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Step-by-step Solution
Step 1: List the species and their acidic protons
The species given are:
1. $HCO_3^-$ (bicarbonate ion)
2. $H_3O^+$ (hydronium ion)
3. $HSO_4^-$ (hydrogen sulfate ion)
4. $HSO_3F$ (fluorosulfuric acid; acidic hydrogen on sulfur).
Step 2: Recall general trends affecting acid strength
• Greater the stabilization of the conjugate base formed after donating a proton, stronger is the acid.
• For oxyacids (like $HSO_4^-$, $HSO_3F$), the presence of highly electronegative atoms and the extent of resonance often increase acid strength.
• Hydronium ion ($H_3O^+$) can release a proton but is typically a strong acid in aqueous solution.
• Species with stronger electron-withdrawing groups attached to the acidic proton tend to have higher acid strength.
Step 3: Compare each pair systematically
3.1 Comparing $HCO_3^-$ and $HSO_4^-$
- $HCO_3^-$ (bicarbonate) can donate a proton to form $CO_3^{2-}$.
$HCO_3^- \rightarrow H^+ + CO_3^{2-}$
The $CO_3^{2-}$ conjugate base is stabilized by resonance but has a $2-$ charge spread over three oxygens.
- $HSO_4^-$ can donate a proton to form $SO_4^{2-}$.
$HSO_4^- \rightarrow H^+ + SO_4^{2-}$
The $SO_4^{2-}$ conjugate base is extensively resonance stabilized, and the negative charge is spread across four oxygens.
Because $SO_4^{2-}$ is more stabilized than $CO_3^{2-}$ (due to greater number of oxygens and resonance), $HSO_4^-$ is a stronger acid than $HCO_3^-$.
Therefore, $HCO_3^- < HSO_4^-$ in acid strength.
3.2 Comparing $HSO_4^-$ and $H_3O^+$
- $H_3O^+$ is usually considered to be one of the stronger acids in aqueous solution. It can donate a proton to form $H_2O$.
$H_3O^+ \rightarrow H^+ + H_2O$
Water ($H_2O$) is very stable and neutral.
Although $HSO_4^-$ is also strong, the equilibrium:
$HSO_4^- \rightarrow H^+ + SO_4^{2-}$
indicates a strong acid, but in general, $H_3O^+$ is still known as a very strong acid in aqueous media. Experimental data show $H_3O^+$ is slightly stronger than $HSO_4^-$.
Hence, $HSO_4^- < H_3O^+$.
3.3 Comparing $H_3O^+$ and $HSO_3F$ (fluorosulfuric acid)
- $HSO_3F$ (fluorosulfuric acid) is one of the strongest known acids. The presence of the highly electronegative fluorine and sulfur-oxygen framework strongly stabilizes the conjugate base.
- Consequently, $HSO_3F$ is stronger than $H_3O^+$.
Therefore, $H_3O^+ < HSO_3F$ in acid strength.
Step 4: Combine the order of acid strengths
Putting everything together, we get:
$HCO_3^- < HSO_4^- < H_3O^+ < HSO_3F$
Or in terms of (i), (iii), (ii), (iv) as given in the question:
(i) $
