Question

: The $pH$ of $0.001M$ $HCN$ is:
A. $3$
B.$11$
C. between $3\& 7$
D. $7$

Answer 1

Hint: First of all it is important for us to recognize whether $HCN$ is a strong acid or a weak acid . Strong acids are strong electrolytes too, so they completely get dissociated into their constituent ions in the solution. The $pH$is given by $pH = - \log [{H^ + }]$. Here $[{H^ + }]$ is the concentration of the hydrogen ion .

Complete step by step answer:
As we know that $HCN$is a weak acid , so it is a weak electrolyte too. It will not get completely dissociated in ${H^ + }$ and $C{N^ - }$ ions. The dissociation constant $({K_a})$ of $HCN$ is $6.2 \times {10^{ - 10}}$. The concentration of $HCN$ is given that is $C = 0.001M$. The concentration of $[{H^ + }]$ of a weak acid is given by $[{H^ + }] = \sqrt {{K_a} \times C} $ . Here ${K_a}$is the dissociation constant of the acid and $C$ is the concentration of the acid. So :
$[{H^ + }] = \sqrt {{K_a} \times C} $
$
   \Rightarrow [{H^ + }] = {(6.2 \times {10^{ - 10}} \times {10^{ - 3}})^{\dfrac{1}{2}}} \\
   \Rightarrow [{H^ + }] = 0.787 \times {10^{ - 7}} \\
 $
Now the $pH$of $0.001M$ $HCN$ solution will be given by,
 $
  pH = - \log [{H^ + }] \\
   \Rightarrow pH = - \log [0.787 \times {10^{ - 7}}] \\
   \Rightarrow pH = 7 - \log (0.787) \\
   \therefore pH = 6.896 \\
 $
From the above explanation ,discussion and calculation it is clear to us that the $pH$ of the given solution is $6.896$. So the correct answer of the question is : C. between $3\& 7$.
Additional information: Some of the examples of strong acids are $HCl,{H_2}S{O_4},HN{O_3}$ and some examples of strong bases are $NaOH,KOH,LiOH$. Strong bases and acids dissociate completely in water . They are also known as strong electrolytes. The $pH$ of acidic solution is always less than $7$ and the $pH$ of a basic solution is always greater than $7$ and less than $14$.

Hence option C is correct.

Note:
Always remember to determine whether the given acid or base is a strong electrolyte or a weak electrolyte before attempting the question. The concentration of hydrogen ion of a weak acid is given by $[{H^ + }] = \sqrt {{K_a} \times C} $ . The $pH$ of a solution is given by $pH = - \log [{H^ + }]$.