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By definition, a strong acid must completely ionize in aqueous solution. However, in order to completely dissociate in water, strong acids must be more acidic than a hydronium ion and hence have a pKa < -1.74.

I have always thought of nitric acid as a strong acid, however, nitric acid has a pKa value of -1.5, which technically should indicate that it is less acidic than the hydronium ion and hence cannot completely dissociate in water like a strong acid does, right?

Could someone please explain whether nitric acid dissociates completely in water or not? There seems to be a lot of vagueness surrounding these definitions and classifications and it seems to me like they contradict each other.

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We are really splitting hairs here. As described in this answer with respect to bases, whether an acid or base is "strong" or "weak" is not cut and dried because the dissociation constant varies continuously across different materials and the apparent behavior may depend on the type of reaction.

Nitric acid does have a lower dissociation constant than hydrochloric or sulfuric acid, but that constant is still strong enough to produce about 97% dissociation at one molar concentration (90% dissociation at one molar would correspond to $pK_a\approx-1$). So in dilute solutions there is no real difference between whether you call nitric acid "strong" or "weak" because of that (to me, dubious) $-1.74$ boundary. And at higher concentrations the reactivity of nitric acid is going to be dominated by its oxidizing power instead of its acidity anyway.

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