text: A speciation calculation is one in which concentrations of all the species in an equilibrium system are calculated, knowing the analytical concentrations, T, T etc. of the reactants A, B etc. This means solving a set of nonlinear equations of mass-balance
  for the free concentrations [A], [B] etc. When the pH (or equivalent e.m.f., E).is measured, the free concentration of hydrogen ions, [H], is obtained from the measured value as   or </blockquote>and only the free concentrations of the other reactants are calculated. The concentrations of the complexes are derived from the free concentrations via the chemical model.
  Some authors include the free reactant terms in the sums by declaring identity (unit)  constants for which the stoichiometric coefficients are 1 for the reactant concerned and zero for all other reactants. For example, with 2 reagents, the mass-balance equations assume the simpler form.
  In this manner, all chemical species, including the free reactants, are treated in the same way, having been formed from the combination of reactants that is specified by the stoichiometric coefficients.
  In a titration system the analytical concentrations of the reactants at each titration point are obtained from the initial conditions, the burette concentrations and volumes. The analytical (total) concentration of a reactant R at the th titration point is given by
  where R is the initial amount of R in the titration vessel,  is the initial volume, [R] is the concentration of R in the burette and  is the volume added. The burette concentration of a reactant not present in the burette is taken to be zero.
  In general, solving these nonlinear equations presents a formidable challenge because of the huge range over which the free concentrations may vary. At the beginning, values for the free concentrations must be estimated. Then, these values are refined, usually by means of Newton–Raphson iterations. The logarithms of the free concentrations may be refined rather than the free concentrations themselves. Refinement of the logarithms of the free concentrations has the added advantage of automatically imposing a non-negativity constraint on the free concentrations. Once the free reactant concentrations have been calculated, the concentrations of the complexes are derived from them and the equilibrium constants.
  Note that the free reactant concentrations can be regarded as implicit parameters in the equilibrium constant refinement process. In that context the values of the free concentrations are constrained by forcing the conditions of mass-balance to apply at all stages of the process.