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Given, ${K_a}$ for $HCN$ is $5 \times {10^{ - 10}}$ at ${25^\circ }C$ . For maintaining a constant $pH$ of 9, the volume of $5M\,KCN$ solution required to be added to $10ml\,of\,2M\,HCN$ solution is:
(A) $2ml$
(B) $4ml$
(C) $7ml$
(D) $9ml$

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Last updated date: 13th Jul 2024
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Answer
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Hint: In order to this question, to find the volume of the given quantity of solution, we will apply the formula to find the $pH$ , that’s how we will find the volume. And then we will also explain the type of solution with respect to this question.

Complete answer:
As we know that- $HCN$ and $KCN$ will form a buffer solution.
Now, we will apply the formula of $pH$ :
$pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}}$
$\Rightarrow pH = - \log 5 \times {10^{ - 10}} + \log [\dfrac{{5 \times V}}{{V + 10}}/\dfrac{{10 \times 2}}{{V + 10}}]$
$\Rightarrow 9 = - \log 5 \times {10^{ - 10}} + \log \dfrac{V}{4}$
$\therefore V = 2ml$

Hence, the correct option is (A) $2ml$ .

Additional Information:-
The buffer solution is a solution able to maintain its Hydrogen ion concentration $(pH)$ with only minor changes on the dilution or addition of a small amount of either acid or base. Buffer Solutions are used in fermentation , food preservatives, drug delivery, electroplating, printing, the activity of enzymes, blood oxygen carrying capacity need specific hydrogen ion concentration $(pH)$ .

Note:
 When a small amount of strong acid or base is applied to it, the $pH$ changes very little, and it is therefore used to avoid a solution's $pH$ shift. Buffer solutions are used in a variety of chemical processes.