Question

The degree of dissociation of $0.1M$ \[HCN\] solution is $0.01\% $ . Its ionisation constant would be:
A. ${10^{ - 3}}$
B. ${10^{ - 5}}$
C. ${10^{ - 7}}$
D. ${10^{ - 9}}$

Answer 1

Hint: The percentage of neutral particles that are ionised, such as those in a gas or aqueous solution, is known as the degree of ionisation. It can be interpreted as an acid or base's ability to ionise itself in the context of electrolytes. The link between the weak electrolyte's dissociation constant, degree of dissociation, and concentration is provided by Ostwald's dilution law.

Complete step-by-step answer:It is given that the concentration, $C$ , of the given $HCN$ solution is $0.1M$ having degree of dissociation, $\alpha $ , equal to $0.01\% $ i.e.,
 $C = 0.1M$ and
 $\alpha = \dfrac{{0.01}}{{100}}$
This implies that $\alpha = {10^{ - 4}}$ .

Now we know that, $K = {\alpha ^2}C$ ...(1)
Substituting the given values in equation (1), we get
 $K = {\left( {{{10}^{ - 4}}} \right)^2}\left( {{{10}^{ - 1}}} \right)$
Hence, $K = {10^{ - 9}}$ .

Option ‘D’ is correct

Additional Information:We need to find its ionisation constant, $K$ .
-Weak electrolytes dissociate less than strong electrolytes, which dissociate more.
-Its value is directly proportional to the temperature.
-Its value increases with dilution. The ionisation increases with dilution. At infinite dilution, ($\alpha $ =1)
The addition of one ion of solute in a solution might alter how well another solute dissociates. The common ion effect is the reason for this.

Note: The dielectric constant of the solvent determines its ionising power. The ionising power of the solvent and the degree of ionisation will both increase with the value of the dielectric constant. For instance, water, which is frequently used as a solvent, has a high dielectric constant.