Question

Given,${K_a}$ for $C{H_3}COOH$ is $1.8 \times {10^{ - 5}}$ and ${K_b}$ for $N{H_4}OH$ is $1.8 \times {10^{ - 5}}$.The $pH$ of ammonium acetate will be:
A. $7.005$
B. $4.75$
C. $7.0$
D. between $6$ and $7$

Answer 1

Hint:
Ammonium acetate is the salt formed between the reaction of acetic acid ($C{H_3}COOH$), an acid, and ammonium hydroxide ($N{H_4}OH$), a base. Thus, the $pH$ of ammonium acetate will be related to the dissociation constants of the acid and base, and is given by the $pH$ equation.
Formulas used: $pH = 7 + \dfrac{1}{2}\left[ {p{K_a} - p{K_b}} \right]$
Where $p{K_a}$ denotes the negative log of the acid dissociation constant (${K_a}$) and $p{K_{\mathbf{b}}}$ denotes the negative log of the base dissociation constant (${K_b}$).
That is, $p{K_a} = - \log ({K_a})$ and $p{K_a} = - \log {K_b}$

Complete step by step answer:
Ammonium acetate is the salt formed due to the neutralization reaction between acetic acid and ammonium hydroxide. The reaction is as follows:
$C{H_3}COOH + N{H_4}OH \rightleftharpoons C{H_3}COON{H_4} + {H_2}O$
Thus, the $pH$ of this solution can be given by the following equation:
$pH = 7 + \dfrac{1}{2}\left[ {p{K_a} - p{K_b}} \right]$
Where $p{K_a}$ denotes the negative log of the acid dissociation constant (${K_a}$) and $p{K_{\mathbf{b}}}$ denotes the negative log of the base dissociation constant (${K_b}$).
Here, in this question, we have the acid and base dissociation constants to be of equal value, since:
${K_a} = {K_b} = 1.8 \times {10^{ - 5}}$
Thus, if we take the negative logarithms on both sides,
$ - \log ({K_a}) = - \log ({K_b})$
But as we know, the negative logarithm of the acid dissociation constant is equal to $p{K_a}$ and the negative logarithm of the base dissociation constant is equal to $p{K_b}$. Hence, in this question:
$p{K_a} = p{K_b} \Rightarrow p{K_a} - p{K_b} = 0$
Substituting this value in our equation for $pH$, we get:
$pH = 7 + \dfrac{1}{2}\left[ 0 \right] = 7$
Hence, the $pH$ of the resulting ammonium acetate solution will be $7.0$.
Hence, the correct option to be marked is option C.

Note: The acid and base dissociation constants represent the relative strength of the acid and base respectively. Larger the value of ${K_a}/{K_b}$, stronger will be the acid/base.
 $pH$ stands for potential of hydrogen, and measures the concentration of hydrogen ions (${H^ + }$) in a solution. $pH$ of less than $7$ indicates an acidic solution, while more than $7$ indicates a basic solution. Note that the $7$, written as the first term in the $pH$ equation, indicates the $pH$ of pure water.