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 concentrations of $H^{+}$ and $H{CO}_3^{-}$ are approximately equal
• B. The concentration of $H^{+}$ is double that of ${CO}_3^{2-}$
• C. Concentration of ${CO}_3^{2-}$ is $0.023M$
• D. The concentration of ${CO}_3^{2-}$ is greater than that of $H{CO}_3^{-}$

Answer 1

The correct option is B The concentration of $H^{+}$ is double that of ${CO}_3^{2-}$

$K_{a_1}>K_{a_2}$. Thus $H^{+}$ ions will be derived mainly from first ionization
$H_2{CO}_3\rightleftharpoons H^{+}+H{CO}_3^{-}$
$K_a=\frac{\left[H^{+}\right]\left[H{CO}_3^{-}\right]}{\left[H_2{CO}_3\right]}=\frac{C\alpha \times C\alpha }{(C-C\alpha )}$
$\left[H^{+}\right]=\sqrt{C{K}_a}$