Question

${{2g}}$ of ${{NaOH}}$ is dissolved in water to make ${{1L}}$ solution. What is ${{pH}}$ of solution?

Answer 1

Hint:${{pH}}$ explains about the acidity or basicity of a solution. It has a range from $0 - 14$. We know that ${{pH}}$ is the negative logarithm of ${{{H}}^ + }$ ions. This is applicable to acids only. ${{NaOH}}$ is a very strong base. In the case of bases, ${{pOH}}$ is used.

Complete step by step answer:
It is given that the mass of ${{NaOH}}$, ${{{m}}_{{{NaOH}}}} = 2{{g}}$
Volume of solution, ${{V = 1L}}$
Molar mass of ${{NaOH}}$, ${{{M}}_{{{NaOH}}}} = 23 + 16 + 1 = 40{{g}}.{{mo}}{{{l}}^{ - 1}}$
When ${{NaOH}}$ is dissolved in water, it dissociates into its constituent ions. The chemical reaction is given below:
${{NaOH}} \to {{N}}{{{a}}^ + } + {{O}}{{{H}}^ - }$
From the given data, we can calculate the number of moles of ${{NaOH}}$.
Number of moles of ${{NaOH}}$, ${{{n}}_{{{NaOH}}}} = \dfrac{{{{{m}}_{{{NaOH}}}}}}{{{{{M}}_{{{NaOH}}}}}} = \dfrac{2}{{40}} = 0.05{{mol}}$
We know that the molarity is the number of moles of solute, i.e. ${{NaOH}}$ in one litre of solution. Thus it can be calculated by dividing the number of moles of ${{NaOH}}$ by ${{1L}}$.
i.e. Molarity, ${{M = }}\dfrac{{0.05}}{1} = 0.05{{M}}$
It denotes that the concentration of ${{O}}{{{H}}^ - }$ ions is ${{0}}{{.05M}}$, i.e. $\left[ {{{O}}{{{H}}^ - }} \right] = 0.05{{M}}$
Therefore, \[{{pOH = - log}}\left[ {{{O}}{{{H}}^ - }} \right]\]
On substituting the value of concentration of ${{O}}{{{H}}^ - }$ ions, we get
\[{{pOH = - log}}0.05 = 1.301\]
We have to find ${{pH}}$ of the solution. We know that ${{pH + pOH = 14}}$
i.e. ${{pH + 1}}{{.301 = 14}} \Leftrightarrow {{pH = 12}}{{.699}} \sim {{12}}{{.7}}$

Thus the ${{pH}}$ of the solution is $12.7$.

Additional information:
When the ${{pH}}$ value is low, then the ${{{H}}^ + }$ concentration is very high. At the same time, when the ${{pH}}$ value is high, then the ${{{H}}^ + }$ concentration is very low or ${{O}}{{{H}}^ - }$ concentration is very high. ${{pH}}$ is usually measured using ${{pH}}$ strips, ${{pH}}$ indicators and ${{pH}}$ meter.

Note:
Generally, acids have ${{pH}}$ value which ranges from $0 - 6$ and bases have ${{pH}}$ value which ranges from $7 - 14$. Thus from the ${{pH}}$ value we obtained, we can conclude that the compound is a base. While neutral compounds like water have a ${{pH}}$ value of $7$.