What is αY(H) and how is it calculated?

αY(H) is the ratio of the total concentration of EDTA not bound to metal to the concentration of free Y⁴⁻, and it measures how much protonation lowers the available Y⁴⁻. It is calculated from the six acid dissociation constants: αY(H) = 1 + [H⁺]/Ka₆ + [H⁺]²/(Ka₆Ka₅) + … + [H⁺]⁶/(Ka₆Ka₅…Ka₁). The lower the pH, the larger it gets: log αY(H) ≈ 6.45 at pH 5, 0.45 at pH 10 and close to 0 above pH 12. This tool uses pKa₁–pKa₆ = 0.9, 1.6, 2.0, 2.67, 6.16 and 10.26.

How do I find the minimum pH for an EDTA titration?

A titration is accurate to 0.1% (with ΔpM = ±0.2) when log c_eq·K′ ≥ 6. Ignoring other side reactions, log K′ = log K − log αY(H), so the largest acceptable log αY(H) is log K + log c_eq − 6, and the pH where αY(H) reaches that value is the minimum pH. With c_eq = 0.01 M this is about pH 7.6 for Ca²⁺, 9.7 for Mg²⁺, 4.0 for Zn²⁺ and 1.2 for Fe³⁺. Plotting these points on the log αY(H)–pH curve gives the Ringbom curve. Hydrolysis of the metal ion sets the practical upper pH limit.

How is water hardness determined with EDTA and converted between units?

A measured volume of water is buffered at pH 10 with NH₃–NH₄Cl and titrated with EDTA to the Eriochrome Black T end point (wine red to blue). This gives Ca²⁺ + Mg²⁺: c = c(EDTA)·V₁ / V(sample). Hardness as CaCO₃ (mg/L) = total (mmol/L) × 100.09. One German degree (°dH) = 10 mg CaO/L, which is mmol/L × 5.608. One French degree (°f) = 10 mg CaCO₃/L. For calcium alone, a second aliquot is taken to pH 12 with NaOH so Mg(OH)₂ precipitates, then titrated with calcon; magnesium is total minus calcium. By the USGS scale, water above 180 mg/L CaCO₃ is very hard.

Why is Eriochrome Black T used for total hardness but not for calcium alone?

EBT works at pH 8–11 and binds Mg²⁺ much more strongly than Ca²⁺: at pH 10 pMg_t ≈ 5.4 but pCa_t is only about 3.8. With calcium alone the indicator changes colour too early and the end point is not sharp. In hard water the Mg²⁺ present controls the colour change, which is sharp. For calcium alone, calcon at pH 12–13 is used so magnesium precipitates and does not interfere. A little Mg–EDTA is sometimes added to calcium solutions to sharpen the EBT end point.

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💎EDTA Titration Calculator - Conditional Constant, Ringbom Curve & Water Hardness

EDTA binds nearly every metal ion 1 : 1, but it is a hexaprotic acid (H₆Y²⁺), so at lower pH less of it is present as Y⁴⁻. This side reaction is expressed by the coefficient αY(H) = 1 + [H⁺]/Ka₆ + [H⁺]²/(Ka₆Ka₅) + …, and the conditional constant is log K′ = log K(MY) − log αY(H) − log αM. At pH 10, log αY(H) = 0.45, so for Ca²⁺ log K′ = 10.69 − 0.45 = 10.24. For Mg²⁺ log K′ = 8.25; at c_eq = 0.01 M, log c·K′ = 6.25 ≥ 6, so the titration is feasible: pMg′ at equivalence is 5.13, the ±0.1% jump runs from 4.85 to 5.40, and Eriochrome Black T (pMg_t = 5.4) gives an end-point error of about 0.1%. The calculator includes the six EDTA pKa values and log K(MY) for 17 metal ions. You can add auxiliary complexation by an NH₃–NH₄⁺ buffer (ammine constants for Zn²⁺, Cu²⁺, Ni²⁺ and Cd²⁺) or enter log αM directly. It finds the minimum pH from log c·K′ ≥ 6 and plots the Ringbom curve with every metal marked. The titration curve is solved exactly from the mass balance of M′ + Y′ ⇌ MY, giving pM′ at equivalence, the ±0.1% jump and the Ringbom end-point error. A table gives the pH ranges and colour changes of Eriochrome Black T, calcon, xylenol orange and PAN. Hardness mode turns titration volumes into results: a 25.00 mL sample that uses 12.50 mL of 0.01000 M EDTA has 5.000 mmol/L total hardness, which is 500.5 mg/L as CaCO₃ or 28.04 °dH. A second titration at pH 12 with calcon splits the total into calcium and magnesium.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use EDTA titration & water hardness

