Water chemistry, speciation and mineral-water interactions

A total dissolved amount can contain several species

Water chemistry distinguishes a total constituent inventory from the separate chemical species that contain it. Acid–base forms, complexes and dissolved gases can contribute to that inventory. An equilibrium description needs temperature, pressure where relevant, composition and compatible equilibrium constants.

Activities enter thermodynamic equilibrium relations. Concentrations can approximate them only under an explicitly stated model and standard normalization. Ionic strength, complexation and interactions can make a total concentration different from the free-species concentration.

Carbon distribution and gas exchange impose different constraints

For an original ideal dilute teaching model at one fixed assigned temperature, normalize concentrations by c°=1 mol L⁻¹ and set water activity to one. Invent concentration-form constants K₁=10⁻⁶⋅⁵ mol L⁻¹, K₂=10⁻¹⁰⋅⁵ mol L⁻¹ and K_w=10⁻¹⁴ mol² L⁻². These are hypothetical conditional constants, not actual seawater thermodynamic data or a seawater pH scale.

Define CO₂* as the combined dissolved CO₂ and H₂CO₃ pool; it has no single molecular formula. At assigned pH 8.50, total inorganic carbon C_T=1.530 mmol L⁻¹ distributes with weights 1:K₁/[H⁺]:K₁K₂/[H⁺]²=1:100:1. The CO₂*/HCO₃⁻/CO₃²⁻ concentrations are 0.0150/1.500/0.0150 mmol L⁻¹.

Include only H⁺, OH⁻, HCO₃⁻, CO₃²⁻ and Na⁺ as ions in this solution. Under the assigned ideal normalization, [H⁺]=3.16227766×10⁻⁹ mol L⁻¹ and [OH⁻]=3.16227766×10⁻⁶ mol L⁻¹. Carbonate alkalinity in molar charge equivalents is T_A=[HCO₃⁻]+2[CO₃²⁻]+[OH⁻]−[H⁺]=1.53315912 mmol L⁻¹. Choose [Na⁺]=T_A, explicitly closing the complete stated charge inventory.

A separate solution at pH 9.50 with the same carbon total gives CO₂*/HCO₃⁻/CO₃²⁻=0.00138964578/1.38964578/0.138964578 mmol L⁻¹. Its required Na⁺ and alkalinity are 1.69919739 mmol L⁻¹. Changing the counterion inventory is part of constructing this second solution; this is not a pH change in an otherwise unchanged sealed sample.

For a separate open-boundary model, prescribe CO₂* coefficient 0.0260 mol L⁻¹ bar⁻¹ and external CO₂ partial pressure 0.000550 bar, so CO₂*=0.0143 mmol L⁻¹. Keep the same hypothetical acid–base constants and fixed Na⁺=T_A=0.740 mmol L⁻¹. Solve the full charge equation for pH: 8.20853259, with C_T=0.748953896 mmol L⁻¹.

Doubling external pressure to 0.00110 bar gives open-equilibrium pH 7.91016767 and C_T=0.765908111 mmol L⁻¹ while Na⁺ and alkalinity stay fixed. An initially identical isolated liquid, sealed with no exchangeable gas headspace and no coupling to that external gas, retains its initial state. A finite sealed gas–liquid headspace would be a different boundary problem.

Inorganic carbon and alkalinity are different quantities

Dissolved inorganic carbon can include dissolved carbon dioxide/carbonic-acid forms, hydrogen carbonate and carbonate under the specified convention. Their distribution depends on acid–base equilibria and boundary conditions. An open gas reservoir and a closed carbon inventory impose different constraints.

Alkalinity characterizes acid-neutralizing capacity under the chosen definition and endpoint convention. It is neither simply pH nor total inorganic carbon. Carbonate species often contribute strongly, but other dissolved constituents can contribute as well.

Saturation and charge bookkeeping need compatible species

For another independent hypothetical case, use calcite CaCO₃(s)⇌Ca²⁺(aq)+CO₃²⁻(aq), unit solid activity, free Ca²⁺ 0.600 mmol L⁻¹ and free CO₃²⁻ 0.0180 mmol L⁻¹. Assign activity coefficients γ_Ca=0.650 and γ_CO3=0.400 and dimensionless equilibrium constant K=4.00×10⁻⁹ for this reaction at its fixed conditions. No complete water composition is supplied.

