Question

In an aqueous solution, the ionization constants for carbonic acid $\left({\mathrm{H}}_2{\mathrm{CO}}_3\right)$ 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 $0.034\mathrm{M}$ solution of carbonic acid.

• A. The concentration of ${\mathrm{CO}}_2^{-3}$ is $0.034\mathrm{M}$
• B. The concentration of ${\mathrm{H}}^{+}$ is double that of ${\mathrm{CO}}_2^{-3}$
• C. The concentration of ${\mathrm{CO}}_2^{-3}$ is greater than that of c
• D. The concentration of ${\mathrm{H}}^{+}$ and ${\mathrm{HCO}}_3^{-}$ are approximately equal.

Answer 1

The correct option is D

The concentration of ${\mathrm{H}}^{+}$ and ${\mathrm{HCO}}_3^{-}$ are approximately equal.

The explanation for the correct answer:-

Option (D):- The Concentration of ${\mathrm{H}}^{+}$ and ${\mathrm{HCO}}_3^{-}$ are approximately equal.

Step 1: Ionization constants for the reaction

$\mathrm{A}\to {\mathrm{H}}_2{\mathrm{CO}}_3\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{HCO}}_3^{-}$

For equilibrium reaction $\mathrm{A}$, ${\mathrm{K}}_1=4.2\times {10}^{-7}$

$\mathrm{B}\to {\mathrm{HCO}}_3^{-}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{CO}}_3^{2-}$

For equilibrium reaction $\mathrm{B}$, ${\mathrm{K}}_2=4.8\times {10}^{-11}$

Because, ${\mathrm{K}}_2<<{\mathrm{K}}_1$

All major, ${\left[{\mathrm{H}}^{+}\right]}_{\mathrm{total}}\approx {\left[{\mathrm{H}}^{+}\right]}_{\mathrm{A}}$

Step 2: Finding the concentration of ${\mathrm{H}}^{+}$ and ${\mathrm{HCO}}_3^{-}$

As ${\left[{\mathrm{H}}^{+}\right]}_{\mathrm{A}}={\mathrm{H}}^{+}$ ion concentration as produced in first step.

So, from equilibrium reaction $\mathrm{A}$,${\left[{\mathrm{H}}^{+}\right]}_{\mathrm{A}}\approx \left[{\mathrm{HCO}}_3^{-}\right]\approx {\left[{\mathrm{H}}^{+}\right]}_{\mathrm{total}}$

And as compared to , $\left[{\mathrm{HCO}}_3^{-}\right]\mathrm{or}{\left[{\mathrm{H}}^{+}\right]}_{\mathrm{total}}$ , $\left[{\mathrm{CO}}_3^{-2}\right]$ ( which is the concentration) is negligible.

Therefore correct option is (D):- The Concentration of ${\mathrm{H}}^{+}$ and ${\mathrm{HCO}}_3^{-}$ are approximately equal.