Question

A solution has a $pH$ = 10. What is the $\left[ {O{H^ - }} \right]$?
A.$1 \times {10^{ - 4}}$M
B.$1 \times {10^{ - 10}}$M
C.$1 \times {10^{ - 2}}$M
D.$1 \times {10^{ - 6}}$M

Answer 1

To calculate the $\left[ {O{H^ - }} \right]$ of a solution we need to know the $\;pOH$ . The $\;pOH$ can be calculated using the expression:
$pH{\text{ }} + {\text{ }}pOH{\text{ }} = {\text{ }}14$
Then $\left[ {O{H^ - }} \right]$ can be calculated by using:
$pOH{\text{ }} = \;{\text{ }} - {\text{log}}[O{H^ - }]$

Complete step by step answer:
In aqueous solution, an acid is a substance which increases the concentration of $[{H^ + }]$ and a base increases the concentration of $[O{H^ - }]$. The concentration of these ions varies over a wide range.
So to avoid dealing with such a wide range of ion concentration, scientists have converted these concentrations into $pH$ and $pOH$.
Where $pH$ is negative log of $[{H^ + }]$ ions concentration and $pOH$ is negative log of $[O{H^ - }]$ ions concentration.
According to the given question
$pH$ = 10
Therefore we know that, the sum of $pH$ and $pOH$ is 14

\Rightarrow pH{\text{ }} + {\text{ }}pOH{\text{ }} = {\text{ }}14 \\\ \Rightarrow pOH = 4 \\\

Now $[O{H^ - }]$ can be calculated as follows,

$pOH{\text{ }} = \;{\text{ }} - {\text{log}}[O{H^ - }] \\\ \Rightarrow [O{H^ - }] = {10^{ - pOH}} \\\ \Rightarrow [O{H^ - }] = {10^{ - 4}} = 1 \times {10^{ - 4}} \\\$

Therefore, the $\left[ {O{H^ - }} \right]$ ion concentration in the given solution is $1 \times {10^{ - 4}}$ M
Thus, option A is the correct answer.

Additional Information:
Converting $[{H^ + }]$ to $pH$, is a convenient way to relate the acidity or basicity of a solution. The $pH$ scale allows us to differentiate substances easily by their $pH$ value.
The $pH$ scale is a negative log scale of concentration of $[{H^ + }]$. The log part indicates that the$pH$ changes by 1 unit for every power of 10 change in concentration of $[{H^ + }]$. The negative sign with log tells that $pH$ and $[{H^ + }]$ are inversely related. When $pH$ Increases $[{H^ + }]$ decreases, and when $pH$ decreases $[{H^ + }]$ increases.

Note:
For aqueous solutions at $25^\circ C$:
$pH$= 7, It is called a Neutral solution.
$pH$< 7, It is called an Acidic solution.
$pH$> 7, It is called a Basic solution.
The lesser the $pH$ value, more acidic the solution will be and higher the $pH$ value, more basic the solution will be.