Question

Write out the stepwise \(K_{\mathrm{a}}\) reactions for the diprotic acid \(\mathrm{H}_{2} \mathrm{SO}_{3}\)

Short answer

The stepwise Ka reactions for the diprotic acid H2SO3 are: 1. First ionization reaction: \( H_{2}SO_{3} (aq) \rightleftharpoons H^+ (aq) + HSO_3^- (aq) \) with the Ka1 expression: \( K_{a1} = \frac{[H^+][HSO_3^-]}{[H_{2}SO_{3}]} \) 2. Second ionization reaction: \( HSO_3^- (aq) \rightleftharpoons H^+ (aq) + SO_3^{2-} (aq) \) with the Ka2 expression: \( K_{a2} = \frac{[H^+][SO_3^{2-}]}{[HSO_3^-]} \)

Step-by-step solution

Identify the diprotic acid and its ionization stages

H2SO3 is the given diprotic acid, meaning it can lose two protons (H+). There will be two ionization stages: 1. The first ionization stage will be when H2SO3 loses one proton and becomes HSO3- (the first conjugate base). 2. The second ionization stage will be when HSO3- loses another proton and becomes SO3^2- (the second conjugate base).

Write the first ionization reaction and Ka1 expression

The first ionization reaction is given by: \( H_{2}SO_{3} (aq) \rightleftharpoons H^+ (aq) + HSO_3^- (aq) \) The expression for the acid dissociation constant (Ka1) for the first ionization reaction is given by: \( K_{a1} = \frac{[H^+][HSO_3^-]}{[H_{2}SO_{3}]} \)

Write the second ionization reaction and Ka2 expression

The second ionization reaction is given by: \( HSO_3^- (aq) \rightleftharpoons H^+ (aq) + SO_3^{2-} (aq) \) The expression for the acid dissociation constant (Ka2) for the second ionization reaction is given by: \( K_{a2} = \frac{[H^+][SO_3^{2-}]}{[HSO_3^-]} \) In summary, the stepwise Ka reactions for the diprotic acid H2SO3 are: 1. First ionization reaction: \( H_{2}SO_{3} (aq) \rightleftharpoons H^+ (aq) + HSO_3^- (aq) \) with the Ka1 expression: \( K_{a1} = \frac{[H^+][HSO_3^-]}{[H_{2}SO_{3}]} \) 2. Second ionization reaction: \( HSO_3^- (aq) \rightleftharpoons H^+ (aq) + SO_3^{2-} (aq) \) with the Ka2 expression: \( K_{a2} = \frac{[H^+][SO_3^{2-}]}{[HSO_3^-]} \)