Question

How do you calculate the $pH$ of an acid base mixture?

Answer 1

A mixture of acid base contains unequal amounts of acid and base, and it cannot be assumed that the concentration of the both are equal in the mixture.
So for the calculation of $pH$ of such mixture, we would use the concentration of the protons in the solution, which would give the precise value of $pH$.

Complete step-by-step answer: Before establishing the formula which tells us how to calculate the $pH$ of an acid base mixture, we must know what acid and bases are and what the word $pH$ means.
So, acid and bases have three definitions which all could define the same thing in terms of different basic concepts. The first definition consists of protons and hydroxide ions. The substances which liberate protons, when they are exposed to aqueous solutions, are called acids, for example hydrochloric acid. Similarly the ones which liberate hydroxide ions, with the addition of water, they are termed as bases, example, sodium hydroxide.
The next definition would be, in terms of protons only. The definition of acid remains the same, as they liberate protons and form hydronium ions in aqueous solutions, for example phosphoric acid. And as far as the definition of base is concerned, it can be defined as the species which accepts protons for example, ammonia.
Now, the third and last definition takes in account the number of electrons accepted and donated by the species. So, the acids are the species which accept electrons, and the bases are the ones which donates them.
The $pH$ of a solution tells us about the acidity or the basicity of a given solution. It is a scale which ranges from $1-14$ where $1$ is the most acidic and $14$ is the most basic. As you may have guessed the $7$ is the neutral value which is present in the middle of both. And $pOH$ tells us the same but in terms of hydroxide ion concentration.
So, the value of sum of $pH$ and $pOH$ is $14$, which could be written as,
$pH+pOH=14$
And also, the $pH$ of a solution can be expressed in terms of concentration of hydronium ions, which is,
$pH=-lo{{g}_{10}}[{{H}_{3}}{{O}^{+}}]$
Which is the required answer.

Note: The $pH$ of a solution takes in account the concentration of the protons which are liberated by the acid and maybe taken up by the base, meaning, the concentration of protons which remains in the solution, tells us about the $pH$ of the solution.
With increase in the proton or hydronium concentration in the solution, the lesser will be the value of $pH$.