Hardness of water is expressed in terms of calcium carbonate equivalent by converting the concentrations of all hardness-causing multivalent metal ions into an equivalent concentration of calcium carbonate (CaCO3), typically reported in parts per million (ppm).
Understanding Water Hardness and Calcium Carbonate Equivalent
Water hardness is primarily caused by the presence of dissolved multivalent metal cations, such as calcium (Ca2+), magnesium (Mg2+), iron (Fe2+), and aluminum (Al3+). To provide a standardized and easily comparable measure of water hardness, these various ions are converted and expressed as if they were all calcium carbonate.
Why Calcium Carbonate (CaCO3)?
The use of calcium carbonate as the reference standard is widespread due to several practical advantages:
- Simplified Calculations: The molecular weight of
CaCO3is approximately 100 g/mol. This convenient integer simplifies calculations significantly when converting concentrations of other hardness-causing ions. - Universal Standard: It provides a consistent benchmark for comparing water hardness levels across different sources, regardless of the specific ions responsible for the hardness.
- Common Precipitant: Calcium carbonate is a common constituent of scale deposits found in pipes and appliances, making it a highly relevant reference for practical applications related to hard water issues.
How to Calculate Hardness as CaCO3 Equivalent
To express water hardness in terms of CaCO3 equivalent, the concentration of each hardness-causing ion is multiplied by a specific conversion factor. This factor relates the chemical equivalent weight of CaCO3 to the equivalent weight of the specific ion.
The general formula for converting the concentration of an ion to its CaCO3 equivalent is:
$$ \text{Hardness as } \text{CaCO}_3 \text{ (mg/L)} = \text{Concentration of ion (mg/L)} \times \left( \frac{\text{Equivalent Weight of } \text{CaCO}_3}{\text{Equivalent Weight of ion}} \right) $$
Where:
- The molecular weight of
CaCO3is approximately 100 g/mol, and its valency is 2, so its equivalent weight is 100/2 = 50 g/equivalent. - The equivalent weight of an ion is its molecular weight divided by its valency.
Let's break down the process with common examples:
- Identify and Measure Ion Concentrations: Determine the concentration of each major hardness-causing ion (e.g.,
Ca2+,Mg2+) in milligrams per liter (mg/L). - Calculate Individual
CaCO3Equivalents: Apply the conversion factor for each ion:- For Calcium (
Ca2+):- Molecular Weight of
Ca2+= 40 g/mol - Valency of
Ca2+= 2 - Equivalent Weight of
Ca2+= 40/2 = 20 g/equivalent - Conversion Factor = 50 (EW of
CaCO3) / 20 (EW ofCa2+) = 2.5 Hardness as CaCO3 from Ca2+ = [Ca2+] (mg/L) × 2.5
- Molecular Weight of
- For Magnesium (
Mg2+):- Molecular Weight of
Mg2+= 24.3 g/mol - Valency of
Mg2+= 2 - Equivalent Weight of
Mg2+= 24.3/2 = 12.15 g/equivalent - Conversion Factor = 50 (EW of
CaCO3) / 12.15 (EW ofMg2+) ≈ 4.115 Hardness as CaCO3 from Mg2+ = [Mg2+] (mg/L) × 4.115
- Molecular Weight of
- For Calcium (
- Sum for Total Hardness: Add the
CaCO3equivalent values from all contributing ions to get the total hardness of the water sample.
Conversion Factors for Common Hardness-Causing Ions
The table below summarizes the molecular weights, equivalent weights, and conversion factors for common ions to CaCO3 equivalent:
| Ion | Molecular Weight (g/mol) | Valency | Equivalent Weight (g/eq) | Conversion Factor to CaCO3 (50/EW) |
|---|---|---|---|---|
CaCO3 (Reference) |
100 | 2 | 50 | 1 |
Ca2+ |
40 | 2 | 20 | 2.5 |
Mg2+ |
24.3 | 2 | 12.15 | ≈ 4.115 |
Fe2+ |
55.8 | 2 | 27.9 | ≈ 1.79 |
Al3+ |
27 | 3 | 9 | ≈ 5.56 |
Units of Expression
The hardness of water is most commonly expressed in:
- Parts per million (ppm): This unit signifies milligrams of
CaCO3per liter of water (mg/L). For dilute aqueous solutions,1 ppmis practically equivalent to1 mg/L. - Grains per gallon (gpg): Another common unit, especially in North America, where 1 gpg of
CaCO3is equivalent to approximately 17.1 mg/L or ppm.
Practical Insights
Understanding water hardness in terms of CaCO3 equivalent helps in:
- Categorizing Water: Water is often categorized as soft, moderately hard, hard, or very hard based on its
CaCO3equivalent concentration.- Soft: < 60 mg/L (ppm)
CaCO3 - Moderately Hard: 60-120 mg/L (ppm)
CaCO3 - Hard: 120-180 mg/L (ppm)
CaCO3 - Very Hard: > 180 mg/L (ppm)
CaCO3
- Soft: < 60 mg/L (ppm)
- Water Treatment: It guides the selection and sizing of water softening systems, which typically remove
Ca2+andMg2+ions. - Industrial Applications: It's critical for industries to prevent scaling in boilers, cooling towers, and piping systems.
By expressing water hardness as calcium carbonate equivalent, a universal and easily manageable metric is established, allowing for effective assessment and management of water quality.
