Question

${\rm{p}}{{\rm{K}}_{\rm{a}}}$ of a weak acid (HA) and ${\rm{p}}{{\rm{K}}_{\rm{b}}}$ of a weak base (BOH) are $3.2$ and $3.4$, respectively. The pH of their salt (AB) solution is:
A. ${\rm{6}}{\rm{.9}}$
B. ${\rm{7}}{\rm{.0}}$
C. ${\rm{1}}{\rm{.0}}$
D. ${\rm{7}}{\rm{.2}}$

Answer 1

We know that the pH value is generally explained as the potential of the hydrogen ion. The ${{\rm{H}}^{\rm{ + }}}$ indicates the pH value of the acid solution and ${\rm{O}}{{\rm{H}}^ - }$ generally indicates the pOH value of the base or alkaline aqueous solution. The addition of pH and pOH is normally equivalent to the value that is$14$.

Complete solution
We have the given values as shown below:
The ${\rm{p}}{{\rm{K}}_{\rm{a}}}$ of weak acid that is HA is $3.2$.
The ${\rm{p}}{{\rm{K}}_{\rm{b}}}$ of weak base that is BOH is $3.4$.
We all know that, when the weak acid and weak base is given, then the pH of their salt solution can be calculated by using the formula as shown below.
${\rm{pH}} = 7 + \dfrac{1}{2}{\rm{p}}{{\rm{K}}_{\rm{a}}} - \dfrac{{\rm{1}}}{{\rm{2}}}{\rm{p}}{{\rm{K}}_{\rm{b}}}$
Where, pH is the potential of hydrogen, ${\rm{p}}{{\rm{K}}_{\rm{a}}}$ is the acid dissociation constant of weak acid, and ${\rm{p}}{{\rm{K}}_{\rm{b}}}$ is the base dissociation constant of weak base.
Now, substitute the respective values in the above equation.
$\Rightarrow {\rm{pH}} = 7 + \dfrac{1}{2} \times {\rm{3}}{\rm{.2}} - \dfrac{{\rm{1}}}{{\rm{2}}} \times {\rm{3}}{\rm{.4}}\\\ \Rightarrow {\rm{pH}} = 7 + 1.6 - 1.7\\\ \Rightarrow {\rm{pH}} = 8.6 - 1.7\\\ \Rightarrow {\rm{pH}} = 6.9$
Thus, the obtained pH value of their salt of acid base solution that is AB is ${\rm{6}}{\rm{.9}}$.

**Hence, the correct option for this question is A that is ${\rm{6}}{\rm{.9}}$.

Note: **
The pH scale is generally utilized for showing the value of acidity and basicity of the aqueous solution. The solution is said to be acidic when the value is below seven while the solution is said to be basic when it has value above seven. At seven, the solution is neutral; there will be no acidic and basic character present in it.