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)

The concentration of $H^+$ and $HCO^-_3$ are approximately equal

Answer 2

$A \to \quad$ ${ H2CO3 <=> H+ + HCO^{-}_3}$ $\quad K_1 = 4.2 \times 10^{-7}$ $B \to \quad$ ${ HCO^{-}_{3} <=> H+ + CO^{-2}_3}$ $\quad K_2 = 4.8 \times 10^{-11}$ 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 $\left[H^{+}\right]_{total}$