Question

What is the hydroxide concentration of a solution at a pH of $10$ at ${25^o}C$ ?
A. ${10^{ - 14}}M$
B. ${10^{ - 10}}M$
C. ${10^{ - 7}}M$
D. ${10^{ - 4}}M$

Answer 1

Hint: The pH takes into consideration only the hydrogen ions present in a solution that is it will measure the acidity of a solution. It is required to find the hydroxide ions, that is we have to measure the basicity of the solution. For this we have to find the pOH.

Formula used: $pH + pOH = 14$
$pH = - \log \left[ {{H^ + }} \right]$
$pOH = - \log \left[ {O{H^ - }} \right]$
The pH is the measure of acidity
$pOH$ is the measure of basicity. $\left[ {O{H^ - }} \right]$ is also the concentration.
$\left[ {{H^ + }} \right]$ is the concentration.

Complete step by step answer:
We know that the pH is $10$ . therefore, plugging it in the equation we get,
$pH + pOH = 14$
$10 + pOH = 14$
Taking $10$ to the other side we get,
$ \Rightarrow pOH = 14 - 10$
$ \Rightarrow pOH = 4$
The pH can be defined as the measure of concentration of hydrogen ions present in a solution, that is it is the negative logarithm of the concentration of hydrogen ions. This can be represented as follows:
$pOH = - \log \left[ {O{H^ - }} \right]$
Substituting the value of pOH from the question in this equation,
$4 = - \log \left[ {O{H^ - }} \right]$
$ \Rightarrow - 4 = \log \left[ {O{H^ - }} \right]$
Taking antilog of the other side, we get,
$ \Rightarrow Anti\log \left( { - 4} \right) = \left[ {O{H^ - }} \right]$
$ \Rightarrow {10^{ - 4}} = \left[ {O{H^ - }} \right]$
Therefore, the concentration of hydroxide ions is ${10^{ - 4}}M$ .
Therefore, the solution is basic since the pH of the solution is more than $7$ . Therefore, we can conclude that the hydroxide ions present in the solution is more than the hydrogen ions.

So, the correct answer is Option D.

Note: Tf the pH of the solution is more than $7$ we can say that the solution is basic. The relation between the pH and pOH is $pH + pOH = 14$ . pOH is the measure of the concentration of hydroxide ions in a solution.