Question

What is the pH of a solution that has a hydronium ion concentration of $1\times {{10}^{-4}}M$ ?

Answer 1

We must be well known with the concepts of acids and bases before solving the respective question. It is states as the pH is the negative log of concentration of hydronium ion i.e.
$pH=-\log \left[ {{H}_{3}}{{O}^{+}} \right]$

Complete answer:
Let us learn about the concepts of hydronium ion and the pH relationship;
The hydronium ion is produced when the two molecules of water collide or when the dissociation of a single molecule of water happens. We can illustrate this simply by;
${{H}_{2}}O+{{H}_{2}}O\to {{H}_{3}}{{O}^{+}}+O{{H}^{-}}$ or ${{H}_{2}}O\to {{H}^{+}}+O{{H}^{-}}$
The pH of the solution is calculated with respect to the concentration of hydronium ions present. It is denoted as stated above i.e.
$pH=-\log \left[ {{H}_{3}}{{O}^{+}} \right]$
Now, from this we can illustrate the given problem as;
Given,
Concentration of hydronium ions = $\left[ {{H}_{3}}{{O}^{+}} \right]=1\times {{10}^{-4}}M$
Putting into the formula, we get;
$\begin{aligned} & pH=-\log \left[ 1\times {{10}^{-4}} \right] \\\ & pH=4 \\\ \end{aligned}$
Thus, the pH of a solution that has a hydronium ion concentration of $1\times {{10}^{-4}}M$ is 4.

Note:
Do note that the $pH=p{{H}_{3}}{{O}^{+}}$ as the hydrogen ions attach to the water molecules to form hydronium ions as stated above. Also, one notable point to be understood is as follows;
$pH+pOH=14$