To determine the acid dissociation constant ([tex]\( K_a \)[/tex]) for the dissociation of hydrocyanic acid ([tex]\( HCN \)[/tex]) in an aqueous solution, we start by considering the dissociation reaction:
[tex]\[ HCN_{(aq)} \rightarrow H^+_{(aq)} + CN^-_{(aq)} \][/tex]
The acid dissociation constant ([tex]\( K_a \)[/tex]) is expressed as the ratio of the concentration of the products to the concentration of the reactant:
[tex]\[ K_a = \frac{ [H^+] [CN^-] }{ [HCN] } \][/tex]
Now we can match this expression with the given options:
A. [tex]\( K_2 = \frac{ \left[ H^+ \|\| C N^- \right] }{ [HCN] } \)[/tex]
- This option closely resembles the correct form of the acid dissociation constant but has extra characters making it incorrect.
B. [tex]\( K_2 = \frac{ [HCN] }{ H^+|C| \Gamma \mid } \)[/tex]
- This option incorrectly places the concentrations of the reactants and products in the denominator and numerator.
C. [tex]\( K_2 = [HCN][H^+ \|\| C N ] \)[/tex]
- This option incorrectly suggests the multiplication of the initial reactant and the products which would not match the definition of [tex]\( K_a \)[/tex].
D. [tex]\( K_2 = \left. | H^+ \|\| C N \right] \)[/tex]
- This option only includes the products' concentrations without considering the reactant, which is incorrect.
From these options, the one that matches the correct expression for the acid dissociation constant is:
[tex]\[ K_a = \frac{ [H^+] [CN^-] }{ [HCN] } \][/tex]
Therefore, the correct answer is:
A. [tex]\( K_2=\frac{\left[ \ H^+ \|\| C N^- \right]}{[ HCN ]} \)[/tex]
(Note: In a more appropriate option formatting, without any extra characters, the correct option would solely match the correct ratio provided.)
