,

,

,

.

The expressions for the fraction of an acid in each form (,, , , ) as a function of pH are obtained by taking account of the equilibrium constant and the mass balance. The fraction of molecules in a certain species is called , where is the number of hydrogens on the undissociated acid molecule and is the number of dissociated hydrogen ions. These are calculated as follows:

,

where

and

.

Moreover, the concentration (M) of the generic species is given by:

,

where is the total concentration of the undissociated acid set to 0.1.

When "fractional composition diagram" is selected, you can change the , , and controls to observe the variation of the values as a function of pH. By changing the pH control, you will obtain the individual values, as highlighted by the dots on the diagram.

When "fractional composition bar chart" is selected, you can change the , , , and pH controls to see the resultant species concentration variations at equilibrium, where the sum of the species concentrations equals . Further, we show the of the different addends in , which accounts for the approximations often used in calculations [1].