1Choose a mode (side reactions and K′, titration curve and indicators, or water hardness), or click an example
2Pick the metal ion, pH and auxiliary ligand, enter metal and EDTA concentrations and volumes, or for hardness enter the sample volume and the two titration volumes
3Read log αY(H), log K′, minimum pH, the Ringbom curve, the pM′ curve, the end-point error and the converted hardness values, with step-by-step working and CSV export

FAQ

What is αY(H) and how is it calculated?: αY(H) is the ratio of the total concentration of EDTA not bound to metal to the concentration of free Y⁴⁻, and it measures how much protonation lowers the available Y⁴⁻. It is calculated from the six acid dissociation constants: αY(H) = 1 + [H⁺]/Ka₆ + [H⁺]²/(Ka₆Ka₅) + … + [H⁺]⁶/(Ka₆Ka₅…Ka₁). The lower the pH, the larger it gets: log αY(H) ≈ 6.45 at pH 5, 0.45 at pH 10 and close to 0 above pH 12. This tool uses pKa₁–pKa₆ = 0.9, 1.6, 2.0, 2.67, 6.16 and 10.26.
How do I find the minimum pH for an EDTA titration?: A titration is accurate to 0.1% (with ΔpM = ±0.2) when log c_eq·K′ ≥ 6. Ignoring other side reactions, log K′ = log K − log αY(H), so the largest acceptable log αY(H) is log K + log c_eq − 6, and the pH where αY(H) reaches that value is the minimum pH. With c_eq = 0.01 M this is about pH 7.6 for Ca²⁺, 9.7 for Mg²⁺, 4.0 for Zn²⁺ and 1.2 for Fe³⁺. Plotting these points on the log αY(H)–pH curve gives the Ringbom curve. Hydrolysis of the metal ion sets the practical upper pH limit.
How is water hardness determined with EDTA and converted between units?: A measured volume of water is buffered at pH 10 with NH₃–NH₄Cl and titrated with EDTA to the Eriochrome Black T end point (wine red to blue). This gives Ca²⁺ + Mg²⁺: c = c(EDTA)·V₁ / V(sample). Hardness as CaCO₃ (mg/L) = total (mmol/L) × 100.09. One German degree (°dH) = 10 mg CaO/L, which is mmol/L × 5.608. One French degree (°f) = 10 mg CaCO₃/L. For calcium alone, a second aliquot is taken to pH 12 with NaOH so Mg(OH)₂ precipitates, then titrated with calcon; magnesium is total minus calcium. By the USGS scale, water above 180 mg/L CaCO₃ is very hard.
Why is Eriochrome Black T used for total hardness but not for calcium alone?: EBT works at pH 8–11 and binds Mg²⁺ much more strongly than Ca²⁺: at pH 10 pMg_t ≈ 5.4 but pCa_t is only about 3.8. With calcium alone the indicator changes colour too early and the end point is not sharp. In hard water the Mg²⁺ present controls the colour change, which is sharp. For calcium alone, calcon at pH 12–13 is used so magnesium precipitates and does not interfere. A little Mg–EDTA is sometimes added to calcium solutions to sharpen the EBT end point.

Features

EDTA αY(H) and species distribution at any pH
log K(MY) for 17 metal ions, plus a custom constant
Auxiliary complexation by NH₃ (free or total ammonia)
Minimum pH from log c·K′ ≥ 6 and an interactive Ringbom curve
Exact pM′ vs volume curve with equivalence point, jump range and hover readout
Ringbom end-point error formula with EBT transition pMg_t filled in
Eriochrome Black T, calcon, xylenol orange and PAN: pH range, colours, blocking ions
Water hardness in mmol/L, mg/L CaCO₃, °dH and °f, with Ca/Mg split and classification

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