Question

In aqueous solution the ionization constants for carbonic acid are
$K_1=4.2\times 10^{-7}$ and $K_2=4.8\times 10^{-11}$
Select the correct statement for a saturated $0.034M$ solution of the carbonic acid.

• A. The concentration of $C{O}_3^{2-}$ is $0.034M$
• B. The concentration of $C{O}_3^{2-}$ is greater than that of $HC{O}_3^{-}$
• C. The concentration of $H^{+}$ and $HC{O}_3^{-}$ are approximately equal
• D. The concentration of $H^{+}$ is double that of $C{O}_3^{2-}$

Answer 1

Answer: (C)

$A\to H_{2}C{O}_3\rightleftharpoons H++HC{O}_3^{-}{K}_1=4.2\times 10^{-7}$
$B\to HC{O}_3^{-}\rightleftharpoons H++C{O}_3^{-2}{K}_2=4.8\times 10^{-11}$
As $K_2<<K_1$
All major ${\left[H^{+}\right]}_{total}\approx {\left[H^{+}\right]}_A$
and from I equilibrium, ${\left[H^{+}\right]}_A\approx \left[HC{O}_3^{-}\right]\approx {\left[H^{+}\right]}_{total}$
$\left[C{O}_3^{-2}\right]$ is negligible compared to $\left[HC{O}_3^{-}\right]$ or ${\left[H^{+}\right]}_{total}$