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

Hint: 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.