Question

The $pH$ value of $\dfrac{N}{{10}}$​ $NaOH$ is:

(A) 9
(B) 10
(C) 12
(D) 13

Answer 1

The $pH$ value of a substance is directly related to the ratio of hydrogen ion $[{H^ + }]$ and hydroxyl ion $[O{H^ - }]$ concentrations. If the $[{H^ + }]$ concentration is greater than the $[O{H^ - }]$, the material is acidic in nature. i.e., the$pH$ value is less than $7$.

Explanation: The $pH$ scale has been selected with values between $0$ and $14$ corresponding to hydrogen ion concentration of $1mold{m^{ - 3}}$ and $10 - 14$ $mold{m^{ - 3}}$. Acknowledgement of the $pH$ value of a solution gives a value for the hydrogen ion $[{H^ + }]$ concentration of that particular solution.
The determination of the hydrogen ion $[{H^ + }]$ concentration inside a weak acids from $pH$ values will not give the real concentration of the weak acid as directly but if the degree of ionization of that particular is known then the concentration can be determined

Complete step-by-step solution: Write the relationship between the molarity and normality for a base as ${\text{Molarity = Acidity }} \times {\text{ Normality}}$ .
Sodium hydroxide is a monoacidic base as one molecule of sodium hydroxide dissociates to give only one hydroxide ion.
Thus, for sodium hydroxide, ${\text{Molarity = 1 }} \times {\text{ Normality = Normality}}$

Here the Molarity of the $NaOH$ is given by, $\dfrac{N}{{10}}$ i.e,$0.1MNaOH$
$NaOH$ is a strong base. So, its concentration is given by $NaOH = 0.1M$
So now the concentration of $[O{H^ - }]$ is given by,
$[O{H^ - }] = 0.1M = {10^{ - 1}}M$
So the Concentration of $[{H^ + }]$ and $[O{H^ - }]$ is given by,
$[{H^ + }][O{H^ - }] = {10^{ - 14}}M$
So, $[{H^ + }] = \dfrac{{{{10}^{ - 14}}}}{{[O{H^ - }]}} = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 1}}}}$
$[{H^ + }] = {10^{ - 13}}$
For calculating the value of $pH$,
So, $pH = - \log [{H^ + }] = - \log [{10^{ - 13}}]$
$pH = 13$

Therefore, the correct answer is option (D),13.

Note: pH is a unit of measure which describes the degree of acidity or alkalinity of a solution. It is measured on a scale. The term $pH$ is abbreviated from “” which is the mathematical symbol for negative logarithm, and “” which is the chemical symbol for Hydrogen. The definition of $pH$ is the negative logarithm of Hydrogen ion $[{H^ + }]$ activity i.e., $pH = - \log \left[ {{H^ + }} \right]$
$pH$ gives needful quantity information by expressing the scale number of activity of an acid or base in terms of its hydrogen ion $[{H^ + }]$ activity.