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]
