Chemistry

Alkalinity (Gran titration)

How the titration runs, the DIC-corrected Gran fit, and what the quality flags mean.

The run

Rinse Cell A twice with tank water; home the acid pump if needed; fill and level to 20.0 mL; stir 15 s; read temperature and starting pH.
Initial dose. 97 % of the acid expected from the previous result (or initial_dose_ul on the first run) in one shot, so the titration lands just short of equivalence.
Approach. 200 µL steps until pH < 4.3.
Titrate. 60 µL steps, waiting for pH drift < 0.005 pH/s after each (timeout 25 s), until pH < 3.0 or 14 points have been collected in the 3.0–3.8 window.
Fit, store, drain, rinse once, park the cell full of tank water.

A typical 8 dKH titration uses 2.9 mL of 0.02 N acid and takes six to eight minutes.

The math

Below pH 4 the carbonate species are essentially all CO₂, and the charge balance on the solution is

[H⁺] = [HCO₃⁻] − TA_remaining, with [HCO₃⁻] ≈ C_T · K₁ / [H⁺]

Multiplying by the total volume (V₀ + v) and substituting TA_remaining·(V₀+v) = TA₀·V₀ − c·v and C_T·(V₀+v) = C_T0·V₀ gives a straight line:

(V₀ + v)·[H⁺] − c·v = −TA₀·V₀ + C_T0 · ( V₀·K₁ / [H⁺] )

A least-squares line of the left side against x = V₀K₁/[H⁺] has intercept −TA₀V₀ and slope C_T0: alkalinity and an estimate of dissolved inorganic carbon from the same points. With pK₁ = 5.86 (seawater, 25 °C), the DIC term is 2–4 % of [H⁺] in the window and ignoring it — as the classic Gran extrapolation does — biases alkalinity 2–5 % low. OpenReef reports both: ta_meq_l (corrected, primary) and ta_classic_meq_l.

dKH = 2.80 × TA (meq/L); 1 meq/L = 50 ppm CaCO₃.

Why it tolerates a mediocre electrode

A constant pH offset changes every [H⁺] by the same factor; the fit’s x-intercept does not move. Slope errors matter more, so calibrate at pH 7 and 4 (bracketing the window) every two weeks, and let the EZO circuit’s temperature compensation run from the DS18B20.

Standardising the acid

Rather than trusting the label, run the titration on a reference of known alkalinity — 0.1000 g/L anhydrous Na₂CO₃ (dried at 250 °C) is 1.887 meq/L = 5.28 dKH — and solve for the normality that reproduces it (POST /api/v1/calibration/alkalinity/standardize). The DIC-corrected fit depends on c, so the solver bisects on c until TA matches. Re-standardise whenever you refill the acid bottle.

Quality flags

Flag	Meaning	What to do
`low_r2`	fit R² < 0.999	electrode noisy or stirring poor; check bubbles on the bulb
`noisy_fit`	relative residual rms > 1 %	same; halves the quality score
`v_eq_outside_expected`	equivalence volume not before the first window point	first dose too large; lower `initial_dose_ul`
`dic_estimate_implausible`	DIC < 0 or > 2× TA	window too narrow or pH scale off; recalibrate pH

The quality score (0–1) is derived from R² and residuals; the dashboard greys out points below 0.5.

Configuration

chemistry:
  alkalinity:
    acid_normality: 0.0200   # replaced by standardisation
    sample_ml: 20.0
    initial_dose_ul: 900
    step_ul: 60
    gran_ph_min: 3.0
    gran_ph_max: 3.8
    min_points: 6
    max_points: 14
    stable_dph_per_s: 0.005
    stable_timeout_s: 25

References

Dickson, Sabine & Christian (eds.), Guide to best practices for ocean CO₂ measurements, PICES Special Publication 3 (2007), SOP 3b — open-cell alkalinity titration.
Gran, G. (1952). Determination of the equivalence point in potentiometric titrations, Part II. Analyst 77:661–671.
Millero, F. J. (2010). Carbonate constants for estuarine waters. Marine and Freshwater Research 61:139–142.