13.4 Hardness Titration, Conductivity & Jar Testing Protocol

Principles of Water Hardness & EDTA Chelation

Water hardness is defined as the characteristic imparted by the presence of multivalent metallic cations in solution. In natural drinking water supplies, hardness is caused almost entirely by two divalent alkaline earth metals:

1. Calcium ions (Ca2+): Dissolved from limestone (CaCO3), dolomite (CaCO3·MgCO3), and gypsum (CaSO4·2H2O).
2. Magnesium ions (Mg2+): Dissolved from magnesite (MgCO3) and dolomitic formations.

Other polyvalent cations—such as iron (Fe2+, Fe3+), manganese (Mn2+), strontium (Sr2+), barium (Ba2+), and aluminum (Al3+)—also contribute to hardness, but they are generally present in negligible concentrations in finished potable water. By universal water industry convention, all hardness fractions are calculated and reported quantitatively as milligrams per liter as calcium carbonate equivalent (mg/L as CaCO3).

The EDTA Chelation Mechanism (Standard Methods 2340 C)

The standard titrimetric method for hardness determination relies on Ethylenediaminetetraacetic acid (EDTA) or its disodium salt (Na2EDTA). EDTA is a hexadentate chelating ligand containing four carboxylate groups and two tertiary amine groups.

[ EDTA Chelation Mechanism ]

Stage 1: Indicator Binding (Sample + EBT at pH 10.0)
Mg2+ + In (Blue) -------------> [ Mg-In Complex ] (Wine-Red)

Stage 2: Chelation Titration (Addition of EDTA titrant)
Ca2+ + EDTA ------------------> [ Ca-EDTA Complex ] (Highly Stable)
Mg2+ + EDTA ------------------> [ Mg-EDTA Complex ]

Stage 3: End Point Extraction (EDTA strips metal from indicator)
[ Mg-In Complex ] (Wine-Red) + EDTA ---> [ Mg-EDTA ] + Free In (Pure Blue)

When added to water containing polyvalent cations, EDTA wraps around the metal atom, forming a non-ionic, highly stable ring-shaped chelate complex in an exact 1:1 stoichiometric molar ratio:

Ca2+ + EDTA^4- -> [Ca-EDTA]^2-

Mg2+ + EDTA^4- -> [Mg-EDTA]^2-

Because the formation constant (Kf) for the calcium-EDTA chelate is substantially higher (log Kf = 10.7) than that for magnesium-EDTA (log Kf = 8.7), EDTA preferentially binds free calcium ions first, followed by free magnesium ions.

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Total Hardness Titration Procedure (pH 10.0)

Under Standard Methods 2340 C, Total Hardness measures the combined sum of calcium and magnesium ions:

1. Sample Preparation: Transfer a representative 50.0-mL water sample into a 250-mL Erlenmeyer flask (diluting to 100 mL with deionized water if hardness exceeds 200 mg/L).
2. Buffering to pH 10.0: Add 1 to 2 mL of ammonium hydroxide/ammonium chloride (NH4OH/NH4Cl) buffer solution. This maintains the solution at pH 10.0 ± 0.1. Maintaining pH 10.0 is critical: at lower pH (< 9.0), the indicator does not bind magnesium crisply; at higher pH (> 10.5), magnesium begins to precipitate as magnesium hydroxide (Mg(OH)2), preventing complete titration.
3. Indicator Addition: Add 1 to 2 drops of Eriochrome Black T (EBT) or Calmagite indicator. In the presence of free magnesium ions at pH 10.0, the indicator forms a distinct wine-red / purple coordination complex.
   • Note: If a sample contains only calcium and zero magnesium, EBT produces an indistinct, sluggish end point. Standard commercial EDTA titrants and buffer formulations incorporate a trace quantity of magnesium-EDTA chelate to ensure crisp indicator color transition.
4. Titration to Pure Blue End Point: Titrate slowly with standard 0.0100 M (or 0.0200 N) EDTA titrant while continuously swirling. As EDTA consumes free Ca2+ and Mg2+, the solution remains wine-red until all free ions are chelated. The final drop of EDTA extracts the magnesium bound to the indicator, releasing the indicator in its unchelated, free ionic form. The end point occurs when the last reddish tinge vanishes, turning the solution a permanent, sharp clear blue.

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Calcium Hardness Titration Procedure (pH 12.0–13.0)

To determine calcium hardness independently, magnesium ions must be chemically eliminated from the titration reaction:

1. Precipitation of Magnesium: Transfer a 50.0-mL water sample to a flask. Add 1.0 to 2.0 mL of 1.0 N sodium hydroxide (NaOH) (or 2.0 N KOH) to raise the sample pH to between 12.0 and 13.0.
2. Mechanism: At pH > 12.0, magnesium cations precipitate quantitatively out of solution as insoluble magnesium hydroxide (Mg(OH)2):

Mg2+ + 2 OH- -> Mg(OH)2 (solid precipitate)

Because magnesium is locked in an insoluble precipitate, it cannot react with indicator or EDTA. 3. Calcium Indicator: Add hydroxy naphthol blue, murexide (ammonium purpurate), or Calver II indicator. In the presence of dissolved calcium at pH 12 to 13, the indicator turns pink/red. 4. Titration End Point: Titrate immediately with standard 0.0100 M EDTA. EDTA binds calcium ions exclusively. At the end point, the solution undergoes a distinct color transition from pink to a sharp royal blue or purple-blue.

