Negative P H - Calculations of PH - General Method

General Method

Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations. With three or more reagents or when many complexes are formed with general formulae such as A_pB_qH_r the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by and equilibrium constant, β.

Failed to parse (lexing error): =β_{pqr}^p^q^R

Next, write down the mass-balance equations for each reagent

Failed to parse (lexing error): C_A = + Σp β_{pqr}^p^q^r

Failed to parse (lexing error): C_B = + Σq β_{pqr}^p^q^r

Failed to parse (lexing error): C_H = + Σr β_{pqr}^p^q^r - K_w^{-1}

Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.

There are 3 non-linear simultaneous equations in the three unknowns, and . Because the equations are non-linear, and because concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations; for details see chemical equilibrium#Computer programs. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this formalism, is a key element in the determination of equilibrium constants by potentiometric titration.