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 $0.034 \,M$ solution of the carbonic acid.

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

Answer 1

Answer: (C)

$A \to H_2CO_3 \rightleftharpoons H+ + HCO^{-}_3 K_1 = 4.2 \times 10^{-7}$
$B \to HCO^{-}_{3}\rightleftharpoons H+ + CO^{-2}_3 K_2 = 4.8 \times 10^{-11}$
As $K_2 << K_1$
All major $\left[H^{+}\right]_{total} \approx \left[H^{+}\right]_{A}$
and from I equilibrium, $\left[H^{+}\right]_{A} \approx \left[HCO^{-}_{3}\right] \approx \left[H^{+}\right]_{total}$
$\left[CO^{-2}_{3}\right]$ is negligible compared to $\left[HCO^{-}_{3}\right]$ or $\left[H^{+}\right]_{total}$