B5 · Publication Volume 10

Aqueous Geochemistry

speciation, complexing, pH, Eh and solubility

Learning goals

After this lesson, you should be able to distinguish an analytical total from dissolved species, concentration from activity, pH from a casual concentration label, and redox measurement from an assumed oxidation-state diagram. You should be able to calculate ionic charge balance and saturation index, describe complexation and acid-base speciation, and construct a reaction model whose components, phases, temperature and standard states are declared.

The lesson treats aqueous calculations as conditional thermodynamic and kinetic models. A solution analysis does not contain a unique list of free ions, mineral reactions or water-rock history. Those are inferred using measured totals, temperature, pressure where relevant, an activity model, equilibrium constants and constraints. The model is useful when these inputs and assumptions remain visible.

Components, species and activities

Aqueous geochemistry evidence chain from sampled water through components, species, activities and mineral saturation
Aqueous geochemistry evidence chain from sampled water through components, species, activities and mineral saturation

An analysis commonly reports components or totals, such as total dissolved calcium or sulfur. A chemical model distributes those components among species: free ions, protonated forms, aqueous complexes, ion pairs, gases and minerals. For example, dissolved carbonate carbon can occur as dissolved carbon dioxide, bicarbonate, carbonate and complexes with metals. Their proportions depend on pH, temperature, ionic strength and the chosen equilibrium constants.

Thermodynamic equilibrium is written in activities. For species i,

$a_i=\gamma_i m_i,$

where m_i is molality and \gamma_i is an activity coefficient under a declared convention. At low ionic strength, activity may approach concentration numerically; in saline solutions the difference can be decisive. Activity models have calibrated domains. Choosing one is a model decision, not a formatting option.

Ionic strength on a molality basis is

$I=\frac{1}{2}\sum_i m_i z_i^2,$

where z_i is charge. Multivalent ions contribute strongly because charge is squared. A table lacking species and charge cannot support this calculation directly; speciation must be solved iteratively with mass balance and equilibrium relations.

Acid-base balance, pH and alkalinity

pH is defined through hydrogen-ion activity,

$\mathrm{pH}=-\log_{10}a_{H^+}.$

It is not simply the negative logarithm of a reported mass concentration. The measurement scale, calibration buffers, temperature, junction effects and matrix matter. A pH measured after prolonged exposure to air may not represent in-situ carbon dioxide conditions.

Alkalinity is an operationally measured acid-neutralising capacity expressed as equivalents per volume or mass under a declared endpoint and method. It is not synonymous with bicarbonate concentration, although bicarbonate often dominates near neutral pH. Carbonate, hydroxide, borate, phosphate, organic bases and metal complexes may contribute. Acidity and alkalinity constrain charge and proton balance and can be more robust model inputs than a calculated bicarbonate value.

A major-ion charge-balance error can be written

$\mathrm{CBE}(\%)=100\frac{\sum cations-\sum anions}{\sum cations+\sum anions},$

where both sums are in charge equivalents. The sign convention must be stated. A small balance does not prove all analyses are correct because compensating errors are possible; a large imbalance signals missing species, unit, valence, basis or analytical problems that must be resolved before interpretation.

Redox, complexation and mineral saturation

Redox state is described by electron-transfer couples, not by one universal electrode number. An Eh measurement, if used, requires electrode type, calibration, temperature, stabilisation behaviour and sample handling. Natural waters may not be at internal redox equilibrium: iron, sulfur, carbon, nitrogen and arsenic couples can record different kinetics and microenvironments. Converting pH and an electrode potential to a single pe value does not force all couples to agree.

Complexation changes effective mobility. A metal with low free-ion activity may remain at high total dissolved concentration if stable ligand complexes form. Ligands may be inorganic, such as chloride, carbonate, sulfate or hydroxide, or organic. A total concentration trend can therefore reflect ligand availability rather than source strength. Measure or bound the components that control the proposed complexes.

For a mineral dissolution reaction, the ion-activity product IAP is compared with the equilibrium constant K:

$SI=\log_{10}\left(\frac{IAP}{K}\right).$

SI<0 indicates undersaturation under the model, SI=0 equilibrium and SI>0 supersaturation. Supersaturation indicates thermodynamic potential, not proof that precipitation occurred. Nucleation barriers, inhibitors, surface area, transport and database uncertainty matter. Likewise, apparent equilibrium can result from a buffered pathway without identifying the controlling mineral uniquely.

