Q. In aqueous solution, the ionisation 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 $CO_{3}^{2 -}$ is 0.034 M
B) The concentration of $CO_{3}^{2 -}$ 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 $CO_{3}^{2 -}$
Explanation
(c)
$H_{2}CO_{3} \rightleftharpoons H^{+} + HCO_{3}^{-}$; $K_{1} = 4.2 \times 10^{- 7}$
$HCO_{3}^{-} \rightleftharpoons H^{+} + C{O_{3}^{2}}^{-}$; $K_{2} = 4.8 \times 10^{- 11}$
$K_{1} > > K_{2}$
$\therefore$ $\left\lbrack H^{+} \right\rbrack = \lbrack HCO_{3}^{-}\rbrack$
$K_{2} = \frac{\left\lbrack H^{+} \right\rbrack\lbrack CO_{3}^{2 -}\rbrack}{\lbrack HCO_{3}^{-}\rbrack}$
So, $\left\lbrack CO_{3}^{2 -} \right\rbrack = K_{2} = 4.8 \times 10^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.