Is there a terminology contradiction about whether the conjugate of a strong acid is a "weak base"?

Question

(Please note, I am not simply asking, "Is the conjugate of a strong acid a weak base?" I'm asking about the contradictory ways those terms seem to be used.)

I was revisiting strong/weak acids/bases to help some high school chemistry students and found a lot of apparent contradictions in the way that sources use the terms. One is whether the conjugate acid of a strong base is considered a "weak acid".

I understand that the strongER the base, the weakER the conjugate acid, and all sources use the relative terms consistently. The contradiction is in the use of the absolute terms "strong" and "weak".

There seem to be two conflicting conventions in use. In Convention I, the conjugate of a strong base is indeed called a weak acid (whereas weak bases and weak acids can also be conjugates), so you have these conjugate pairings:

\begin{array}{cc} \hline \text{acid} & \text{base} \\ \hline \text{strong} & \text{weak} \\ \text{weak} & \text{weak} \\ \text{weak} & \text{strong} \\ \hline \end{array}

In Convention II, the conjugate of a weak acid is a weak base, and vice versa; the conjugate of a strong base is too weak to be considered an acid, and the conjugate of a strong acid is too weak to be considered a base:

\begin{array}{cc} \hline \text{acid} & \text{base} \\ \hline \text{strong} & \text{not a base} \\ \text{weak} & \text{weak} \\ \text{not an acid} & \text{strong} \\ \hline \end{array}

You can find examples of both just by googling "conjugate of a strong acid", "conjugate of a weak base", etc. Many sources complete the sentence "conjugate of a strong acid [or base]" with "is a weak base [or acid]" (Convention I). On the other hand many sources complete "conjugate of a weak acid [or base]" with "is a weak base [or acid]" (Convention II).

I just want confirmation different sources really are using these terms in ways that contradict each other, so I can pass that on to my students and move on.

So, which of the following is true?

1. There is no contradiction; I'm reading it wrong. (This seems unlikely since you can literally google "conjugate of a weak acid" and get what seem to be multiple contradictory answers.)

2. One usage of these terms is correct, and the sources that say otherwise are using the terms incorrectly. (In particular, the more reliable sources seem to skew towards saying that the conjugate of a weak acid is a weak base, i.e. Convention II. Maybe the sources that say "the conjugate of a strong base is a weak acid" are wrong, and they're just garbling the (correct) statement that the strongER the base, the weakER the conjugate acid.)

3. There is no agreed-upon definition of "weak acid" and different sources use it in contradictory ways, but real chemists don't care because they just use Ka values.

To avoid horrible confusion, please be clear in your answer if you're voting for #1, #2, or #3, or something else not listed here.

Answer 1

(Would rather have made this a comment than an answer but still new. So please don't hang me.)

Through high-school, I was also bugged by this. No, you are not going mad, there are many different views on this matter when you google it. The problem is that like many other scales humans create, the way we define 'strong' or 'weak' is a rather relative concept, especially when it gets to the mid-ranges. It is only a way for us to explain what we observe and get a handle on things.

One thing all chemists would agree on is that you should rather look at how strong an acid or base is relative to another (based on Ka or Kb values). In the end, these are the things you would actually use. However, as you need an answer in a school context I would suggest the following:

At school (at least where I come from) we mainly dealt with Bronsted-Lowry acids and bases. Here the strength of an acid depends on how easily it donates ("accepts" for bases) protons. If your students already know a bit about Ka values then anything with a Ka>1 can be considered (reasonably) strong: on a school level, this is usually limited to HI, HBr, HCl, HNO3, H2SO4 and sometimes HClO3 and HClO4. You might want to look at the relative strengths of these 'strong acids' (I seem to recall an exam question about why HI is a stronger acid than HCl (how stable are the ions) and why HF isn't considered a strong acid - the answer is H-bonding). Anything with Ka<1 can be seen as weak.

As to conjugates. Your statement in 2 about 'The stronger the Acid the weaker the conjugate base' and its inverse applies. Here you also work comparatively rather than absolute. You could try explaining it by saying if something gives away a proton easily (acid strength) why would it want to take that proton back later on? Mathematically this can be expressed by relating the Ka value to the Kb value of its conjugate Ka = Kw/Kb (Kw = 1e-14). You would notice that very few 'weak bases' (Kb<1) will give you a Ka>1, from there the confusion about "the conjugate of a weak base is a weak acid". eg. H2PO4^- (Ka = 6.23e-8) is neither a particularly strong base nor acid, but if it reacts as a base and forms H3PO4 this conjugate still only has a Ka = 7.52e-3 - which is still very weak compared to HI.

Answer 2

@ Bennett, I feel your pain. The first table you show is most unhelpful for students as they are trying to understand conjugate acid-base pairs. For what it's worth, I like to use a version of table 2 where I substitute, "Negligible acid/base" as the conjugate of a "Strong" (rather than "Not an acid/base"). I find this helpful as students understand the difference between an acid such as ammonium (weak acid, pKa = 9.25) and Na+ (negligible acid pKa = 13.8). Dissolving a salt containing the ammonium ion (at a reasonable concentration) will give a measurable effect on pH but the sodium ion will not. However, a hydrated sodium ion can, in extremis, act as an acid.

Although our definitions of "Strong" (and, therefore "Negligible") are somewhat arbitrary, students in most exams will need to understand and apply them, so they aren't going away.

Of your options, I believe that #2 is the closest (I feel that convention 1 is inherently misleading, at least to students with no schema). Having worked in research, I find that chemists still do use "Strong" acids and bases in the same way that we were taught in school, but with a bit more understanding and the ability to accept the grey areas.