How to calculate fraction ionized of a weak acid in solution

A monoprotic weak acid (HA) partially ionize when dissolved in water to produce hydronium ions (H₃O⁺) and the conjugate base (A^-) as described in the following chemical equation. 

                                                                    HA + H2O ↔ H₃O⁺ + A^-

At equilibrium, the concentration of the conjugate base (A^-) depends on the following factors:

1. Concentration of the unionized form of the acid (HA).

2. Concentration of the hydronium ion (H₃O⁺) in solution, (i.e. pH of the solution).

3. Ka of the acid.

The relation between the concentration of the ionized form and the above mentioned factors is shown in the following equations:

Keep in mind that [A^-] +  [HA] = Ca

Where Ca is the initial concentration (before any dissociation) of the acid dissolved in solution. Thus, the fraction ionized (α) can be expressed as the following equations show:

So the fraction ionized of a dissolved monoprotic weak acid depends only on Ka and the pH of the solution. The fraction unionized of the acid is equal to 1 - α.

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