Weak acid HX has dissociation constant $1 \times 10^{-5}$. Calculate the percent dissociation in its $0.1…

Weak acid HX has dissociation constant $1 \times 10^{-5}$. Calculate the percent dissociation in its $0.1 \mathrm{M}$ solution.
  1. $2.2 \%$
  2. $3.5 \%$
  3. $4.2 \%$
  4. $1.0 \%$

Solution

$\begin{aligned} & \mathrm{K}_{\mathrm{a}}=1 \times 10^{-5}, \mathrm{c}=0.1 \mathrm{M} \\ \mathrm{K}_{\mathrm{a}} & =\alpha^2 \mathrm{c} \\ \therefore \quad \alpha & =\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{c}}}=\sqrt{\frac{1 \times 10^{-5}}{0.1}}=\sqrt{1 \times 10^{-4}}=0.01\end{aligned}$ $\begin{aligned} & \alpha=\frac{\text { Percent dissociation }}{100} \\ & \text { Percent dissociation }=\alpha \times 100 \\ & =0.01 \times 100=1.0 \% \\ & \end{aligned}$

Asked in: MHT CET 2023 (10 May Shift 2)

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