Answer
405.3k+ views
Hint: Here in the question we can observe that we are given a mixture of weak acid $HCN$ and a salt of it that is $KCN$ . So it is an acidic buffer. In an acidic buffer the $pH$remains constant. $KCN$ is formed when $HCN$ reacts with $KOH$.
Complete step by step answer: As in the question we are given the ${K_a}$ for $HCN$ at $25^\circ C$ that is $5 \times {10^{ - 10}}$. The $pH = 9$ is constant. For an acidic buffer we can write $ \Rightarrow pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}}$.
Here $[salt]$ i s the concentration of salt , that is $KCN$. $[acid]$ is the concentration of acid that is $HCN$. Let the volume of $KCN$ added be $v$$ml$. The total volume of the solution will be $V = (v + 10)ml$. Total moles of $KCN$ will be $5v$$mmoles$, as $moles = concentration \times volume$. Concentration of $KCN$ will be $ \Rightarrow [salt] = [KCN] = \dfrac{{moles}}{V} = \dfrac{{5v}}{{v + 10}}$.
Similarly the moles of $HCN$ will be $20mmoles$, the total volume will be $V = (v + 10)ml$. So the concentration of $HCN$ will be $ \Rightarrow [acid] = [HCN] = \dfrac{{moles}}{V} = \dfrac{{20}}{{v + 10}}$.
Now we can directly apply the formula of acidic buffer:
$
\Rightarrow pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}} \\
\Rightarrow 9 = - \log (5 \times {10^{ - 10}}) + \log \dfrac{{[\dfrac{{5v}}{{v + 10}}]}}{{[\dfrac{{20}}{{v + 10}}]}} \\
\Rightarrow 9 = 9.3 + \log \dfrac{{5v}}{{20}} \\
\Rightarrow - 0.3 = \log (v) - \log 4 \\
\Rightarrow \log (v) = 0.6 - 0.3 = 0.3 \\
\Rightarrow v = 2 \\
$
We will have to add $2ml$ $KCN$in order to maintain a constant $pH$. So from the above explanation and calculation it is clear to us that
The correct answer of the given question is option: C. $2ml$
Additional information:
$HCN$ or hydrogen cyanide is a very useful compound . It is used commercially for mining, electroplating , fumigation and chemical synthesis. It is also used in the production of plastics , dyes, pesticides and synthetic fibres.
Note:
Always remember that we use the formula $ \Rightarrow pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}}$ for an acidic buffer. In a buffer solution the $pH$ always remains constant. Always try to avoid calculation errors and silly mistakes while solving the numerical. SO solve the question carefully.
Complete step by step answer: As in the question we are given the ${K_a}$ for $HCN$ at $25^\circ C$ that is $5 \times {10^{ - 10}}$. The $pH = 9$ is constant. For an acidic buffer we can write $ \Rightarrow pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}}$.
Here $[salt]$ i s the concentration of salt , that is $KCN$. $[acid]$ is the concentration of acid that is $HCN$. Let the volume of $KCN$ added be $v$$ml$. The total volume of the solution will be $V = (v + 10)ml$. Total moles of $KCN$ will be $5v$$mmoles$, as $moles = concentration \times volume$. Concentration of $KCN$ will be $ \Rightarrow [salt] = [KCN] = \dfrac{{moles}}{V} = \dfrac{{5v}}{{v + 10}}$.
Similarly the moles of $HCN$ will be $20mmoles$, the total volume will be $V = (v + 10)ml$. So the concentration of $HCN$ will be $ \Rightarrow [acid] = [HCN] = \dfrac{{moles}}{V} = \dfrac{{20}}{{v + 10}}$.
Now we can directly apply the formula of acidic buffer:
$
\Rightarrow pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}} \\
\Rightarrow 9 = - \log (5 \times {10^{ - 10}}) + \log \dfrac{{[\dfrac{{5v}}{{v + 10}}]}}{{[\dfrac{{20}}{{v + 10}}]}} \\
\Rightarrow 9 = 9.3 + \log \dfrac{{5v}}{{20}} \\
\Rightarrow - 0.3 = \log (v) - \log 4 \\
\Rightarrow \log (v) = 0.6 - 0.3 = 0.3 \\
\Rightarrow v = 2 \\
$
We will have to add $2ml$ $KCN$in order to maintain a constant $pH$. So from the above explanation and calculation it is clear to us that
The correct answer of the given question is option: C. $2ml$
Additional information:
$HCN$ or hydrogen cyanide is a very useful compound . It is used commercially for mining, electroplating , fumigation and chemical synthesis. It is also used in the production of plastics , dyes, pesticides and synthetic fibres.
Note:
Always remember that we use the formula $ \Rightarrow pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}}$ for an acidic buffer. In a buffer solution the $pH$ always remains constant. Always try to avoid calculation errors and silly mistakes while solving the numerical. SO solve the question carefully.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)