equations in three unknowns. When an acid is dissolved in water CA = CH = Ca, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained. Solution of this quadratic equation gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in an ICE table which can also be used to calculate the pH when some additional (strong) acid or alkaline has been added to the system, that is, when CA ≠ CH. For example, what is the pH of a 0.01M solution of benzoic acid, pKa = 4.19? Step 1: Step 2: Set up the quadratic equation. Step 3: Solve the quadratic equation. For alkaline solutions an additional term is added to the mass-balance equation for hydrogen. Since addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to In this case the resulting equation in [H] is a cubic equation. 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 ApBqHr,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. Next, write down the mass-balance equations for each reagent: 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, [A], [B] and [H]. 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. 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. See also pH indicator Arterial blood gas Chemical equilibrium p pKa References External links Acid–base chemistry Equilibrium chemistry Units of measurement Water quality indicators Logarithmic scales of measurement General chemistry