In aqueous solution the ionization constants for carbonic acid are $\mathrm{K}_{1}=4.2 \times 10^{-7}$ and $\mathrm{K}_{2}=4.8 \times 10^{-11}$ Select the correct statement for a saturated 0.034 M solution of the carbonic acid.

(C) The concentration of $\mathrm{H}^{+}$and $\mathrm{HCO}_{3}^{-}$are approximately equal.

(A) The concentration of $\mathrm{CO}_{3}^{2-}$ is 0.034 M.

(B) The concentration of $\mathrm{CO}_{3}^{2-}$ is greater than that of $\mathrm{HCO}_{3}^{-}$.

(D) The concentration of $\mathrm{H}^{+}$is double that of $\mathrm{CO}_{3}^{2-}$.

JEE Main · 2010 · 11 Apr 2010 · Offline · Equilibrium

In aqueous solution the ionization constants for carbonic acid are

K_{1} = 4.2 \times 1 0^{- 7}

and

K_{2} = 4.8 \times 1 0^{- 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.✓ Correct
(D)The concentration of $H^{+}$ is double that of $CO_{3}^{2 -}$ .

Answer: (C)

Carbonic acid ionises in two steps, but the second constant

K_{2} = 4.8 \times 1 0^{- 11}

is some four orders of magnitude smaller than the first,

K_{1} = 4.2 \times 1 0^{- 7}

, so the second step barely proceeds. Essentially all the hydrogen ion comes from the first ionisation,

H_{2} C O_{3} ⇌ H^{+} + HC O_{3}^{-}

, which makes

H^{+}

and

HC O_{3}^{-}

in equal amounts. So in the saturated solution

[H^{+}]

and

[HC O_{3}^{-}]

are approximately equal, while

[C O_{3}^{2 -}]

stays negligibly small.

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option