Can the numerical sum of Cl⁻ (mg/L), hardness (mg/L as CaCO₃), and alkalinity (mg/L as CaCO₃) ever be greater than the reported TDS (mg/L)?
Good question, indeed!
Yes, it's possible—though it's usually a sign of incomplete or inconsistent data or different measurement bases.
Why?
TDS represents the total amount of all inorganic and organic substances dissolved in water, typically including:
- Major cations (Ca²⁺, Mg²⁺, Na⁺, K⁺)
- Major anions (Cl⁻, SO₄²⁻, HCO₃⁻, NO₃⁻)
- Minor constituents
TDS is often:
- Measured directly (gravimetrically, via residue on evaporation)
- Or estimated using a formula like: TDS (mg/L) ≈ 0.64 × conductivity (µS/cm) (empirical)
Three key reasons the sum can appear larger than TDS:
- Hardness and alkalinity are expressed as mg/L of CaCO₃, not as the actual ions (Ca²⁺, Mg²⁺, HCO₃⁻).
- This gives them a heavier molecular weight base (100 g/mol).
- So their values are not directly additive with TDS unless converted to the actual ion weights.
- If TDS is measured, it may exclude volatile or unstable compounds.
- If estimated from EC, it may underestimate TDS in some waters.
- Different samples, lab errors, or outdated data can cause discrepancies.
- A lab might have omitted ions that contribute significantly to TDS (e.g., sulfate, sodium).
Example:
Parameter Value (mg/L)
Cl⁻ 200, Actual ion
Hardness 300 (as CaCO₃), Really about 120 mg/L of Ca²⁺ + Mg²⁺
Alkalinity 150 (as CaCO₃), About 90 mg/L HCO₃⁻
Sum 650 Mixed units—not actual TDS
TDS (reported): 600 Measured
Here the sum (650) > TDS (600)—but the hardness and alkalinity are reported as CaCO₃ equivalents, not directly additive with Cl⁻.
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