Question

The $p{{K}_{a}}$ of acetic acid and $p{{K}_{b}}$ of ammonium hydroxide are 4.76 and 4.75 respectively. The pH of the resulting solution is made by mixing 100 ml each of 0.1M acetic acid and 0.1 M ammonium hydroxide.
A. 3
B. 7.005
C. 6.5
D. 14

Answer 1

Hint: The resulting solution that will be made after mixing ammonium hydroxide and acetic acid is ammonium acetate. Here is the mixture of ammonium hydroxide a weak base and acetic acid a weak acid. Formula to find pH,
\[pH=7+\dfrac{1}{2}\left[ p{{K}_{a}}-p{{K}_{b}} \right]\]

Complete step by step answer:
From your chemistry lessons you have learned about salt hydrolysis. Salt hydrolysis is a reaction in which the anion or cation or both of a salt react with water to show alkalinity or acidity.
For this question we are going to deal with the salt of weak acid and weak base.
In this case maximum hydrolysis takes place because maximum hydrolysis is seen when both anion as well as cation are reactive and they react with water, so they can produce ${{H}^{+}}$ and OFT ions. Solution is usually neutral but if both the reaction takes place at slightly different rates then it can be either slightly acidic or basic.
The acids and base given in the question are weak acid and weak base.
 Ammonium hydroxide $(N{{H}_{4}}OH)$ is a weak base and acetic acid $(C{{H}_{3}}COOH)$ is a weak acid and both of them react to form salt of ammonium acetate $(C{{H}_{3}}COON{{H}_{4}})$ and water.
So, the reaction that will take place is,

\[C{{H}_{3}}COOH+N{{H}_{4}}OH\rightleftharpoons C{{H}_{3}}COON{{H}_{4}}+{{H}_{2}}O\]
So, we have a formula to find the pH of salt of weak acid and weak base which is given as,

\[pH=7+\dfrac{1}{2}\left[ p{{K}_{a}}-p{{K}_{b}} \right]\]………………… (1)
In the question some of the value are given such as,
      \[p{{K}_{a}}\]of acetic acid = 4.76
\[p{{K}_{b}}\] of ammonium hydroxide = 4.75
Here, we have to find the of pH ammonium acetate (salt),

\[pH=7+\dfrac{1}{2}\left[ 4.76-4.75 \right]=7+\dfrac{1}{2}\times 0.1=7.005\]
So, the correct answer is “Option B”.

Note: Salt hydrolysis is the reverse of the neutralization process. In the reaction acetic acid and ammonium hydroxide combine in 1:1 ratio because the concentration of both acid and base are same i.e, 100ml of 0.1 M acetic acid and 100 ml of 0.1 M ammonium hydroxide. pH can also be find in term of concentration using the formula,

\[pH=7+\dfrac{1}{2}\left[ p{{K}_{a}}-\log C \right]\]