Hardness Calculations & Elemental Cation Conversion

Hardness (mg/L as CaCO3) = (A * M * 100,090) / (Sample Volume in mL)

Where:

• A = Volume of EDTA titrant consumed (mL)
• M = Molarity of EDTA titrant (0.0100 M)
• 100,090 = Molecular weight of CaCO3 (100.09 g/mol * 1,000 mg/g)

When using a standard 50.0-mL sample and 0.0100 M EDTA:

Hardness (mg/L as CaCO3) = (A * 0.0100 * 100,090) / 50.0 = A * 20.0

Rule: Every 1.0 mL of 0.0100 M EDTA consumed titrating a 50-mL sample equals 20.0 mg/L as CaCO3.

Determining Magnesium Hardness and Elemental Cations

1. Magnesium Hardness Calculation:

Magnesium Hardness (mg/L as CaCO3) = Total Hardness (mg/L as CaCO3) - Calcium Hardness (mg/L as CaCO3)

1. Elemental Calcium Ion Concentration (Ca2+):

Ca2+ (mg/L) = Calcium Hardness (mg/L as CaCO3) * (40.08 g/mol Ca / 100.09 g/mol CaCO3) = Calcium Hardness * 0.400

1. Elemental Magnesium Ion Concentration (Mg2+):

Mg2+ (mg/L) = Magnesium Hardness (mg/L as CaCO3) * (24.31 g/mol Mg / 100.09 g/mol CaCO3) = Magnesium Hardness * 0.243

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Specific Conductance & Total Dissolved Solids (TDS)

Specific Conductance (Electrical Conductivity, EC) measures the ability of an aqueous solution to conduct an electric current. Pure deionized water is an electrical insulator (EC < 0.1 µS/cm); current is conducted via the migration of dissolved inorganic ions: cations (Ca2+, Mg2+, Na+, K+) and anions (HCO3-, Cl-, SO4(2-), NO3-).

• Units and Temperature Standardization: Measured in micromhos per centimeter (µmhos/cm) or microsiemens per centimeter (µS/cm) (where 1 µmho/cm = 1 µS/cm). Electrical conductivity increases by approximately 1.9% to 2.1% for every 1.0°C rise in temperature due to decreased liquid viscosity and accelerated ionic velocity. All conductivity meters must standardize readings to 25.0°C.
• Empirical Relationship to Total Dissolved Solids (TDS): In natural potable drinking waters, conductivity correlates directly with gravimetric TDS:

TDS (mg/L) ≈ (0.55 to 0.70) * Specific Conductance (µS/cm)

For typical municipal surface and groundwaters dominated by calcium, bicarbonate, and sulfate, an empirical multiplier of 0.65 is standard (TDS ≈ 0.65 * EC). In highly saline or brackish waters with elevated sodium chloride, the factor increases toward 0.75 to 0.85.

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Jar Testing Protocol for Coagulation Optimization

The laboratory jar test is the essential bench-scale pilot procedure used by Class II operators to simulate and optimize full-scale plant coagulation, rapid flash mixing, flocculation, and sedimentation.

[ Standard 6-Paddle Jar Test Apparatus ]

     [ Variable-Speed Electronic Gang Drive (0 - 300 RPM) ]
       |          |          |          |          |          |
   [ Paddle ] [ Paddle ] [ Paddle ] [ Paddle ] [ Paddle ] [ Paddle ]
       |          |          |          |          |          |
     +---+      +---+      +---+      +---+      +---+      +---+
     | 1 |      | 2 |      | 3 |      | 4 |      | 5 |      | 6 |  <-- Square B-Ker Jars
     +---+      +---+      +---+      +---+      +---+      +---+      (Anti-Vortex Baffles)
    [==================== Illuminated Base ====================]

Critical Apparatus: Square B-Ker Jars vs. Round Beakers

Standard jar testing utilizes a multi-station gang stirrer equipped with six flat-paddle impellers and 2-liter square B-Ker jars (Phipps & Bird jars):

• Why Square Jars are Mandatory: When fluid is agitated inside a standard round laboratory beaker, the entire liquid mass rotates in a solid circular vortex. Centrifugal forces throw heavy flocs outward, and mixing energy dissipates without generating fluid shear. In contrast, the 90° square vertical corners of B-Ker jars act as integral hydraulic baffles. The corners interrupt rotational flow, preventing vortexing and driving fluid inward to replicate the turbulent velocity gradients (G-values) of full-scale plant flocculators.

