Editing PH (section)

=== General method ===
Some systems, such as with [[polyprotic]] acids, are amenable to spreadsheet calculations.<ref>{{cite book |last1=Billo |first1=E.J. |title=EXCEL for Chemists |publisher=Wiley-VCH |year=2011 |isbn=978-0-470-38123-6 |edition=3rd}}</ref> With three or more reagents or when many complexes are formed with general formulae such as A<sub>p</sub>B<sub>q</sub>H<sub>r</sub>, the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, ''β''.
: <math chem="">[\ce{A}_p\ce{B}_q\ce{H}_r] =\beta_{pqr}[\ce A]^{p}[\ce B]^{q}[\ce H]^{r}</math>

Next, write down the mass-balance equations for each reagent:
: <math chem="">\begin{align}
C_\ce{A} &= [\ce A] + \Sigma p \beta_{pqr}[\ce A]^p[\ce B]^q[\ce H]^{r} \\
C_\ce{B} &= [\ce B] + \Sigma q \beta_{pqr}[\ce A]^p[\ce B]^q[\ce H]^r \\
C_\ce{H} &= [\ce H] + \Sigma r \beta_{pqr}[\ce A]^p[\ce B]^q[\ce H]^r - K_w[\ce H]^{-1}
\end{align}</math>

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 three [[simultaneous equation]]s in the three unknowns, [A], [B] and [H]. Because the equations are non-linear and their 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. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this approach, is a key element in the [[determination of equilibrium constants]] by [[potentiometric titration]].