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Chapter 13: Problem 105

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

Short Answer

Expert verified
The stepwise dissociation reactions for the diprotic acid H2SO3 are as follows: 1. First dissociation reaction: \[ \mathrm{H}_{2} \mathrm{SO}_{3} \rightleftharpoons \mathrm{HSO}_{3}^- + \mathrm{H}^{+} \] with Ka1 expression: \[ K_{a1} = \frac{[\mathrm{HSO}_{3}^-][\mathrm{H}^+]}{[\mathrm{H}_{2} \mathrm{SO}_{3}]} \] 2. Second dissociation reaction: \[ \mathrm{HSO}_{3}^- \rightleftharpoons \mathrm{SO}_{3}^{2-} + \mathrm{H}^{+}\] with Ka2 expression: \[ K_{a2} = \frac{[\mathrm{SO}_{3}^{2-}][\mathrm{H}^+]}{[\mathrm{HSO}_{3}^-]} \]

Step by step solution

01

Write the first dissociation reaction.

For the first step of dissociation, one proton (H⁺) will be lost from the H2SO3 molecule, forming a bisulfite ion (HSO3−) and releasing a hydrogen ion (H⁺). The equation for this reaction is: \[ \mathrm{H}_{2} \mathrm{SO}_{3} \rightleftharpoons \mathrm{HSO}_{3}^- + \mathrm{H}^{+} \]
02

Write the expression for the first dissociation constant (Ka1).

The dissociation constant (Ka1) for this first reaction represents the degree to which H2SO3 dissociates into HSO3− and H⁺. The Ka1 expression is as follows: \[ K_{a1} = \frac{[\mathrm{HSO}_{3}^-][\mathrm{H}^+]}{[\mathrm{H}_{2} \mathrm{SO}_{3}]} \]
03

Write the second dissociation reaction.

After the first proton has been lost from H2SO3, the bisulfite ion (HSO3−) can lose another proton (H⁺). The equation for this second reaction is: \[ \mathrm{HSO}_{3}^- \rightleftharpoons \mathrm{SO}_{3}^{2-} + \mathrm{H}^{+}\]
04

Write the expression for the second dissociation constant (Ka2).

The second dissociation constant (Ka2) represents the degree to which HSO3− dissociates into SO3²⁻ and H⁺. The Ka2 expression is as follows: \[ K_{a2} = \frac{[\mathrm{SO}_{3}^{2-}][\mathrm{H}^+]}{[\mathrm{HSO}_{3}^-]} \] Now we have the dissociation reactions and the corresponding Ka expressions for the diprotic acid, H2SO3.

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