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 0.04 M solution of the carbonic acid

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

Answer 1

The correct option is C The concentrataion of $H^{+}$ and $HC{O}_3^{-}$ are approximately equal.

$A\to H_{2}C{O}_3(aq.)\rightleftharpoons H^{+}(aq.)+HC{O}_3^{-}(aq.)K_1=4.2\times {10}^{-7}B\to HC{O}_3^{-}(aq.)\rightleftharpoons H^{+}(aq.)+C{O}_3^{2-}(aq.)K_2=4.8\times {10}^{-11}As,K_2<<K_1$. So, all major part of $\left[H^{+}\right]$ comes from dissociation of $H_{2}C{O}_3$.
$[H^{+}{]}_{total}\approx [H^{+}{]}_A$ and from first equilibrium.
$[H^{+}{]}_A\approx [HC{O}_3^{-}]\approx [H^{+}{]}_{total}$
$\left[C{O}_3^{-2}\right]$ is negligible compared to
$\left[HC{O}_3^{-}\right]$ or $[H^{+}{]}_{total}$
Theory :
$K_a$ for weak acids
For the following reaction : $HA\left(aq\right)+H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}\left(aq\right)+A^{-}\left(aq\right)$
$K_a=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]}$
$K_b$ for weak bases
For the following reaction : $MOH\left(aq\right)+H_{2}O\left(l\right)\rightleftharpoons M^{+}\left(aq\right)+O{H}^{-}\left(aq\right)$
$K_b=\frac{[M+]\left[O{H}^{-}\right]}{\left[MOH\right]}$
Note : More the values of $K_{a}or{K}_b$ more is the strength of acid or base