Question

For a weak acid $\text{HA}$
\[\text{HA}\,\,\rightleftharpoons \,\,{{\text{H}}^{\text{+}}}\text{+}\,{{\text{A}}^{\text{-}}}\,\,\,\,{{\text{K}}_{\text{a}}}\text{=10}\]
When the concentration of the acid is $\text{10M}$, then the degree of dissociation of acid is-
(A) $1$
(B) $0.618$
(C) $0.309$
(D) None of them

Answer 1

Hint:. For a weak electrolyte the degree of dissociation is directly proportional to the square root of dilution or inversely proportional to square root of concentration. This law is known as Ostwald Dilution law.
- At infinite dilution the value of degree of dissociation becomes one.


Complete step by step answer:
To calculate the degree of dissociation we will apply Ostwald Dilution law.
For a weak acid
\[\begin{align}
  & \text{HA}\,\,\rightleftharpoons \,\,{{\text{H}}^{\text{+}}}\text{+}\,{{\text{A}}^{\text{-}}}\, \\
 & \,\,\,\begin{matrix}
   \text{C} & \,\,\,\,\,\,\,\text{0} & \text{0} \\
\end{matrix}\, \\
 & \begin{matrix}
   \text{C-C }\!\!\alpha\!\!\text{ } & \text{C }\!\!\alpha\!\!\text{ } & \text{C }\!\!\alpha\!\!\text{ } \\
\end{matrix}\,\,\,\,\,\,\,\,\,\,\{\text{where}\,\,\,\,\,\text{ }\!\!\alpha\!\!\text{ }\,\,\text{= degree}\,\text{of dissociation}\,\} \\
 & \text{so,}\,\,\,\text{from}\,\text{law}\,\text{of}\,\text{mass}\,\,\text{action}\,\,\,\,\,\,\,\,\,\,\,{{\text{K}}_{\text{a}}}\text{=}\dfrac{\text{ }\!\![\!\!\text{ }{{\text{H}}^{\text{+}}}\text{ }\!\!]\!\!\text{ }\,\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{-}}}\text{ }\!\!]\!\!\text{ }}{\text{ }\!\![\!\!\text{ HA }\!\!]\!\!\text{ }}........(i)\,\,\,\,\,\,\,\,\,\,\{\text{where}\,\,\,\,\,{{\text{K}}_{\text{a}}}=\text{ionisation}\,\text{constant}\,\text{of}\,\text{acid}\} \\
\end{align}\]
So from equation (i) we get
\[\]\[\begin{align}
 & {{\text{K}}_{\text{a}}}\text{=}\,\,\text{C}{{\text{ }\!\!\alpha\!\!\text{ }}^{\text{2}}} \\
 & \text{so}\,\,\,\,\text{ }\!\!\alpha\!\!\text{ =}\,\,\sqrt{\dfrac{{{\text{K}}_{\text{a}}}}{\text{C}}}.......(ii) \\
\end{align}\]
After putting the value of \[\,{{K}_{a}}=10\]and $\text{C = 10M}$ in the equation (ii)
We get
\[\begin{align}
 & \text{ }\!\!\alpha\!\!\text{ =}\,\,\sqrt{\dfrac{{{\text{K}}_{\text{a}}}}{\text{C}}}.......(ii) \\
 & \text{ }\!\!\alpha\!\!\text{ =}\,\,\sqrt{\dfrac{10}{10}} \\
 & \text{ }\!\!\alpha\!\!\text{ }=\,1 \\
\end{align}\]
So, the correct answer is “Option A”.

Additional information: Weak acids are weak electrolytes which are partially ionized in the aqueous solution.
- Degree of dissociation also depends on temperature. On increasing temperature ionisation increases because dissociation is an endothermic process.
- Value of \[\text{ }\!\!\alpha\!\!\text{ }\] for strong electrolyte is one. The degree of dissociation of an electrolyte also depends on the nature of the solvent. If the dielectric constant of solvent increases then the value of \[\text{ }\!\!\alpha\!\!\text{ }\] also increases

Note: Ostwald dilution law is applicable for weak electrolyte not for the strong electrolyte.
According to dilution law when weak electrolyte is diluted the degree of dissociation of solution increases.
- The value of concentration should be in terms of molarity and normality to calculate the value of degree of dissociation.
- ${{\text{K}}_{\text{a}}}$ Represent the ionisation constant of weak acid which remains constant at constant temperature.