg/L, and a Low Standard that is 10 mg/L.3 You can replace the standards using these
directions:
High Standard (1000 mg/L Ca2+)
a. Add 2.771 g of CaCl2 (or 3.669 g of CaCl2¥2H2O) to enough distilled water to prepare
oneÊliter of solution.
Low Standard (10 mg/L Ca2+)
b. Dilute the High Standard from 1000 mg/L to 100 mg/L by combining 100 mL of the High
Standard with 900 mL of distilled water. Mix well.
c. Combine 100 mL of the 100-mg/L solution with 900 mL of distilled water. Mix well. This
standard is now 10 mg/L Ca2+ .
3. The Calcium ISE can be used in a wide range of pH values, pH 3 to 10. The ions that are
known to interfere with the Calcium ISE (Pb2+ , Hg2+ , Sr2+ , Cu2+ , Ni2+ ) will not generally be
encountered in significant concentrations in freshwater samples.
4. Even better results can be obtained if you bring all samples to the same ionic strength. This is
especially important when working with very low concentrations of ions. This can be
accomplished by the addition of ionic strength adjuster, ISA. Add Calcium ISA in the ratio of
approximately 1 to 50; for example, if your water sample is 50 mL in volume, add about
1ÊmL of ISA.
A bottle of Calcium ISA solution was provided with Calcium Ion-Selective Electrodes prior
to 1999. To prepare 100 mL of Calcium ISA solution, 1.0 M KCl, add 7.46 g of solid
potassium chloride, KCl, to enough water to prepare 100 mL of solution.
5. Soaking your ISE prior to use is very important. The Advanced Preparation section
recommends approximately 30 minutes of soaking in the High Standard solution. This is
usually sufficient, but an hour-long soak is even better. If you are going out into the field,
you can Òsoak as you goÓ using the ISE Soaking Bottle. We began shipping ISE Soaking
Bottles with Vernier Ion-Selective Electrodes in January of 1999. If you purchased your ISEs
prior to this and would like to use ISE Soaking Bottles, they can be purchased from Vernier
Software (BTL-ISE, $10 per package of 5 bottles). Important: Do not let the ISE soak
longer than 24 hours. ISEs are designed to be stored dry.
6. The Calcium ISE has a PVC membrane with a limited life expectancy. It is warranted to be
free from defects for a period of twelve (12) months from the date of purchase; it is possible,
however, that you may get somewhat longer use than the warranty period. If you start to
3
Prior to 1999, the Low Standard Solution shipped with each Calcium ISE was 100 mg/L Ca2+ . This
standard can
be diluted to 10 mg/L by carefully measuring out 10 mL of the 100 mg/L standard, and adding enough distilled
water (~90 mL) to make 100 mL of 10 mg/L standard.
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Water Quality with Computers
Calcium and Water Hardness
Ca2+
notice a reduced response (e.g., distinctly different voltages or voltage ranges during
calibration), it is probably time to replace the membrane module. Important: Do not order
membrane modules far in advance of the time you will be using them; the process of
degradation takes place even when they are stored dry on the shelf.
How the Calcium Ion-Selective Electrode Works
The Calcium Ion-Selective Electrode is a membrane-based electrode that measures calcium ions
in an aqueous solution. The membrane is a porous plastic disk, permeable to the ion exchanger,
but impermeable to water. When the membrane of the ISE is in contact with a solution
containing the calcium ion, a voltage, dependent on the level of calcium in the solution, develops
at the membrane. Logger Pro reads the voltage and calculates the ion concentration.
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