Theory of interaction intensities, buffer capacities, and pH stability in aqueous systems, with application to the pH of seawater and a heterogeneous model ocean system

The choice of convenient basic constituents for evaluating pH stability of aqueous systems is discussed, and two useful interaction parameters are defined and related to the buffer capacity: the interaction capacity, δ′_X,Y= ∂pX ∂TOTY, and the interaction intensity, δ_{X, Y} = ∂pX ∂pTOTY; for pH and TOTH, δ′_{H, H} = -β_H^-1, where β_H is the pH buffer capacity. A method is presented for the computation of exact values of all interaction capacities and intensities through inversion of the Jacobian matrix of the system of non-linear equations describing the aqueous system. The major species of an aqueous system (H₂O, H⁺, solid phases, gases, and the most abundant solute species) are shown to constitute a useful set of basic constituents for evaluation of approximate pH buffer capacities according to a simple rule: the major-minor species rule for zeroth order pH-TOTH interaction. The concepts of buffering and pH-statting are examined and contrasted; it is demonstrated that the buffer capacity of an aqueous system cannot be infinite: it is limited by the concentration of solutes in solution. The effect upon pH of variations in constituents other than H⁺ is described in terms of first order interactions via complex formation and solid formation; approximate formulas for calculation are derived. Higher order interactions are derived from combinations of first order ones. The pH stability of the ocean system is examined in terms of an aqueous phase model including ion-association reactions and a heterogeneous model incorporating CO₂ in the gas phase, quartz, kaolinite, calcite, chlorite, and illite, in addition to the aqueous phase. There is an approximately three-fold enhancement of buffer capacity in the aqueous model as a consequence of ion-association. Only a few interaction pathways are of quantitative significance in establishing the buffer capacity. Results for the heterogeneous ocean model lend quantitative support to Sillén's notion of pH stability: the buffer capacity is about four hundred times greater than that of the aqueous phase model.