Question

The $pH$ of ${10^{ - 4}}M\,KOH$ solution will be:
A. $4$
B. $11$
C. $10.5$
D. $10$

Answer 1

pH is the measurement of acidic or basic property of a solution.
pH of a solution is the negative logarithm of ${H^ + }$ ion concentration of the solution.
$pH + pOH = 14$

Complete step by step answer:
pH is a measure of acidic or basic characteristic of a solution. $pH$ of a solution is defined as the negative logarithm of ${H^ + }$ ion concentration of the solution.
The aqueous solution of $KOH$ gives rise to two ions i.e., ${K^ + }$ and $O{H^ - }$.
$KOH \rightleftharpoons {K^ + } + O{H^ - }$
Since, the concentration of KOH is ${10^{ - 4}}M$, the concentration of ${K^ + }$ is ${10^{ - 4}}M$and concentration of $O{H^ - }$ is also ${10^{ - 4}}M$.
We know that the product of concentration of ${H^ + }$ and $O{H^ - }$ is always equal to ${10^{ - 14}}$ at room temperature.
Or, $[{H^ + }][O{H^ - }] = {10^{ - 14}}$
$[{H^ + }]$ is the concentration of ${H^ + }$ ion and $[O{H^ - }]$ is the concentration of $O{H^ - }$ ion.
Now, $[{H^ + }] = \dfrac{{{{10}^{ - 14}}}}{{[O{H^ - }]}} = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 4}}}} = {10^{ - 10}}$
$pH = - \log [{H^ + }] = - \log ({10^{ - 10}}) = 10$
Alternatively, we know that, $pH + pOH = 14$
Here, concentration of $O{H^ - }$ ion =$[O{H^ - }]$=${10^{ - 4}}M$
So, $pOH = - \log [O{H^ - }] = - \log ({10^{ - 4}}) = 4$
$\Rightarrow pH = 14 - pOH = 14 - 4 = 10$
pH of $KOH$ is $10$ which implies that $KOH$ has basic property.
Hence, the correct answer is (D).

Note:
$pH$ stands for. The pH value is measured from $0$ to $14$. pH value of pure water at normal temperature is$7$. The pH value less than $7$ denotes the acidic properties of the solution and pH greater than $7$ denotes the basic properties of the solution.