Question

Concentration of \[C{N^ - }\] in \[0.1{\text{ }}M{\text{ }}HCN\] is \[\left[ {{K_a} = 4 \times {{10}^{ - 10}}} \right]\]
A. $2.5 \times {10^{ - 6}}M$
B. $4.5 \times {10^{ - 6}}M$
C. $6.3 \times {10^{ - 6}}M$
D. $9.2 \times {10^{ - 6}}M$

Answer 1

Hint: We need to understand the relationship between an acid's equilibrium constant and the concentration of its ions in order to answer this question. Acid dissociation constant helps in finding to what extent an acidic substance would produce ions in water, to acquire a better understanding of the same.

Complete step-by-step answer:Ionization, is the process by which an atom or molecule gains or loses electrons to acquire a negative or positive charge, frequently in conjunction with other chemical changes. Ions are the electrically charged atoms or molecules that arise.
We must keep in mind that the amount of original acid that has been ionised in solution is represented by the acid ionisation. Actually, it is a reflection of an acid's intensity. Strong acids and bases are those that, when dissolved in water, totally separate into ions.
 $HCN$ Dissociate into ${H^ + }$ and \[C{N^ - }\] ions in its aqueous solution.
In the given question, concentration of $HCN$ is $0.1M$ , that is, $\left[ {HCN} \right] = 0.1M$
Also value of equilibrium constant is, \[{K_a} = 4 \times {10^{ - 10}}\]
We need to find the concentration of \[C{N^ - }\] .
We know that $HCN$ dissociates as follows,
 $HCN\,\, \rightleftharpoons \,\,{H^ + }\, + \,C{N^ - }$
Therefore, ${K_a} = \dfrac{{\left[ {{H^ + }} \right]\left[ {C{N^ - }} \right]}}{{\left[ {HCN} \right]}}$
Let, $\left[ {{H^ + }} \right] = x$
And $\left[ {C{N^ - }} \right] = x$
Therefore, we get, $4 \times {10^{ - 10}} = \dfrac{{x \times x}}{{0.1}}$
This implies that ${x^2} = 4 \times {10^{ - 10}} \times 0.1$
So, $x = \sqrt {4 \times {{10}^{ - 11}}} $
We get, $x = 6.3 \times {10^{ - 6}}M$
Thus, the concentration of \[C{N^ - }\] is $6.3 \times {10^{ - 6}}$ .

Option ‘C’ is correct

Additional Information:The very toxic gas or liquid hydrogen cyanide (HCN) is colourless, swiftly acting, and has the aroma of bitter almonds. At the point of manufacture, the majority of HCN is employed as an intermediary. The production of nylon, polymers, and fumigants are a few notable uses.

Note:The hydrogen cyanide (HCN) is a weak acid and its acid dissociation constant for hydrogen cyanide is very low which indicates that the hydrogen cyanide preferred to stay as HCN than in ion forms.