Why would "an mule" be used instead of "a mule"? [closed]

The original printing had "an ass" instead of "an mule". That error was not lost on the chemistry community. See, for instance, Krenos's 2004 review of the text in the Journal of Chemical Education:

In Chapter 10, bonding in extended conjugated systems and resonance are introduced with the horse + donkey = ass analogy (it is likely the hybrid animal mule is intended instead of ass, however).

It seems the editors subsequently made an error mistake.

It's just a typo, and it probably originally said "an ass". That would have been changed because it's incorrect (an ass is a donkey, not a horse–donkey cross) and, even if it were correct, the fact that ass means well, you know, ass, might be distracting enough to make it worth changing.

Another source of this kind of typo is when an adjective has been added or removed and the article hasn't been updated (e.g., "an elephant" becoming "an big elephant" or "an amazing coincidence" becoming "an coincidence"). That's presumably not happened in this particular text, since there are several instances of "an mule".