1. Identify the acidic species and compare their strengths

We need the increasing order of acid strength among:

• $\mathrm{HCO_3^-}$
• $\mathrm{H_3O^+}$
• $\mathrm{HSO_4^-}$
• $\mathrm{HSO_3F}$

Acid strength increases as the tendency to donate $\mathrm{H^+}$ increases, i.e. as $K_a$ increases or $pK_a$ decreases.

2. Examine each species

(i) $\mathrm{HCO_3^-}$

This is bicarbonate ion. It is amphiprotic, but as an acid it is very weak: $\mathrm{HCO_3^- \rightleftharpoons CO_3^{2-} + H^+}$ Its acidic strength is much smaller than the others listed.

So, $\mathrm{HCO_3^-}$ is the weakest acid here.

(iii) $\mathrm{HSO_4^-}$

This is hydrogen sulfate ion: $\mathrm{HSO_4^- \rightleftharpoons SO_4^{2-} + H^+}$ It is a moderately strong acid (second dissociation of sulfuric acid), stronger than $\mathrm{HCO_3^-}$.

Thus: $\mathrm{HCO_3^- < HSO_4^-}$

(ii) $\mathrm{H_3O^+}$

Hydronium ion is the strongest acid that can exist in aqueous solution under normal conditions. It is stronger than $\mathrm{HSO_4^-}$.

Thus: $\mathrm{HSO_4^- < H_3O^+}$

(iv) $\mathrm{HSO_3F}$

This is fluorosulfuric acid. It is a superacid, stronger than sulfuric acid and stronger than $\mathrm{H_3O^+}$.

Hence: $\mathrm{H_3O^+ < HSO_3F}$

3. Combine the order

Therefore, increasing acid strength is: $\mathrm{HCO_3^- < HSO_4^- < H_3O^+ < HSO_3F}$

In terms of labels: $i < iii < ii < iv$

4. Match with the options

This corresponds to Option C.

5. Comparison with stored correct answer

Stored correct answer: C

Our derived answer: C

So they agree.