Weak acids are those acids which in solution does not dissociate completely. As acids (**Bronsted-Lowry / Arrhenius theories**), in solution they donate a proton to **H _{2}O (A is a generic counterion, that does not give hydrolysis):**

The acid dissociation constant is given by:

Take for example acetic acid, a very common weak acid:

In presence of water the acetic acid will dissociate into his constituents ions and , while in part will remain undissociated as:

Then we will have to find out the balance achieved in solution between the species , and . To calculate the pH we just need the equation of **Ka**:

We must therefore find as pH is equal to -log [H_{3}O^{+}].

We call **C _{a}** is the initial molar concentration of acid, before the dissociation in water. We denote instead with "

**X**" the amount of acid that dissociates.

If **X** **mol/L** of acetic acid dissociate, we will get **X** **mol/L** of **H _{3}O^{+}** and

**X**

**mol/L**

**CH**.

_{3}COO^{-} So we will have **X = [H _{3}O^{+}] = [CH_{3}COO^{-}]**

The concentration of **CH _{3}COOH** that remains undissociated will be (

**Ca**-

**X**)

**mol/L**

Substituting in the expression of the Ka:

This is a quadratic equation that we are perfectly able to solve. It can be however, further simplificated. Since we are dealing with a weak acid, we can suppose that for the most part it remains undissociated.

This means that we can say with good approximation that:

Our expression therefore becomes:

and given that **X** = **[H _{3}O^{+}]**

that, rearranged as a function of becomes:

It can be derived that the final formula to calculated calculate the pH is:

**pH calculation of a weak base**

The pH of a weak base can be calculated similarly, by the same steps and the same approximations. Firstly we calculate [**OH**^{- }]:

And consequently the pOH:

The pH will be simply found as: