Why does the inverse relationship between the strengths of an acid and its conjugate base appear to be violated in the case of chloric(I) acid?

Question

Hypochlorous acid is a weak acid with $\mathrm{p}K_\mathrm{a}(\ce{HClO}) = 7.53$. Then why is its conjugate base, $\ce{ClO-}$, a weak base in water? Shouldn't the strength of the base be inversely proportional and shouldn't hypochlorite be a strong base?

If $\ce{HClO}$ is a weak acid, that means it does not readily give up a proton and has a strong pull on them. So when it becomes a conjugate base, $\ce{ClO-}$, shouldn't it readily take protons and therefore be a strong base in water?

Also, when an acid is dissolved in water, and some of that acid dissociates into $\ce{H3O+}$, is the $K_\mathrm{w}$ of water negligible and you only consider the $K_\mathrm{a}$ when finding $\mathrm{pH}?$ But that confuses me because I thought you use 14, the exponent of $K_\mathrm{w},$ when finding $\mathrm{pH}.$

Answer 1

$K_\mathrm a\times K_\mathrm b = K_\mathrm w$. Some teachers tell their students that the conjugate base of a weak acid is strong but it's not true. What is true is that the stronger the acid, the weaker the conjugate base and vice versa.

Yes to your second question. When calculating the pH of a solution, the hydronium ion concentration is usually controlled by the strongest acid in the solution. This is the case in the type of problems found in lower level chem classes. In a higher level class problems with acids close enough in strength so that both acids matter may be encountered.

Answer 2

It's true that as the strength of an acid goes up, the strength of its conjugate base goes down. For example, hydrochloric acid ($\mathrm{p}K_\mathrm{a} \approx -7$) is really strong and chloride anion is a really weak base. On the other side of the spectrum, an alkane ($\mathrm{p}K_\mathrm{a} \approx 50$) is a very weak acid, but its conjugate base will deprotonate nearly anything. So at the extremes it's clear: strong acid gives weak conjugate base and weak acid gives strong conjugate base.

For compounds with $\mathrm{p}K_\mathrm{a}$'s between 0 and 14, such as hypochlorous acid with an intermediate $\mathrm{p}K_\mathrm{a}$, both the acid and the conjugate base are weak. We call them "weak" acids because they don't completely dissociate in water. However, their conjugate bases are also "weak" because they're weaker than hydroxide.

It comes down to just how weak do you mean by "weak".

Answer 3

A weak acid $\ce{AH}$ is in equilibrium with its conjugate base $\ce{A-}$ when dissolved in water:

$$\ce{AH(aq) <=> A-(aq) + H+(aq)}$$

In contrast, a strong acid such as $\ce{HCl}$ dissociates fully, i.e. the following reaction goes to completion:

$$\ce{HCl(aq) -> Cl-(aq) + H+(aq)}$$

Likewise, a strong base such as $\ce{NaOCH3}$ accepts a proton from water, i.e. the following reaction goes to completion:

$$\ce{NaOCH3(aq) + H+(aq) -> CH3OH(aq) + Na+(aq)}$$

Neither $\ce{Cl-(aq)}$ nor $\ce{CH3OH(aq)}$ are typically thought of as acid or bases in aqueous solution. They are spectators as far as aqueous acid/base chemistry is concerned.

So the concept of conjugate acid and conjugate base applies only to weak acids and bases. Saying that a conjugate base is strong would mean that its conjugate acid is not an acid at all but rather a spectator species.

Said in a positive way, the conjugate base of a weak acid is also weak because the reaction goes to equilibrium, not to completion (no matter on which side you start). What you might incorrectly call "the conjugate base of a strong acid" is really a spectator ion (or molecule).

Answer 4

There is a widespread inconsistency in how the terms "weak" and "strong" are used for acids and bases, something I posted about here:
Is there a terminology contradiction about whether the conjugate of a strong acid is a "weak base"?
All sources agree that the strongER the acid, the weakER the conjugate base. However, some sources say that the conjugate of a strong acid is a (very) weak base. Other sources say that the conjugate of a strong acid is too weak to be considered a base, therefore when they say "the conjugate of a weak acid is a weak base", they mean that the conjugate of a strong acid is not a base at all.

Google turns up dozens of sources which say "the conjugate of a strong base is a weak acid" (or something similar), and also dozens of other sources which say "the conjugate of a weak acid is a weak base" (or something similar). Taken at face value, these statements contradict each other -- if there is at least one strong base whose conjugate is a weak acid, then it cannot be true that the conjugate of a weak acid is always a weak base.

Nonetheless, despite this inconsistency, most sources agree that a weak acid and a weak base can be conjugates of each other, e.g. the weak base $\ce{NH3}$ and the weak acid $\ce{NH4+}$.