What is the equilibrium constant expression, [tex]\( K_i \)[/tex], for the following weak acid?

[tex]\[ H_2SO_3(aq) \leftrightarrow H^+(aq) + HSO_3^-(aq) \][/tex]

A. [tex]\( K_i = \frac{[H_2SO_3]}{[H^+][HSO_3^-]} \)[/tex]

B. [tex]\( K_i = \frac{[H^+]^2[HSO_3^-]}{[H_2SO_3]} \)[/tex]

C. [tex]\( K_i = \frac{[H_2SO_3]}{[H^+]^2[SO_3^{2-}]} \)[/tex]

D. [tex]\( K_i = \frac{[H^+]^2[SO_3^{2-}]}{[H_2SO_3]} \)[/tex]

E. [tex]\( K_i = \frac{[H^+][HSO_3^-]}{[H_2SO_3]} \)[/tex]



Answer :

To determine the equilibrium constant expression, [tex]\(K_i\)[/tex], for the dissociation of the weak acid [tex]\( \text{H}_2 \text{SO}_3 \)[/tex], we must consider its balanced dissociation reaction:

[tex]\[ \text{H}_2 \text{SO}_3 \text{(aq)} \leftrightarrow \text{H}^+ \text{(aq)} + \text{HSO}_3^- \text{(aq)} \][/tex]

The equilibrium constant expression for a dissociation reaction is based on the concentrations of the products divided by the concentration of the reactants.

The general form of the equilibrium constant expression for the dissociation reaction [tex]\( A \leftrightarrow B + C \)[/tex] is given by:

[tex]\[ K_i = \frac{[\text{B}][\text{C}]}{[\text{A}]} \][/tex]

For our specific reaction:

- The reactant is [tex]\( \text{H}_2 \text{SO}_3 \)[/tex]
- The products are [tex]\( \text{H}^+ \)[/tex] and [tex]\( \text{HSO}_3^- \)[/tex]

Thus, the equilibrium constant expression [tex]\( K_i \)[/tex] for the given reaction is:

[tex]\[ K_i = \frac{[\text{H}^+][\text{HSO}_3^-]}{[\text{H}_2 \text{SO}_3]} \][/tex]

Examining the given options, the correct expression is:

[tex]\[ K_i = \left[ \text{H}^+ \right] \left[ \text{HSO}_3^- \right] / \left[ \text{H}_2 \text{SO}_3 \right] \][/tex]

Thus, the correct option is:
[tex]\[ Ki = \left[ H^+ \right] \left[ HSO_3^- \right] / \left[ H_2SO_3 \right] \][/tex]