The total hardness of a water sample, primarily caused by dissolved calcium and magnesium ions, is calculated by converting the concentrations of these ions to an equivalent amount of calcium carbonate (CaCO₃).
Understanding Water Hardness
Water hardness refers to the concentration of dissolved divalent cations in water, mainly calcium (Ca²⁺) and magnesium (Mg²⁺) ions. While other ions like strontium, iron, and manganese can contribute, calcium and magnesium are the most common and significant contributors. Total hardness is typically expressed in milligrams per liter (mg/L) as equivalent calcium carbonate (CaCO₃).
Calculating Total Hardness (mg/L as CaCO₃)
To calculate the total hardness using the concentrations of calcium and magnesium ions, a specific conversion method is used. This method converts the mass concentration of each ion into its equivalent mass concentration of calcium carbonate.
The calculation requires knowing the individual concentrations of calcium ions and magnesium ions in milligrams per liter (mg/L).
Step-by-Step Calculation
Based on the provided reference, the calculation follows these specific steps:
| Step | Action | Calculation |
|---|---|---|
| 1 | Calculate Calcium Contribution | Multiply Ca²⁺ concentration (mg/L) by 2.497 |
| 2 | Calculate Magnesium Contribution | Multiply Mg²⁺ concentration (mg/L) by 4.118 |
| 3 | Calculate Total Hardness | Add the results from Step 1 and Step 2 |
Here are the steps detailed:
- Multiply the calcium ion concentration by 2.497. This converts the mass of calcium ions into the equivalent mass of calcium carbonate.
- Multiply the magnesium ion concentration by 4.118. This converts the mass of magnesium ions into the equivalent mass of calcium carbonate.
- Add the two numbers to obtain the water hardness in mg-CaCO₃/L. The sum represents the total concentration of hardness-causing ions expressed as if they were all calcium carbonate.
Why These Factors (2.497 and 4.118)?
The factors 2.497 and 4.118 are derived from the molecular weights of calcium (Ca), magnesium (Mg), and calcium carbonate (CaCO₃). They are the ratios needed to convert the mass of Ca²⁺ or Mg²⁺ to the equivalent mass of CaCO₃ that contains the same number of divalent charges.
- Molecular weight of CaCO₃ ≈ 100.09 g/mol
- Atomic weight of Ca ≈ 40.08 g/mol
- Atomic weight of Mg ≈ 24.31 g/mol
Factor for Ca: (MW of CaCO₃) / (AW of Ca) = 100.09 / 40.08 ≈ 2.497
Factor for Mg: (MW of CaCO₃) / (AW of Mg) = 100.09 / 24.31 ≈ 4.118
Example Calculation
Let's assume a water sample has:
- Calcium ion concentration: 60 mg/L
- Magnesium ion concentration: 25 mg/L
Using the steps:
- Calcium contribution: 60 mg/L * 2.497 = 149.82 mg-CaCO₃/L
- Magnesium contribution: 25 mg/L * 4.118 = 102.95 mg-CaCO₃/L
- Total Hardness: 149.82 + 102.95 = 252.77 mg-CaCO₃/L
Thus, the total hardness of this water sample is approximately 252.77 mg/L as CaCO₃. This calculated value is commonly used to classify water as soft, moderately hard, hard, or very hard, although classification ranges can vary slightly by standard.
