Question

The ${\text{p}}{{\text{K}}_{\text{a}}}$ value of acetic acid ${\text{p}}{{\text{K}}_{\text{b}}}$ value of ammonium hydroxide are $4.76$ and $4.75$ respectively. Calculate the ${\text{pH}}$ of ammonium acetate solution.
A. $6.02$
B. $7.005$
C. $8$
D. $5.602$

Answer 1

Hint: ${\text{pH}}$ means power of hydrogen. It is the negative log of proton concentration. Similarly, ${\text{p}}{{\text{K}}_{\text{a}}}$ is the negative log of ${{\text{K}}_{\text{a}}}$ value. ${{\text{K}}_{\text{a}}}$ value is referred to the equilibrium constant of acid or acid dissociation constant and ${{\text{K}}_{\text{b}}}$ is the equilibrium constant of base or base dissociation constant. They are used to determine the ability to donate or accept the protons.

Complete step by step answer:
${\text{p}}{{\text{K}}_{\text{a}}}$, ${\text{p}}{{\text{K}}_{\text{b}}}$ and ${\text{pH}}$ are used to measure the strength of acids and bases. It tells how acidic or basic the solution is.
${\text{p}}{{\text{K}}_{\text{a}}}$ and ${\text{p}}{{\text{K}}_{\text{b}}}$ have a simple relation which is shown below:
${\text{p}}{{\text{K}}_{\text{a}}} + {\text{p}}{{\text{K}}_{\text{b}}} = 14$
Ammonium acetate is a salt formed by reacting acetic acid with ammonium hydroxide. Both acid and base are weak. Thus maximum hydrolysis occurs since both are very reactive in water.
Thus ${\text{pH}}$ can be written as:
${\text{pH}} = 7 + \dfrac{1}{2}\left( {{\text{p}}{{\text{K}}_{\text{a}}} - {\text{p}}{{\text{K}}_{\text{b}}}} \right)$
Substituting the values of ${\text{p}}{{\text{K}}_{\text{a}}}$ and ${\text{p}}{{\text{K}}_{\text{b}}}$, we get
${\text{pH}} = 7 + \dfrac{1}{2}\left( {4.76 - 4.75} \right) = 7 + \dfrac{{0.01}}{2} = 7 + 0.005 = 7.005$
Since the ${\text{pH}}$ is almost equal to $7$, the product formed is neutral.
Hence the option B is correct.

Additional information:
When ${\text{p}}{{\text{K}}_{\text{a}}} > {\text{p}}{{\text{K}}_{\text{b}}}$, solution will be alkaline. It is because the acid will be weaker than base. Thus ${\text{pH}}$ value will be more than $7$.
When ${\text{p}}{{\text{K}}_{\text{a}}}{\text{ < p}}{{\text{K}}_{\text{b}}}$, solution will be acidic because acid is comparatively stronger than base. Thus ${\text{pH}}$ value will be less than $7$.

Note:
In a chemical reaction, when acid is stronger than base, the solution is acidic. When the base is stronger than acid, the solution is basic. When both the acid and base are either strong or weak, the solution will be neutral.