Step-by-Step Jar Testing Procedure

1. Raw Water Characterization: Collect a fresh, representative composite sample of raw water. Immediately measure and record temperature, raw turbidity, pH, total alkalinity, and color.
2. Dosing Matrix: Fill six 2-liter square jars with exactly 2,000 mL of raw water. Arrange an incremental series of coagulant dosages (e.g., Jar 1 = 10 mg/L; Jar 2 = 20 mg/L; Jar 3 = 30 mg/L; Jar 4 = 40 mg/L; Jar 5 = 50 mg/L; Jar 6 = 60 mg/L). Prepare chemical dosing syringes with diluted primary coagulant (alum, ferric chloride) and any auxiliary alkalis (lime, caustic soda) or coagulant aid polymers.
3. Rapid Flash Mix: Start the gang stirrer at 100 to 150 RPM (generating a high velocity gradient G >= 300 to 700 s^-1). Inject the coagulant doses simultaneously into all six jars beneath the liquid surface. Flash mix for exactly 1.0 minute (60 seconds) to disperse chemicals and destabilize colloidal surface charges.
4. Tapered Flocculation: Reduce stirrer speed to simulate full-scale multi-stage flocculation basins. A standard tapered agitation sequence comprises:
   • High Flocculation: 50 RPM for 10 minutes (promotes initial micro-floc particle collisions)
   • Medium Flocculation: 30 RPM for 10 minutes (builds cohesive macro-floc matrices)
   • Low Flocculation: 20 RPM for 10 minutes (maintains solids suspension without shearing fragile flocs)
   • Total flocculation time: 30 minutes.
5. Quiescent Settling: Shut off the gang stirrer, raise the paddles carefully out of the jars, and allow the water to settle under undisturbed, quiescent gravity conditions for 15 to 30 minutes (simulating 2 to 4 hours of plant basin detention).
6. Floc Evaluation During Settling: Observe and record qualitative floc characteristics:
   • Floc nucleation time: Minutes to initial visible pin floc formation
   • Floc morphology: Tiny pin floc, loose feather/fluffy floc, or dense cohesive agglomerates
   • Settling velocity: Rate of sludge blanket descent (inches per minute)

Supernatant Sampling Protocol

To ensure accurate, reproducible data, supernatant water must be sampled with extreme precision:

• Sampling Location: Withdraw sample water through the jar's built-in sampling petcock or by using a pipette positioned precisely 2 inches (5 cm) below the water surface.
• Why 2 Inches Below Surface? Sampling at the water surface captures floating scum, oils, and buoyant pin flocs that bias results. Sampling deeper down (or near the bottom) aspirates settling floc blankets. Withdrawing sample from 2 inches below the surface simulates the water layer skimming over plant sedimentation basin effluent launder weirs.
• Laboratory Testing of Supernatant: Analyze settled water for turbidity (NTU), settled sludge volume, final pH, residual alkalinity, and dissolved residual metal (aluminum or iron).

Optimum Coagulant Dose Selection

Plot settled water turbidity (Y-axis) versus coagulant dosage (X-axis). The optimal economic dose is the lowest coagulant concentration that produces the target settled turbidity (typically < 1.0 to 2.0 NTU) with a compact settled sludge volume and adequate residual alkalinity (> 20 to 30 mg/L as CaCO3) to prevent corrosive pH crashes in downstream filtration.

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Comparative Technical References

Table 13.4.1: EDTA Hardness Titration Parameters (Total vs. Calcium)

| Analytical Parameter | Total Hardness Titration (SM 2340 C) | Calcium Hardness Titration (SM 2340 C) | |---|---|---|---| | Target Chemical Species | Calcium (Ca2+) + Magnesium (Mg2+) | Calcium (Ca2+) exclusively | | Sample Buffer Chemistry | Ammonium hydroxide/chloride (NH4OH/NH4Cl) | Sodium hydroxide (1.0 N NaOH) | | Controlled Reaction pH | pH 10.0 ± 0.1 | pH 12.0 to 13.0 | | Interfering Ion Suppression | Chelates all multivalent cations equally | Magnesium precipitated as insoluble Mg(OH)2 solid | | Indicator System | Eriochrome Black T (EBT) or Calmagite | Hydroxy naphthol blue or Murexide | | End Point Color Transition | Wine-Red / Purple -> Pure Clear Blue | Pink / Red -> Royal Blue / Purple | | Standard Titrant | 0.0100 M Na2EDTA (1 mL = 20 mg/L CaCO3) | 0.0100 M Na2EDTA (1 mL = 20 mg/L CaCO3) |

Table 13.4.2: Standard Jar Test Bench Run Sheet & Supernatant Logging Matrix

Diagnostic Interpretation: Jar 4 represents the optimal economic dose. Increasing the dose to 50 mg/L produces a negligible turbidity improvement (0.55 -> 0.52 NTU) while generating 46% more chemical sludge; increasing to 60 mg/L triggers colloidal restabilization (turbidity rises to 0.75 NTU).

Table 13.4.3: Water Hardness Classification Scale

Conversion Factor: 1.0 Grain per Gallon (gpg) = 17.12 mg/L as CaCO3.