Question

Assertion :When $0.1M$ weak diprotic acid $H_{2}A$ dissociates with its dissociation constants $K_{a_1}={10}^{-3}$ and $K_{a_2}={10}^{-8}$, then $\left[A^{2-}\right]$ is almost equal to ${10}^{-3}M$ Reason: Since $K_{a_2}\ll K_{a_1}$ for $0.1M{H}_{2}A$, so $\left[A^{2-}\right]$ is negligible w.r.t. $\left[H{A}^{-}\right]$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

$H_{2}A\leftrightharpoons H{A}^{-}+H^{+}$

$0.1-C$ $C$ $C$

${K_a}_1=\frac{C^2}{0.1-C}={10}^{-3}$

$\therefore C^2+{10}^{-3}C-{10}^{-4}=0$

$⟹C=9.5\times {10}^{-3}$ $M$ $\left(1\right)$

$H{A}^{-}\leftrightharpoons H^{+}+A^{2-}$

$C-C^{\prime }$ $C^{\prime }$ $C^{\prime }$

${K_a}_2=\frac{C^{\prime 2}}{C-C^{\prime }}={10}^{-8}$

$C^{\prime 2}+{10}^{-8}{C}^{\prime }-{10}^{-8}C=0$

i.e., $C^{\prime 2}+{10}^{-8}{C}^{\prime }=9.5\times {10}^{-11}=0$ [From $1$]

$⟹C^{\prime }=9.74\times {10}^{-6}$ $M$

Hence, $\left[A^{2-}\right]$ is almost equal to $9.74\times 10-6$ $M$

Hence, the assertion is incorrect.

Further, $C=\left[H{A}^{-}\right]=9.5\times {10}^{-3}$ $M$ and $C^{\prime }=\left[A^{2-}\right]=9.74\times {10}^{-6}$ $M$

Hence, $\left[A^{2-}\right]$ is not so negligible with respect to $\left[H{A}^{-}\right]$

Hence, the reason is incorrect.