With a_i=γ_i c_i/c°, the activities are 0.000390 and 0.00000720. Their ion-activity product is 2.808×10⁻⁹, ratio IAP/K=0.702 and saturation index SI=log₁₀(IAP/K)=−0.153662888. The net balances Ca₁C₁O₃ and zero total charge; the activity example does not establish whole-sample electroneutrality or a dissolution rate.

Ignoring both assigned coefficients while retaining those concentrations and the same numerical K would give apparent product 1.08×10⁻⁸, ratio 2.70 and apparent SI=+0.431363764. This approximation changes the sign. It is not evidence that coefficients can physically change without a corresponding compositional change.

For a separate charge-only inventory in mmol L⁻¹, list Ca²⁺ 1.10, Mg²⁺ 0.350, Na⁺ 0.800, Cl⁻ 1.50, HCO₃⁻ 1.66, SO₄²⁻ 0.250, CO₃²⁻ 0.0200, and H⁺/OH⁻ each 0.000100. Neutral CO₂* is 0.0300 mmol L⁻¹. Positive and negative charge magnitudes each sum to 3.7001 milliequivalents L⁻¹. The charge-squared concentration sum gives ionic strength I=½Σc_i z_i²=5.4201 mmol L⁻¹; dissolved inorganic carbon is 1.710 mmol L⁻¹.

This listed inventory is a bookkeeping exercise, not an assertion that its carbonate proportions equilibrate at the implied hydrogen-ion concentration. Revising only Cl⁻ to 1.80 mmol L⁻¹ gives net charge −0.300 milliequivalents L⁻¹. Mathematically changing Na⁺ to 1.10 mmol L⁻¹ restores closure, but a convenient correction does not identify which observation is actually wrong.

Mineral equilibrium compares a defined activity product with a constant

For a specified dissolution reaction, an ion-activity product can be compared with the equilibrium constant for the same reaction and conditions. A saturation index uses the ratio of these compatible quantities. Different reaction definitions require different quotients.

A thermodynamic tendency does not itself establish a measured precipitation or dissolution rate. Nucleation, kinetics, competing phases and limited inventories can constrain what happens. An equilibrium model must also conserve the elements and maintain a consistent charge balance.

A water sample can change after collection

Gas exchange, precipitation, oxidation and other processes can change a sample’s species distribution. A measured pH or constituent result therefore belongs to its collection and measurement context. Filtered and whole-water inventories can answer different questions.

Use compatible observations to constrain a model and state unresolved species or boundary assumptions. The original equilibrium cases below contain no drinking-water safety limits or recommendations based on a hypothetical composition.

Worked examples

Try it yourself

1. Construct the separate pH 9.50 solution with the same carbon total. Find its carbonate pools and required Na⁺.

   Show the answer and reasoning

   CO₂*/HCO₃⁻/CO₃²⁻=0.00138964578/1.38964578/0.138964578 mmol L⁻¹; Na⁺=1.69919739 mmol L⁻¹.

   Weights 1:1000:100 close the carbon pool; the changed counterion closes its different charge requirement.

2. Double external CO₂ pressure to 0.00110 bar. Compare the open solution with the initially identical isolated no-headspace liquid.

   Show the answer and reasoning

   Open pH 7.91016767 and C_T=0.765908111 mmol L⁻¹; isolated pH and carbon stay at 8.20853259 and 0.748953896 mmol L⁻¹.

   Open neutral CO₂ exchange changes carbon at fixed alkalinity. The isolated liquid has no coupling to the external change.

3. Set both activity coefficients to one while keeping the listed concentrations and numerical K. Find the apparent SI.

   Show the answer and reasoning

   Apparent SI=+0.431363764, opposite in sign to the assigned activity result.

   The concentration-only product is 1.08×10⁻⁸ and ratio 2.70. This comparison tests the approximation, not an actual new composition.

4. Change only listed Cl⁻ to 1.80 mmol L⁻¹. Find the imbalance and a Na⁺ entry that mathematically closes it.

   Show the answer and reasoning

   Net −0.300 milliequivalents L⁻¹; Na⁺ 1.10 mmol L⁻¹ would close the ledger.

   It needs an additional 0.300 mmol L⁻¹ of positive monovalent charge. This does not prove that Na⁺ is the erroneous observation.

What to carry forward

• A total carbon pool differs from its separate acid–base forms.
• An open gas boundary and a closed carbon inventory impose different constraints.
• A saturation index needs activities and a compatible reaction constant.
• A closed analytical charge ledger need not prove equilibrium or measurement truth.