Sampling, preservation and model inputs

Define whether a result is field, filtered, dissolved, total recoverable or total; record filter material and pore size, container, preservation, holding time, temperature and headspace. Filtration can remove colloids or allow smaller colloids through; acidification can dissolve particles. A dissolved label is operational, not a guarantee of molecular solution.

Measure unstable parameters such as temperature, pH, specific conductance, dissolved oxygen and redox indicators as close to in-situ conditions as the method requires. Record flow, purge or sampling stabilisation and whether gas exchange was controlled. Preserve alkalinity titration data, not only the final value. Major ions, dissolved inorganic carbon and density or salinity may be required for a defensible charge and speciation model.

Before modelling, convert all units to moles or equivalents on a declared mass or volume basis, honour censored values, and check analytical balance. Choose a thermodynamic database and activity model appropriate to temperature, pressure and composition; record versions. Do not tune uncertain mineral phases until a poor analytical balance has been explained.

Worked synthetic example

A synthetic water has the following millimolar totals, with the listed valence used for a first charge check: Ca 2.00, Mg 1.00, Na 3.00, K 0.20, bicarbonate 4.00, sulfate 1.50, chloride 2.00 and nitrate 0.10. Cation equivalents are

$2(2.00)+2(1.00)+1(3.00)+1(0.20)=9.20\ \mathrm{meq/L}.$

Anion equivalents are

$1(4.00)+2(1.50)+1(2.00)+1(0.10)=9.10\ \mathrm{meq/L}.$

Using the stated convention, \mathrm{CBE}=100(9.20-9.10)/(9.20+9.10)=0.55\%. This is a useful consistency result, not proof that speciation or every measurement is correct.

Suppose pH is 7.00 and the model gives \gamma_{H^+}=0.80. Then a_{H^+}=10^{-7} and the corresponding molality is m_{H^+}=1.25\times10^{-7} mol/kg under this simplified convention. If a candidate mineral reaction has IAP=2.0\times10^{-9} and K=1.0\times10^{-8} at the model temperature,

$SI=\log_{10}(0.20)=-0.70,$

so the water is undersaturated with respect to that reaction under the chosen database and activity model. A change of temperature, complex distribution or analytical input may change the result; report sensitivity rather than treating SI as an observed property.

Interpretation workflow and uncertainty

  1. Define the water body, sampling time, flow regime and operational fraction.
  2. Preserve field conditions, preparation and unstable measurements.
  3. Convert totals to consistent molal or equivalent units and check charge balance.
  4. Select components, phases, gases, temperature, pressure, activity model and database version.
  5. Solve speciation before interpreting free-ion activity or saturation.
  6. Compare multiple redox couples and mineralogical observations; do not force one equilibrium state.
  7. Test reaction paths, mixing and gas exchange against field gradients and mass balance.
  8. Vary uncertain analytical inputs and thermodynamic choices.
  9. State which outputs are measured, calculated and geologically interpreted.

Failure modes

Typical errors are using mg/L as mol/L, calculating charge balance from mass rather than equivalents, equating filtered with truly dissolved, treating pH as hydrogen concentration without an activity convention, and accepting a saturation index without checking database and temperature. Another is inferring a unique mineral control from equilibrium when several phases share components.

Uncertainty includes sampling transience, gas exchange, filtration artefacts, titration and calibration, censored data, activity coefficients, equilibrium constants and missing kinetic constraints. Model ensembles are often more honest than a single deterministic species table.

Practice and review

  1. Convert a supplied synthetic major-ion table from mg/L to mmol/L and meq/L, documenting formula masses and valence.
  2. Recalculate charge balance after omitting one divalent anion and explain the diagnostic pattern.
  3. Draw carbonate-species proportions qualitatively across a pH range and list the assumptions that prevent the sketch from being quantitative.
  4. Design field observations that distinguish mineral dissolution, evaporation and mixing as causes of rising total dissolved solids.
  5. Compare two activity models conceptually and state what composition domain would make their difference important.

For the completion exercise, build a synthetic water-reaction ledger with measured totals, field conditions, charge balance, a selected mineral reaction and low-central-high input cases. Report at least one model that fails and explain why its failure is informative.

Sources and further reading