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A solution contains $0.2M$ $N{{H}_{4}}OH$ and $0.2M$ $N{{H}_{4}}Cl$ .If $1.0ml$ of $0.001M$ $HCl$ is added to it. What will be the $O{{H}^{-}}$ of the resulting solution $\left[ {{K}_{b}}=2\times {{10}^{-5}} \right]$ $?$
A.$2\times {{10}^{-5}}$
B.$5\times {{10}^{-10}}$
C.$2\times {{10}^{-3}}$
D.None of the above

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Last updated date: 20th Jun 2024
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Answer
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Hint:In this question, Henderson equation is used to calculate the value of $pOH$ which is further used to calculate the concentration of hydroxyl ions in the solution. Decrease in dissociation constant of an acid will increase the value of $pOH$ .

Complete step by step answer:
Here, it is given that the concentration of $N{{H}_{4}}OH$ is $0.2M$
The concentration of $N{{H}_{4}}Cl$ is $0.2M$
The concentration of $HCl$ is $0.001M$
The dissociation constant of a base is $2\times {{10}^{-5}}$
${{K}_{b}}=2\times {{10}^{-5}}$
$p{{K}_{b}}=-\log {{K}_{b}}$
Substituting the value in above formula we get,
$p{{K}_{b}}=-\log \left( 2\times {{10}^{-5}} \right)$
$p{{K}_{b}}=5-\log 2$
If we apply the Henderson equation ,
$pOH=p{{K}_{b}}+\log \left[ \dfrac{S}{B} \right]$
Where, $pOH$ is the basicity level
$p{{K}_{b}}$ is the dissociation constant of a base
$S$ is the concentration of salt
$B$ is the concentration of base
Now, if we substitute the values in the above formula we get,
$pOH=5-\log 2+\log \left[ \dfrac{0.2}{0.2} \right]$
$pOH=5-\log 2$
$\left[ O{{H}^{-}} \right]=2\times {{10}^{-5}}$
Therefore, the correct option is A.

Additional information
-$pH$ is defined as the scale to measure the acidity and basicity of an aqueous solution or liquid. The $pH$ before seven considers an acid and $pH$ after seven considers as a base.
-${{K}_{b}}$ is defined as the dissociation constant of a base. If the value of dissociation constant of a base is high then it is a strong base whereas if the value of the dissociation constant of base is low then it is a weak base.
Buffers consist of salt of conjugate base and acid. It is of two types:
A.Simple buffer- it is defined as a salt of weak acid and weak base.
B.Mixed buffer- it can be acidic and it can be basic.

Note:
The concentration of hydroxyl ions is calculated through the value of $pOH$ .If the value of $p{{K}_{b}}$ is lower then it is a weak base otherwise if the value of $p{{K}_{b}}$ is higher than it is a strong base.