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 H2O (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 [H3O+].
We call Ca 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 H3O+ and X mol/L CH3COO-.
So we will have X = [H3O+] = [CH3COO-]
The concentration of CH3COOH 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 = [H3O+]
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: