Calculations of PH
The calculation of the pH of a solution containing acids and/or bases is an example of a chemical speciation calculation, that is, a mathematical procedure for calculating the concentrations of all chemical species that are present in the solution. The complexity of the procedure depends on the nature of the solution. For strong acids and bases no calculations are necessary except in extreme situations. The pH of a solution containing a weak acid requires the solution of a quadratic equation. The pH of a solution containing a weak base may require the solution of a cubic equation. The general case requires the solution of a set of non-linear simultaneous equations.
A complicating factor is that water itself is a weak acid and a weak base. It dissociates according to the equilibrium
- 2H2O H3O+(aq) + OH-(aq)
with a dissociation constant, Kw defined as
- Kw =
where stands for the concentration of the aquated hydronium ion and represents the concentration of the hydroxide ion. Kw has a value of about 10−14 at 25°C, so pure water has a pH of about 7. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.
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