Calculate pH of 0.001M solution of benzoic acid, pK_a=4.19.

We will start with the simplified formula 8.13.

From formula we get [H⁺]=2.54×10^-4 M and pH=3.60. Is it correct? To be sure we have to check if the 5% rule is obeyed, that is if the dissociation fraction is less than 5%.

Dissociated acid concentration is the same as [H⁺], thus dissociation fraction is 2.54×10^-4/0.001 - above 25%. We can't use simplified formula 8.13! We have to use more precise equation 8.10:

This time we get pH=3.65, exactly the same result as from our pH calculator.