Manually calculating the Total Dissolved Solids (TDS) of water, assuming you have a detailed water analysis report listing the concentrations of individual ions, involves summing the weights of all dissolved cations and anions.
Understanding the Calculation
TDS represents the total weight of all solids that are dissolved in a given volume of water. These dissolved solids are typically inorganic salts, organic matter, and other dissolved materials. While the standard laboratory method for determining TDS involves evaporating a water sample and weighing the residue, you can estimate TDS manually by summing the concentrations of the ions identified in a water analysis report.
This calculation method relies on the principle that the total mass of dissolved substances is the sum of the masses of its components.
The Manual Calculation Process
To manually calculate TDS using a water analysis report, follow these steps:
- Obtain a Water Analysis Report: Ensure you have a recent water analysis report that lists the concentrations of the major cations and anions present in the water sample, typically reported in milligrams per liter (mg/L) or parts per million (ppm). (Note: 1 mg/L is approximately equal to 1 ppm for dilute aqueous solutions).
- Sum the Cation Concentrations: Identify all the reported cation concentrations in mg/L or ppm. Cations are positively charged ions (e.g., Sodium, Calcium, Magnesium, Potassium).
- Cations (mg/L) = Sum of [Na⁺] + [Ca²⁺] + [Mg²⁺] + [K⁺] + other reported cations...
- Sum the Anion Concentrations: Identify all the reported anion concentrations in mg/L or ppm. Anions are negatively charged ions (e.g., Chloride, Sulfate, Nitrate, Carbonate). According to the reference, this sum includes:
- Anions (mg/L) = [Cl⁻] + [H₂PO₄⁻] + [SO₃²⁻] + [SO₄²⁻] + [CO₃²⁻] + [HCO₃⁻] + [F⁻] + [NO₃⁻] + [NO₂⁻] + [SiO₄⁴⁻] + other reported anions...
- Sum the Total Cations and Anions: Add the total sum of the cation concentrations and the total sum of the anion concentrations. This sum provides an estimated value for the TDS in mg/L or ppm.
- Estimated TDS (mg/L or ppm) = Total Cations (mg/L) + Total Anions (mg/L)
Example Calculation
Let's assume a simplified water analysis report provides the following concentrations:
| Ion | Concentration (mg/L) | Charge | Type |
|---|---|---|---|
| Calcium (Ca²⁺) | 50 | +2 | Cation |
| Magnesium (Mg²⁺) | 20 | +2 | Cation |
| Sodium (Na⁺) | 30 | +1 | Cation |
| Potassium (K⁺) | 5 | +1 | Cation |
| Chloride (Cl⁻) | 40 | -1 | Anion |
| Sulfate (SO₄²⁻) | 70 | -2 | Anion |
| Bicarbonate (HCO₃⁻) | 150 | -1 | Anion |
| Nitrate (NO₃⁻) | 10 | -1 | Anion |
Step 1: Sum Cations
Total Cations = [Ca²⁺] + [Mg²⁺] + [Na⁺] + [K⁺]
Total Cations = 50 mg/L + 20 mg/L + 30 mg/L + 5 mg/L = 105 mg/L
Step 2: Sum Anions
Total Anions = [Cl⁻] + [SO₄²⁻] + [HCO₃⁻] + [NO₃⁻]
Total Anions = 40 mg/L + 70 mg/L + 150 mg/L + 10 mg/L = 270 mg/L
Step 3: Sum Total Cations and Anions
Estimated TDS = Total Cations + Total Anions
Estimated TDS = 105 mg/L + 270 mg/L = 375 mg/L
In this example, the estimated TDS would be 375 mg/L.
Important Considerations
- This manual calculation method provides an estimate of TDS based on the reported ions. It may not perfectly match a value obtained by the evaporation method because:
- Not all dissolved substances (like some organic compounds or dissolved gases) may be included in a standard ion analysis.
- The analysis might not measure all trace ions present.
- Some ions might be reported as compounds (e.g., Silica as SiO₂) rather than their ionic form.
- Ensure all concentrations are in the same units (mg/L or ppm) before summing.
