At $27^{\circ} \mathrm{C}$, the degree of dissociation of weak acid (HA) in its 0.5 M aqueous solution is $1…

At $27^{\circ} \mathrm{C}$, the degree of dissociation of weak acid (HA) in its 0.5 M aqueous solution is $1 \%$. Its $\mathrm{K}_{\mathrm{a}}$ value is approximately
  1. $5 \times 10^{-4}$
  2. $5 \times 10^{-5}$
  3. $5 \times 10^{-6}$
  4. $5 \times 10^{-8}$

Solution

degree of dissociation of weak acid (HA) $=1 \%$ $\alpha=1 \%$ $\Rightarrow \frac{1}{100}=0.01$ Dissociation constant $\left(\mathrm{K}_{\mathrm{a}}\right)=\mathrm{C} \alpha^2$ where, $C(\text { concentration })=0.5 \mathrm{M}$ $\begin{aligned} & \alpha(\text { degree of dissociation })=0.01 \\ & \therefore \mathrm{~K}_{\mathrm{a}}=0.5 \times(0.01)^2\end{aligned}$ $\begin{aligned} & =5 \times 10^{-1} \times\left(10^{-2}\right)^2 \\ & =5 \times 10^{-1} \times 10^{-4} \\ & \mathrm{~K}_{\mathrm{a}}=5 \times 10^{-5}\end{aligned}$

Asked in: AP EAMCET 2024 (18 May Shift 1)

Practice more Ionic Equilibria questions on Aicharya